Step-by-step Maths Level 5 Adding and subtracting whole numbers to a million: check-up and practice test questions

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 8 is at least 3, so subtract directly.
   8 - 3 = 5
2. Subtract the tens column. 6 is at least 2, so subtract directly.
   6 - 2 = 4
3. Subtract the hundreds column. 2 is less than 4, so exchange 1 thousands for 10 hundreds.
   12 - 4 = 8
4. Subtract the thousands column. 7 is at least 5, so subtract directly.
   7 - 5 = 2
5. Subtract the ten thousands column. 3 is less than 9, so exchange 1 hundred thousands for 10 ten thousands.
   13 - 9 = 4
6. Subtract the hundred thousands column. 0 is at least 0, so subtract directly.
   0 - 0 = 0
7. Write the answer. Read the digits from the left, and put commas in.
   42,845

Check. Check: 95,423 + 42,845 = 138,268.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Use the inverse operation to find the missing number.

1. Think about the total. The missing number is what is left when we take the known number away.
   604,641 - 258,175
2. Subtract to find the missing number. Use the column method.
   604,641 - 258,175 = 346,466
3. Check by adding. The missing number and the known number must make the total.
   258,175 + 346,466 = 604,641
4. Write the missing number. This is the number in the box.
   346,466

Check. Check: put 346,466 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Method. Check by using the inverse: subtract for a sum, or add back for a difference.

1. Take one number away from the answer. If the sum is correct, taking one number away gives the other.
   575,432 - 442,296 = 133,136
2. Compare with the other number. Is 133,136 the same as 133,146?
   Not the same
3. Write Yes or No. Yes if the check works; No if it does not.
   No

Check. The correct answer is 575,442.

Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 5 is less than 9, so exchange 1 tens for 10 ones.
   15 - 9 = 6
2. Subtract the tens column. 3 is less than 9, so exchange 1 hundreds for 10 tens.
   13 - 9 = 4
3. Subtract the hundreds column. 6 is at least 3, so subtract directly.
   6 - 3 = 3
4. Subtract the thousands column. 3 is less than 6, so exchange 1 ten thousands for 10 thousands.
   13 - 6 = 7
5. Subtract the ten thousands column. 3 is at least 2, so subtract directly.
   3 - 2 = 1
6. Subtract the hundred thousands column. 5 is at least 3, so subtract directly.
   5 - 3 = 2
7. Write the answer. Read the digits from the left, and put commas in.
   217,346

Check. Check: 326,399 + 217,346 = 543,745.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Use the inverse operation to find the missing number.

1. Add the number taken away to the answer. Adding undoes subtracting.
   338,690 + 211,998
2. Work out the sum. Use the column method.
   338,690 + 211,998 = 550,688
3. Check by subtracting. The answer must go back to the missing number.
   550,688 - 211,998 = 338,690
4. Write the missing number. This is the number in the box.
   550,688

Check. Check: put 550,688 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Method. Use the inverse operation to find the missing number.

1. Think about the total. The missing number is what is left when we take the known number away.
   409,082 - 102,640
2. Subtract to find the missing number. Use the column method.
   409,082 - 102,640 = 306,442
3. Check by adding. The missing number and the known number must make the total.
   102,640 + 306,442 = 409,082
4. Write the missing number. This is the number in the box.
   306,442

Check. Check: put 306,442 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 7 in the ones column.
   1 + 6 = 7
2. Add the tens column. Write 3 and carry 1 to the hundreds column.
   5 + 8 = 13
3. Add the hundreds column. Write 9 and carry 1 to the thousands column.
   9 + 9 + 1 carried = 19
4. Add the thousands column. Write 0 and carry 1 to the ten thousands column.
   9 + 0 + 1 carried = 10
5. Add the ten thousands column. Write 4 and carry 1 to the hundred thousands column.
   8 + 5 + 1 carried = 14
6. Add the hundred thousands column. Write 9 in the hundred thousands column.
   8 + 0 + 1 carried = 9
7. Write the answer. Put the digits together, with commas between groups of three.
   940,937

Check. Check: 940,937 - 50,986 = 889,951.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 8 is at least 5, so subtract directly.
   8 - 5 = 3
2. Subtract the tens column. 7 is less than 9, so exchange 1 hundreds for 10 tens.
   17 - 9 = 8
3. Subtract the hundreds column. 3 is less than 8, so exchange 1 thousands for 10 hundreds.
   13 - 8 = 5
4. Subtract the thousands column. 7 is less than 8, so exchange 1 ten thousands for 10 thousands.
   17 - 8 = 9
5. Subtract the ten thousands column. 5 is at least 3, so subtract directly.
   5 - 3 = 2
6. Subtract the hundred thousands column. 4 is at least 0, so subtract directly.
   4 - 0 = 4
7. Write the answer. Read the digits from the left, and put commas in.
   429,583

Check. Check: 38,895 + 429,583 = 468,478.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 0 and carry 1 to the tens column.
   7 + 3 = 10
2. Add the tens column. Write 5 in the tens column.
   2 + 2 + 1 carried = 5
3. Add the hundreds column. Write 3 and carry 1 to the thousands column.
   4 + 9 = 13
4. Add the thousands column. Write 7 in the thousands column.
   4 + 2 + 1 carried = 7
5. Add the ten thousands column. Write 9 in the ten thousands column.
   9 + 0 = 9
6. Add the hundred thousands column. Write 4 in the hundred thousands column.
   0 + 4 = 4
7. Write the answer. Put the digits together, with commas between groups of three.
   497,350

Check. Check: 497,350 - 402,923 = 94,427.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 3 is less than 5, so exchange 1 tens for 10 ones.
   13 - 5 = 8
2. Subtract the tens column. 2 is at least 2, so subtract directly.
   2 - 2 = 0
3. Subtract the hundreds column. 2 is less than 6, so exchange 1 thousands for 10 hundreds.
   12 - 6 = 6
4. Subtract the thousands column. 1 is at least 1, so subtract directly.
   1 - 1 = 0
5. Subtract the ten thousands column. 7 is at least 4, so subtract directly.
   7 - 4 = 3
6. Subtract the hundred thousands column. 7 is at least 1, so subtract directly.
   7 - 1 = 6
7. Write the answer. Read the digits from the left, and put commas in.
   630,608

Check. Check: 141,625 + 630,608 = 772,233.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Round each number first, then calculate with the rounded numbers.

1. Round the first number. Look at the thousands digit: 5 or more rounds up.
   249,766 is about 250,000
2. Round the second number. Use the same rule.
   351,138 is about 350,000
3. Add the rounded numbers. This is the estimate.
   250,000 + 350,000 = 600,000
4. Write the estimate. The exact answer should be close to this.
   600,000

Check. The exact answer is 600,904, which is close to 600,000.

Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 6 in the ones column.
   5 + 1 = 6
2. Add the tens column. Write 1 and carry 1 to the hundreds column.
   5 + 6 = 11
3. Add the hundreds column. Write 8 in the hundreds column.
   4 + 3 + 1 carried = 8
4. Add the thousands column. Write 9 in the thousands column.
   6 + 3 = 9
5. Add the ten thousands column. Write 4 and carry 1 to the hundred thousands column.
   7 + 7 = 14
6. Add the hundred thousands column. Write 9 in the hundred thousands column.
   5 + 3 + 1 carried = 9
7. Write the answer. Put the digits together, with commas between groups of three.
   949,816

Check. Check: 949,816 - 373,361 = 576,455.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 1 is at least 1, so subtract directly.
   1 - 1 = 0
2. Subtract the tens column. 4 is at least 2, so subtract directly.
   4 - 2 = 2
3. Subtract the hundreds column. 4 is at least 0, so subtract directly.
   4 - 0 = 4
4. Subtract the thousands column. 7 is less than 9, so exchange 1 ten thousands for 10 thousands.
   17 - 9 = 8
5. Subtract the ten thousands column. 0 is less than 1, so exchange 1 hundred thousands for 10 ten thousands.
   10 - 1 = 9
6. Subtract the hundred thousands column. 7 is at least 1, so subtract directly.
   7 - 1 = 6
7. Write the answer. Read the digits from the left, and put commas in.
   698,420

Check. Check: 119,021 + 698,420 = 817,441.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 9 in the ones column.
   5 + 4 = 9
2. Add the tens column. Write 6 in the tens column.
   3 + 3 = 6
3. Add the hundreds column. Write 3 and carry 1 to the thousands column.
   4 + 9 = 13
4. Add the thousands column. Write 0 and carry 1 to the ten thousands column.
   3 + 6 + 1 carried = 10
5. Add the ten thousands column. Write 8 in the ten thousands column.
   7 + 0 + 1 carried = 8
6. Add the hundred thousands column. Write 9 in the hundred thousands column.
   8 + 1 = 9
7. Write the answer. Put the digits together, with commas between groups of three.
   980,369

Check. Check: 980,369 - 106,934 = 873,435.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Add the columns from the right. Carry any ten into the next column on the left.

1. Add the ones column. Write 7 in the ones column.
   6 + 1 = 7
2. Add the tens column. Write 7 and carry 1 to the hundreds column.
   9 + 8 = 17
3. Add the hundreds column. Write 4 in the hundreds column.
   2 + 1 + 1 carried = 4
4. Add the thousands column. Write 2 and carry 1 to the ten thousands column.
   8 + 4 = 12
5. Add the ten thousands column. Write 8 in the ten thousands column.
   5 + 2 + 1 carried = 8
6. Add the hundred thousands column. Write 5 in the hundred thousands column.
   4 + 1 = 5
7. Write the answer. Put the digits together, with commas between groups of three.
   582,477

Check. Check: 582,477 - 124,181 = 458,296.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 4 is less than 7, so exchange 1 tens for 10 ones.
   14 - 7 = 7
2. Subtract the tens column. 1 is less than 3, so exchange 1 hundreds for 10 tens.
   11 - 3 = 8
3. Subtract the hundreds column. 7 is at least 2, so subtract directly.
   7 - 2 = 5
4. Subtract the thousands column. 9 is at least 5, so subtract directly.
   9 - 5 = 4
5. Subtract the ten thousands column. 8 is at least 4, so subtract directly.
   8 - 4 = 4
6. Subtract the hundred thousands column. 1 is at least 0, so subtract directly.
   1 - 0 = 1
7. Write the answer. Read the digits from the left, and put commas in.
   144,587

Check. Check: 45,237 + 144,587 = 189,824.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

1. Subtract the ones column. 4 is less than 8, so exchange 1 tens for 10 ones.
   14 - 8 = 6
2. Subtract the tens column. 1 is less than 3, so exchange 1 hundreds for 10 tens.
   11 - 3 = 8
3. Subtract the hundreds column. 3 is less than 4, so exchange 1 thousands for 10 hundreds.
   13 - 4 = 9
4. Subtract the thousands column. 5 is at least 0, so subtract directly.
   5 - 0 = 5
5. Subtract the ten thousands column. 7 is at least 3, so subtract directly.
   7 - 3 = 4
6. Subtract the hundred thousands column. 9 is at least 3, so subtract directly.
   9 - 3 = 6
7. Write the answer. Read the digits from the left, and put commas in.
   645,986

Check. Check: 330,438 + 645,986 = 976,424.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Method. Check by using the inverse: subtract for a sum, or add back for a difference.

1. Take one number away from the answer. If the sum is correct, taking one number away gives the other.
   845,615 - 633,340 = 212,275
2. Compare with the other number. Is 212,275 the same as 211,275?
   Not the same
3. Write Yes or No. Yes if the check works; No if it does not.
   No

Check. The correct answer is 844,615.

Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.

Method. Use the inverse operation to find the missing number.

1. Think about the total. The missing number is what is left when we take the known number away.
   494,697 - 460,804
2. Subtract to find the missing number. Use the column method.
   494,697 - 460,804 = 33,893
3. Check by adding. The missing number and the known number must make the total.
   460,804 + 33,893 = 494,697
4. Write the missing number. This is the number in the box.
   33,893

Check. Check: put 33,893 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Method. Use the inverse operation to find the missing number.

1. Think about the total. The missing number is what is left when we take the known number away.
   539,434 - 351,316
2. Subtract to find the missing number. Use the column method.
   539,434 - 351,316 = 188,118
3. Check by adding. The missing number and the known number must make the total.
   351,316 + 188,118 = 539,434
4. Write the missing number. This is the number in the box.
   188,118

Check. Check: put 188,118 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.