Adding and subtracting

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the tens place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   235 = 200 + 30 + 5
2. Find the place of the number we add. 40 is 4 tens, so only the tens digit changes.
   40 = 4 tens
3. Add in the tens place only. The other places stay the same.
   3 tens + 4 tens = 7 tens
4. Put the parts back together. Write each place, then read the number.
   200 + 70 + 5
5. Write the answer.
   275

Check. 275 − 40 = 235. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the hundreds place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   618 = 600 + 10 + 8
2. Find the place of the number we take away. 100 is 1 hundred, so only the hundreds digit changes.
   100 = 1 hundred
3. Take away in the hundreds place only. The other places stay the same.
   6 − 1 = 5 hundreds
4. Put the parts back together. Write each place, then read the number.
   500 + 10 + 8
5. Write the answer.
   518

Check. 518 + 100 = 618. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the ones place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   473 = 400 + 70 + 3
2. Find the place of the number we add. 6 is 6 ones, so only the ones digit changes.
   6 = 6 ones
3. Add in the ones place only. The other places stay the same.
   3 ones + 6 ones = 9 ones
4. Put the parts back together. Write each place, then read the number.
   400 + 70 + 9
5. Write the answer.
   479

Check. 479 − 6 = 473. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the hundreds place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   129 = 100 + 20 + 9
2. Find the place of the number we add. 300 is 3 hundreds, so only the hundreds digit changes.
   300 = 3 hundreds
3. Add in the hundreds place only. The other places stay the same.
   1 hundreds + 3 hundreds = 4 hundreds
4. Put the parts back together. Write each place, then read the number.
   400 + 20 + 9
5. Write the answer.
   429

Check. 429 − 300 = 129. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the ones place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   578 = 500 + 70 + 8
2. Find the place of the number we take away. 3 is 3 ones, so only the ones digit changes.
   3 = 3 ones
3. Take away in the ones place only. The other places stay the same.
   8 − 3 = 5 ones
4. Put the parts back together. Write each place, then read the number.
   500 + 70 + 5
5. Write the answer.
   575

Check. 575 + 3 = 578. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the tens place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   284 = 200 + 80 + 4
2. Find the place of the number we add. 50 is 5 tens, so only the tens digit changes.
   50 = 5 tens
3. Add in the tens place only. The total is ten or more, so we carry into the next place.
   8 + 5 = 13, which is 1 hundred and 3 tens
4. Carry the hundred into the hundreds place. The carried number is added to the next place.
   2 + 1 = 3 hundreds
5. Put the parts back together. Write each place, then read the number.
   300 + 30 + 4
6. Write the answer.
   334

Check. 334 − 50 = 284. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the tens place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   746 = 700 + 40 + 6
2. Find the place of the number we take away. 20 is 2 tens, so only the tens digit changes.
   20 = 2 tens
3. Take away in the tens place only. The other places stay the same.
   4 − 2 = 2 tens
4. Put the parts back together. Write each place, then read the number.
   700 + 20 + 6
5. Write the answer.
   726

Check. 726 + 20 = 746. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   355 + [ ] = 385
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   385 − 355 = 30
3. Check by adding the answer back. The check must give the total.
   355 + 30 = 385
4. Write the answer.
   30

Check. 355 + 30 = 385. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract c from a to find the box.

1. Look at the calculation. The box is the number taken away from a.
   712 − [ ] = 612
2. Work out what is taken away. Take c away from a to find the box.
   712 − 612 = 100
3. Check by taking the answer away. The result must be c.
   712 − 100 = 612
4. Write the answer.
   100

Check. 712 − 100 = 612. ✓

Watch out. The box is the number taken away, so it is not c.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the hundreds place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   395 = 300 + 90 + 5
2. Find the place of the number we take away. 100 is 1 hundred, so only the hundreds digit changes.
   100 = 1 hundred
3. Take away in the hundreds place only. The other places stay the same.
   3 − 1 = 2 hundreds
4. Put the parts back together. Write each place, then read the number.
   200 + 90 + 5
5. Write the answer.
   295

Check. 295 + 100 = 395. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Add the 30 first, then the 4.

1. Add the 30. Only the tens digit changes.
   346 + 30 = 376
2. Add the 4. Six ones and 4 ones make 10 ones, which is 1 more ten.
   376 + 4 = 380
3. Write the answer.
   380

Check. 380 − 4 − 30 = 346. ✓

Watch out. Add one number at a time, and check each step.

Method. Split 258 and add 60 in the tens place.

1. Look at the tens. Adding 60 changes the tens, so Ben has not finished.
   5 tens + 6 tens = 11 tens
2. Change 11 tens into hundreds and tens. 11 tens is 1 hundred and 1 ten.
   11 tens = 1 hundred and 1 ten
3. Work out the answer. Add the new hundred to the hundreds.
   2 hundreds + 1 hundred = 3 hundreds
4. Decide. Ben is not right, because the hundreds digit changes too.
   No. 258 + 60 = 318

Check. 318 − 60 = 258. ✓

Watch out. The tens digit is worth ten times as much as its face value. Carry when it goes past 9.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   234 + 412
2. Add the ones first. Start on the right.
   4 + 2 = 6, write 6
3. Add the tens. Nothing is carried into this column.
   3 + 1 = 4, write 4
4. Add the hundreds. Nothing is carried into this column.
   2 + 4 = 6, write 6
5. Write the answer. Read the digits from the bottom line.
   646

Check. 646 − 412 = 234. ✓

Watch out. Keep the columns straight, so that the ones are under the ones.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   521 + 137
2. Add the ones first. Start on the right.
   1 + 7 = 8, write 8
3. Add the tens. Nothing is carried into this column.
   2 + 3 = 5, write 5
4. Add the hundreds. Nothing is carried into this column.
   5 + 1 = 6, write 6
5. Write the answer. Read the digits from the bottom line.
   658

Check. 658 − 137 = 521. ✓

Watch out. Keep the columns straight, so that the ones are under the ones.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   375 + 219
2. Add the ones first. Start on the right.
   5 + 9 = 14, write 4 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   7 + 1 + 1 carried = 9, write 9
4. Add the hundreds. Nothing is carried into this column.
   3 + 2 = 5, write 5
5. Write the answer. Read the digits from the bottom line.
   594

Check. 594 − 219 = 375. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   648 + 97
2. Add the ones first. Start on the right.
   8 + 7 = 15, write 5 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   4 + 9 + 1 carried = 14, write 4 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   6 + 0 + 1 carried = 7, write 7
5. Write the answer. Read the digits from the bottom line.
   745

Check. 745 − 97 = 648. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   296 + 58
2. Add the ones first. Start on the right.
   6 + 8 = 14, write 4 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   9 + 5 + 1 carried = 15, write 5 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   2 + 0 + 1 carried = 3, write 3
5. Write the answer. Read the digits from the bottom line.
   354

Check. 354 − 58 = 296. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   589 + 267
2. Add the ones first. Start on the right.
   9 + 7 = 16, write 6 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   8 + 6 + 1 carried = 15, write 5 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   5 + 2 + 1 carried = 8, write 8
5. Write the answer. Read the digits from the bottom line.
   856

Check. 856 − 267 = 589. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   376 + 485
2. Add the ones first. Start on the right.
   6 + 5 = 11, write 1 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   7 + 8 + 1 carried = 16, write 6 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   3 + 4 + 1 carried = 8, write 8
5. Write the answer. Read the digits from the bottom line.
   861

Check. 861 − 485 = 376. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   258 + 189
2. Add the ones first. Start on the right.
   8 + 9 = 17, write 7 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   5 + 8 + 1 carried = 14, write 4 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   2 + 1 + 1 carried = 4, write 4
5. Write the answer. Read the digits from the bottom line.
   447

Check. 447 − 189 = 258. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   463 + 258
2. Add the ones first. Start on the right.
   3 + 8 = 11, write 1 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   6 + 5 + 1 carried = 12, write 2 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   4 + 2 + 1 carried = 7, write 7
5. Write the answer. Read the digits from the bottom line.
   721

Check. 721 − 258 = 463. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Work backwards from the answer. Each column must give the digit in the answer.

1. Add the ones. The answer ends in 1, so 6 + 5 must make 11.
   6 + 5 = 11, write 1 and carry 1 ten
2. Work out the tens. The box, plus 4, plus the carried 1, must make 9.
   [ ] + 4 + 1 = 9, so [ ] = 4
3. Check the hundreds. The hundreds must add to 5.
   2 + 3 = 5 ✓
4. Write the answer. The missing digit is in the tens.
   4

Check. 246 + 345 = 591. ✓

Watch out. Add the digits in each column. Do not guess the box, work it out.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add each column again, carrying where needed, and then compare with Tom.

1. Add the ones. Start on the right.
   8 + 5 = 13, write 3 and carry 1 ten
2. Add the tens. Include the carried ten.
   7 + 5 + 1 = 13, write 3 and carry 1 hundred
3. Add the hundreds. Include the carried hundred.
   3 + 2 + 1 = 6
4. Compare with Tom. Tom wrote 5 hundreds, so he did not carry the hundred from the tens.
   633

Check. 633 − 255 = 378. ✓

Watch out. A carried hundred must go into the hundreds column. Do not leave it out.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   186 + 247
2. Add the ones first. Start on the right.
   6 + 7 = 13, write 3 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   8 + 4 + 1 carried = 13, write 3 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   1 + 2 + 1 carried = 4, write 4
5. Write the answer. Read the digits from the bottom line.
   433

Check. 433 − 247 = 186. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   498 + 376
2. Add the ones first. Start on the right.
   8 + 6 = 14, write 4 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   9 + 7 + 1 carried = 17, write 7 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   4 + 3 + 1 carried = 8, write 8
5. Write the answer. Read the digits from the bottom line.
   874

Check. 874 − 376 = 498. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   689 − 254
2. Subtract the ones. Take the bottom digit away from the top digit.
   9 − 4 = 5
3. Subtract the tens. Take the bottom digit away from the top digit.
   8 − 5 = 3
4. Subtract the hundreds. Take the bottom digit away from the top digit.
   6 − 2 = 4
5. Write the answer. Read the answer from the bottom line.
   435

Check. 435 + 254 = 689. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   746 − 215
2. Subtract the ones. Take the bottom digit away from the top digit.
   6 − 5 = 1
3. Subtract the tens. Take the bottom digit away from the top digit.
   4 − 1 = 3
4. Subtract the hundreds. Take the bottom digit away from the top digit.
   7 − 2 = 5
5. Write the answer. Read the answer from the bottom line.
   531

Check. 531 + 215 = 746. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   528 − 136
2. Subtract the ones. Take the bottom digit away from the top digit.
   8 − 6 = 2
3. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 5 → 4, tens: 2 → 12
4. Subtract the tens. Take the bottom digit away from the top digit.
   12 − 3 = 9
5. Subtract the hundreds. Take the bottom digit away from the top digit.
   4 − 1 = 3
6. Write the answer. Read the answer from the bottom line.
   392

Check. 392 + 136 = 528. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   413 − 267
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 1 → 0, ones: 3 → 13
3. Subtract the ones. Take the bottom digit away from the top digit.
   13 − 7 = 6
4. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 4 → 3, tens: 0 → 10
5. Subtract the tens. Take the bottom digit away from the top digit.
   10 − 6 = 4
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   3 − 2 = 1
7. Write the answer. Read the answer from the bottom line.
   146

Check. 146 + 267 = 413. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   300 − 125
2. Exchange 1 hundred for 10 tens. The ones digit on top is too small, so we break one hundred up.
   hundreds: 3 → 2, tens: 0 → 10
3. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 10 → 9, ones: 0 → 10
4. Subtract the ones. Take the bottom digit away from the top digit.
   10 − 5 = 5
5. Subtract the tens. Take the bottom digit away from the top digit.
   9 − 2 = 7
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   2 − 1 = 1
7. Write the answer. Read the answer from the bottom line.
   175

Check. 175 + 125 = 300. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   500 − 348
2. Exchange 1 hundred for 10 tens. The ones digit on top is too small, so we break one hundred up.
   hundreds: 5 → 4, tens: 0 → 10
3. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 10 → 9, ones: 0 → 10
4. Subtract the ones. Take the bottom digit away from the top digit.
   10 − 8 = 2
5. Subtract the tens. Take the bottom digit away from the top digit.
   9 − 4 = 5
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   4 − 3 = 1
7. Write the answer. Read the answer from the bottom line.
   152

Check. 152 + 348 = 500. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   642 − 375
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 4 → 3, ones: 2 → 12
3. Subtract the ones. Take the bottom digit away from the top digit.
   12 − 5 = 7
4. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 6 → 5, tens: 3 → 13
5. Subtract the tens. Take the bottom digit away from the top digit.
   13 − 7 = 6
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   5 − 3 = 2
7. Write the answer. Read the answer from the bottom line.
   267

Check. 267 + 375 = 642. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   475 − 268
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 7 → 6, ones: 5 → 15
3. Subtract the ones. Take the bottom digit away from the top digit.
   15 − 8 = 7
4. Subtract the tens. Take the bottom digit away from the top digit.
   6 − 6 = 0
5. Subtract the hundreds. Take the bottom digit away from the top digit.
   4 − 2 = 2
6. Write the answer. Read the answer from the bottom line.
   207

Check. 207 + 268 = 475. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   613 − 129
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 1 → 0, ones: 3 → 13
3. Subtract the ones. Take the bottom digit away from the top digit.
   13 − 9 = 4
4. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 6 → 5, tens: 0 → 10
5. Subtract the tens. Take the bottom digit away from the top digit.
   10 − 2 = 8
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   5 − 1 = 4
7. Write the answer. Read the answer from the bottom line.
   484

Check. 484 + 129 = 613. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   400 − 185
2. Exchange 1 hundred for 10 tens. The ones digit on top is too small, so we break one hundred up.
   hundreds: 4 → 3, tens: 0 → 10
3. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 10 → 9, ones: 0 → 10
4. Subtract the ones. Take the bottom digit away from the top digit.
   10 − 5 = 5
5. Subtract the tens. Take the bottom digit away from the top digit.
   9 − 8 = 1
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   3 − 1 = 2
7. Write the answer. Read the answer from the bottom line.
   215

Check. 215 + 185 = 400. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Work out each column from the right. Exchange wherever the top digit is too small.

1. Ones. We cannot take 7 from 2, so we exchange 1 ten.
   2 < 7, so tens 1 → 0 and ones 2 → 12. 12 − 7 = 5
2. Tens. The tens digit is now 0, so we exchange 1 hundred.
   0 < 6, so hundreds 5 → 4 and tens 0 → 10. 10 − 6 = 4
3. Hundreds. Take the hundreds away.
   4 − 1 = 3
4. Find the missing digit. The digit in the box is the tens digit of 512, which is 1.
   1

Check. 512 − 167 = 345. ✓

Watch out. The box is in the tens place of the first number. Work out the subtraction, then read the digit.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   400 − 187
2. Exchange 1 hundred for 10 tens. The ones digit on top is too small, so we break one hundred up.
   hundreds: 4 → 3, tens: 0 → 10
3. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 10 → 9, ones: 0 → 10
4. Subtract the ones. Take the bottom digit away from the top digit.
   10 − 7 = 3
5. Subtract the tens. Take the bottom digit away from the top digit.
   9 − 8 = 1
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   3 − 1 = 2
7. Write the answer. Read the answer from the bottom line.
   213

Check. 213 + 187 = 400. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Method. Estimate first, then check with the exact answer.

1. Estimate. Round 504 to 500 and 267 to 270.
   500 − 270 = 230
2. Compare with 250. The estimate is 230, which is less than 250.
   230 < 250
3. Check with the exact answer. Use the column method.
   504 − 267 = 237, and 237 is less than 250
4. Write the answer.
   Less

Check. 237 is less than 250, so the answer is less. ✓

Watch out. An estimate tells you the answer is about right. Check it with the exact answer when it is close.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Look at the digit that decides, then round to the nearest 100.

1. Look at the digit that decides. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   362: the tens digit is 6
2. Round the number. 362 is closer to 400 than to the other multiples of 100.
   362 → 400
3. Write the answer.
   400

Check. 400 is a multiple of 100, and it is the closest one to 362. ✓

Watch out. Round to the nearest 100 and not to the next one down.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Look at the digit that decides, then round to the nearest 10.

1. Look at the digit that decides. Look at the ones digit. A 5 or more rounds up. A 4 or less rounds down.
   748: the ones digit is 8
2. Round the number. 748 is closer to 750 than to the other multiples of 10.
   748 → 750
3. Write the answer.
   750

Check. 750 is a multiple of 10, and it is the closest one to 748. ✓

Watch out. Round to the nearest 10 and not to the next one down.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Look at the digit that decides, then round to the nearest 100.

1. Look at the digit that decides. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   851: the tens digit is 5
2. Round the number. 851 is closer to 900 than to the other multiples of 100.
   851 → 900
3. Write the answer.
   900

Check. 900 is a multiple of 100, and it is the closest one to 851. ✓

Watch out. Round to the nearest 100 and not to the next one down.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 296 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   296 → 300
2. Round 183 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   183 → 200
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   300 + 200 = 500
4. Write the answer. This is the estimate.
   500

Check. The exact answer is 479, which is close to 500. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 514 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   514 → 500
2. Round 238 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   238 → 200
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   500 + 200 = 700
4. Write the answer. This is the estimate.
   700

Check. The exact answer is 752, which is close to 700. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 809 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   809 → 800
2. Round 392 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   392 → 400
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   800 − 400 = 400
4. Write the answer. This is the estimate.
   400

Check. The exact answer is 417, which is close to 400. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 633 to the nearest 10. Look at the ones digit. A 5 or more rounds up. A 4 or less rounds down.
   633 → 630
2. Round 287 to the nearest 10. Look at the ones digit. A 5 or more rounds up. A 4 or less rounds down.
   287 → 290
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   630 − 290 = 340
4. Write the answer. This is the estimate.
   340

Check. The exact answer is 346, which is close to 340. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. An inverse operation undoes another. Addition and subtraction are inverses. To check a + b = c, take b away from c and you should get a.

Method. Take the second number away from Ben's answer. Then work out the correct total.

1. Take 149 away from 521. If Ben is right, this gives 362.
   521 − 149 = 372
2. Compare with 362. 372 is not 362, so Ben is wrong.
   372 ≠ 362
3. Work out the correct total. Use the column method.
   362 + 149 = 511
4. Check with subtraction. The answer take away 149 must give 362.
   511 − 149 = 362 ✓
5. Write the answer.
   511

Check. 511 − 149 = 362. ✓

Watch out. Check with the inverse operation. It finds the mistake quickly.

Key words. An inverse operation undoes another. Addition and subtraction are inverses. To check a + b = c, take b away from c and you should get a.

Method. Check with the inverse: add the answer and the number taken away.

1. Add 439 to 387. If the answer is right, we get 826.
   387 + 439 = 826
2. Compare with 826. The two totals match.
   826 = 826
3. Write the answer. The answer is right.
   Yes

Check. 387 + 439 = 826. ✓

Watch out. If the check does not match, look for a column that was not carried or exchanged.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 612 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   612 → 600
2. Round 298 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   298 → 300
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   600 − 300 = 300
4. Write the answer. This is the estimate.
   300

Check. The exact answer is 314, which is close to 300. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number, then work out the estimate.

1. Round 395 to 400 and 208 to 200. The tens digits are 9 and 0.
   400 + 200
2. Work out the estimate. Add the rounded numbers.
   400 + 200 = 600
3. Compare with Ravi. Ravi said about 500, but the estimate is 600.
   600 is not 500
4. Write the answer.
   No, it is about 600

Check. The exact answer is 603, which is close to 600. ✓

Watch out. Round each number before you add. Then compare the estimate with the answer you were given.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Estimate with the rounded numbers, and compare with 800.

1. Round 536 to 500 and 245 to 200. Both numbers are rounded to the nearest 100.
   500 + 200
2. Work out the estimate. The estimate is 700.
   500 + 200 = 700
3. Compare with 800. 700 is less than 800, so the answer is probably less than 800.
   700 < 800
4. Write the answer. The exact total is 781, which is also less than 800.
   Less

Check. 536 + 245 = 781, and 781 is less than 800. ✓

Watch out. The estimate tells you which side of 800 the answer is on.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   356 + [ ] = 600
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   600 − 356 = 244
3. Check by adding the answer back. The check must give the total.
   356 + 244 = 600
4. Write the answer.
   244

Check. 356 + 244 = 600. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: add to find the missing number.

1. Look at the calculation. The box is the start number, and we take b away to get c.
   [ ] − 178 = 400
2. Use the inverse: add the number taken away back on. Addition undoes subtraction.
   400 + 178 = 578
3. Check by taking the number away. The check must give c.
   578 − 178 = 400
4. Write the answer.
   578

Check. 578 − 178 = 400. ✓

Watch out. Adding the number back gives the start. Do not take it away again.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract c from a to find the box.

1. Look at the calculation. The box is the number taken away from a.
   900 − [ ] = 450
2. Work out what is taken away. Take c away from a to find the box.
   900 − 450 = 450
3. Check by taking the answer away. The result must be c.
   900 − 450 = 450
4. Write the answer.
   450

Check. 900 − 450 = 450. ✓

Watch out. The box is the number taken away, so it is not c.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   275 + [ ] = 512
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   512 − 275 = 237
3. Check by adding the answer back. The check must give the total.
   275 + 237 = 512
4. Write the answer.
   237

Check. 275 + 237 = 512. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract c from a to find the box.

1. Look at the calculation. The box is the number taken away from a.
   450 − [ ] = 385
2. Work out what is taken away. Take c away from a to find the box.
   450 − 385 = 65
3. Check by taking the answer away. The result must be c.
   450 − 65 = 385
4. Write the answer.
   65

Check. 450 − 65 = 385. ✓

Watch out. The box is the number taken away, so it is not c.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Find how many beads he has, then find how many more he needs to reach 600.

1. Find the beads he has. Add the two boxes.
   214 + 289 = 503
2. Find how many more he needs. Take the beads he has away from 600.
   600 − 503 = 97
3. Check. Add the extra beads to the beads he has.
   503 + 97 = 600 ✓
4. Write the answer.
   97

Check. 503 + 97 = 600. ✓

Watch out. Work out the total first, then find the difference from 600.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   387 − 268
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 8 → 7, ones: 7 → 17
3. Subtract the ones. Take the bottom digit away from the top digit.
   17 − 8 = 9
4. Subtract the tens. Take the bottom digit away from the top digit.
   7 − 6 = 1
5. Subtract the hundreds. Take the bottom digit away from the top digit.
   3 − 2 = 1
6. Write the answer. Read the answer from the bottom line.
   119

Check. 119 + 268 = 387. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Find the sheets used, then take them away from 500.

1. Find the sheets used. Add the sheets for art and maths.
   178 + 143 = 321
2. Find the sheets left. Take the sheets used away from 500.
   500 − 321 = 179
3. Check. Add the sheets used to the sheets left.
   321 + 179 = 500 ✓
4. Write the answer.
   179

Check. 321 + 179 = 500. ✓

Watch out. Use both amounts before you take away. Do not take away only one of them.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   620 − 487
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 2 → 1, ones: 0 → 10
3. Subtract the ones. Take the bottom digit away from the top digit.
   10 − 7 = 3
4. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 6 → 5, tens: 1 → 11
5. Subtract the tens. Take the bottom digit away from the top digit.
   11 − 8 = 3
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   5 − 4 = 1
7. Write the answer. Read the answer from the bottom line.
   133

Check. 133 + 487 = 620. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Find the pages read, then take them away from 300.

1. Find the pages read. Add the pages read on Monday and Tuesday.
   135 + 98 = 233
2. Find the pages left. Take the pages read from the total.
   300 − 233 = 67
3. Check. Add the pages left to the pages read.
   233 + 67 = 300 ✓
4. Write the answer.
   67

Check. 233 + 67 = 300. ✓

Watch out. Two days of reading means two amounts to add.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   508 − 275
2. Subtract the ones. Take the bottom digit away from the top digit.
   8 − 5 = 3
3. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 5 → 4, tens: 0 → 10
4. Subtract the tens. Take the bottom digit away from the top digit.
   10 − 7 = 3
5. Subtract the hundreds. Take the bottom digit away from the top digit.
   4 − 2 = 2
6. Write the answer. Read the answer from the bottom line.
   233

Check. 233 + 275 = 508. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Look at the hundreds digit: 4 hundreds take away 3 hundreds.

1. Look at the hundreds. The hundreds digit of 452 is 4, not 5.
   4 hundreds − 3 hundreds = 1 hundred
2. Find the answer. The tens and ones are 5 and 2, so they stay the same.
   452 − 300 = 152
3. Check. Add 300 back on.
   152 + 300 = 452 ✓
4. Write the answer. Ben was not right.
   No, it is 152

Check. 152 + 300 = 452. ✓

Watch out. Look at the digit in the right place. Here the place is the hundreds.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   245 + [ ] = 600
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   600 − 245 = 355
3. Check by adding the answer back. The check must give the total.
   245 + 355 = 600
4. Write the answer.
   355

Check. 245 + 355 = 600. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the tens place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   327 = 300 + 20 + 7
2. Find the place of the number we add. 60 is 6 tens, so only the tens digit changes.
   60 = 6 tens
3. Add in the tens place only. The other places stay the same.
   2 tens + 6 tens = 8 tens
4. Put the parts back together. Write each place, then read the number.
   300 + 80 + 7
5. Write the answer.
   387

Check. 387 − 60 = 327. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the hundreds place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   540 = 500 + 40
2. Find the place of the number we take away. 100 is 1 hundred, so only the hundreds digit changes.
   100 = 1 hundred
3. Take away in the hundreds place only. The other places stay the same.
   5 − 1 = 4 hundreds
4. Put the parts back together. Write each place, then read the number.
   400 + 40
5. Write the answer.
   440

Check. 440 + 100 = 540. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   463 + 285
2. Add the ones first. Start on the right.
   3 + 5 = 8, write 8
3. Add the tens. Nothing is carried into this column.
   6 + 8 = 14, write 4 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   4 + 2 + 1 carried = 7, write 7
5. Write the answer. Read the digits from the bottom line.
   748

Check. 748 − 285 = 463. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   705 − 268
2. Exchange 1 hundred for 10 tens. The ones digit on top is too small, so we break one hundred up.
   hundreds: 7 → 6, tens: 0 → 10
3. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 10 → 9, ones: 5 → 15
4. Subtract the ones. Take the bottom digit away from the top digit.
   15 − 8 = 7
5. Subtract the tens. Take the bottom digit away from the top digit.
   9 − 6 = 3
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   6 − 2 = 4
7. Write the answer. Read the answer from the bottom line.
   437

Check. 437 + 268 = 705. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   378 + 96
2. Add the ones first. Start on the right.
   8 + 6 = 14, write 4 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   7 + 9 + 1 carried = 17, write 7 and carry 1 hundred
4. Add the hundreds. Add the carried ten or hundred too.
   3 + 0 + 1 carried = 4, write 4
5. Write the answer. Read the digits from the bottom line.
   474

Check. 474 − 96 = 378. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Look at the digit that decides, then round to the nearest 100.

1. Look at the digit that decides. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   463: the tens digit is 6
2. Round the number. 463 is closer to 500 than to the other multiples of 100.
   463 → 500
3. Write the answer.
   500

Check. 500 is a multiple of 100, and it is the closest one to 463. ✓

Watch out. Round to the nearest 100 and not to the next one down.

Key words. To estimate is to find an answer that is close to the exact one. We usually round each number to the nearest 10 or 100 first.

Method. Round each number first, then work out the answer with the rounded numbers.

1. Round 589 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   589 → 600
2. Round 213 to the nearest 100. Look at the tens digit. A 5 or more rounds up. A 4 or less rounds down.
   213 → 200
3. Work out the estimate with the rounded numbers. These numbers are easy to work with.
   600 + 200 = 800
4. Write the answer. This is the estimate.
   800

Check. The exact answer is 802, which is close to 800. ✓

Watch out. An estimate is not the exact answer. It tells you whether an answer is sensible.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   368 + [ ] = 700
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   700 − 368 = 332
3. Check by adding the answer back. The check must give the total.
   368 + 332 = 700
4. Write the answer.
   332

Check. 368 + 332 = 700. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. An inverse operation undoes another. Addition and subtraction are inverses. To check a + b = c, take b away from c and you should get a.

Method. Use the inverse to check Ruby's answer, then work out the correct one.

1. Check Ruby's answer. Add 189 to 364. If Ruby is right, we get 425.
   364 + 189 = 553
2. Compare. 553 is not 425, so Ruby is wrong.
   553 ≠ 425
3. Work out the correct answer. Use the column method.
   425 − 189 = 236
4. Check. Add 189 back on.
   236 + 189 = 425 ✓
5. Write the answer.
   236

Check. 236 + 189 = 425. ✓

Watch out. Check with the inverse. Adding back on is quicker than starting again.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Take each amount away from 350 in turn, or add the two amounts first.

1. Add the two amounts. Both amounts are taken away.
   128 + 97 = 225
2. Take the total away. The number left is 350 minus the total.
   350 − 225 = 125
3. Check. Add the amount left to the total taken.
   125 + 225 = 350 ✓
4. Write the answer.
   125

Check. 125 + 225 = 350. ✓

Watch out. Both amounts are taken away, so both must be used.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the tens place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   350 = 300 + 50
2. Find the place of the number we add. 40 is 4 tens, so only the tens digit changes.
   40 = 4 tens
3. Add in the tens place only. The other places stay the same.
   5 tens + 4 tens = 9 tens
4. Put the parts back together. Write each place, then read the number.
   300 + 90
5. Write the answer.
   390

Check. 390 − 40 = 350. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Split the number, change only the hundreds place, then put the parts back together.

1. Split the number into hundreds, tens and ones. Then we can see the digit in each place.
   627 = 600 + 20 + 7
2. Find the place of the number we take away. 300 is 3 hundreds, so only the hundreds digit changes.
   300 = 3 hundreds
3. Take away in the hundreds place only. The other places stay the same.
   6 − 3 = 3 hundreds
4. Put the parts back together. Write each place, then read the number.
   300 + 20 + 7
5. Write the answer.
   327

Check. 327 + 300 = 627. ✓

Watch out. Work only in the place that is named. If that place goes past 9, carry into the next place.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Add the ones first, then the tens, then the hundreds. When a column makes ten or more, carry to the next column.

1. Write the numbers in columns. Line up the ones, the tens and the hundreds, so each digit is added to the same kind of digit.
   254 + 138
2. Add the ones first. Start on the right.
   4 + 8 = 12, write 2 and carry 1 ten
3. Add the tens. Add the carried ten or hundred too.
   5 + 3 + 1 carried = 9, write 9
4. Add the hundreds. Nothing is carried into this column.
   2 + 1 = 3, write 3
5. Write the answer. Read the digits from the bottom line.
   392

Check. 392 − 138 = 254. ✓

Watch out. Do not forget the carried number. Write it small, and add it in the next column.

Key words. A column is a line of digits with the same place value, such as the ones. A carry is a ten or a hundred moved to the next column on the left. An exchange breaks one ten (or one hundred) into ten ones (or ten tens).

Method. Start on the right. If the top digit is too small, exchange from the next place, then subtract each column.

1. Write the numbers in columns. Put the number being taken away underneath, with the ones under the ones.
   812 − 345
2. Exchange 1 ten for 10 ones. The ones digit on top is too small, so we break one ten up.
   tens: 1 → 0, ones: 2 → 12
3. Subtract the ones. Take the bottom digit away from the top digit.
   12 − 5 = 7
4. Exchange 1 hundred for 10 tens. The tens digit on top is too small, so we break one hundred up.
   hundreds: 8 → 7, tens: 0 → 10
5. Subtract the tens. Take the bottom digit away from the top digit.
   10 − 4 = 6
6. Subtract the hundreds. Take the bottom digit away from the top digit.
   7 − 3 = 4
7. Write the answer. Read the answer from the bottom line.
   467

Check. 467 + 345 = 812. ✓

Watch out. Exchange only when the top digit is too small. If the next place is a zero, break up the next place that is not zero.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Use the inverse: subtract to find the missing number.

1. Look at the calculation. The box is added to a to make c.
   465 + [ ] = 700
2. Use the inverse: take the number you know away from the total. Subtraction undoes addition.
   700 − 465 = 235
3. Check by adding the answer back. The check must give the total.
   465 + 235 = 700
4. Write the answer.
   235

Check. 465 + 235 = 700. ✓

Watch out. Take the number you know away from the total, not the other way round.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Find the total made, then take away the cakes sold.

1. Find the total made. Add the two days.
   460 + 295 = 755
2. Find the cakes left. Take the cakes sold away from the total.
   755 − 540 = 215
3. Check. Add the cakes sold to the cakes left.
   215 + 540 = 755 ✓
4. Write the answer.
   215

Check. 215 + 540 = 755. ✓

Watch out. The question asks for the cakes left, not the total made.

Key words. An inverse operation undoes another. Addition and subtraction are inverses. To check a + b = c, take b away from c and you should get a.

Method. Check Mia's answer with addition, then work out the correct one.

1. Check Mia's answer. Add 289 to 387. If Mia is right, we get 576.
   387 + 289 = 676
2. Compare. 676 is not 576, so Mia is wrong.
   676 ≠ 576
3. Work out the correct answer. Use the column method.
   576 − 289 = 287
4. Check. Add 289 back on.
   287 + 289 = 576 ✓
5. Write the answer.
   287

Check. 287 + 289 = 576. ✓

Watch out. Check with the inverse, so you can see which digit went wrong.

Key words. A missing number is shown by a box, [ ]. Use the inverse operation to find it.

Method. Add the two amounts given away, then take them away from 400.

1. Find the total given away. Add the stickers given to Leo and to Priya.
   138 + 65 = 203
2. Find the stickers left. Take the total given away from 400.
   400 − 203 = 197
3. Check. Add the stickers given away to the stickers left.
   197 + 203 = 400 ✓
4. Write the answer.
   197

Check. 197 + 203 = 400. ✓

Watch out. Both amounts are given away, so take both of them away.

Key words. The place of a digit tells us what it is worth. In a three-digit number the places are hundreds, tens and ones. Only the place that is named changes.

Method. Look at how far each number is from 300.

1. Look at 298. It is 2 less than 300.
   300 − 2 = 298
2. Look at 302. It is 2 more than 300.
   300 + 2 = 302
3. Put them together. The 2 less and the 2 more cancel out, so the total is 300 + 300.
   300 + 300 = 600
4. Write the answer. So 298 + 302 is 600, and no column method is needed.
   600

Check. 298 + 302 = 600. ✓

Watch out. Look for numbers that are close to a round number, like 300. This is quicker than the column method.