Year 6 Arithmetic (SATs) Place value and the four operations: check-up and practice test questions

Method. Find the column of the 8, then multiply.

1. Find the column of the digit. Count from the right: this is the ten thousands column.
   digit 8 in the ten thousands column
2. Multiply the digit by the column value. Each column is worth ten times the column on its right.
   8 × 10,000 = 80,000
3. Write the answer.
   80,000

Check. The 8 is in the ten thousands column: 80,000 + 6,200,000 + 491 = 6,280,491. ✓

Method. Look at the thousands digit.

1. Find the two multiples of the rounding amount either side of the number. The number lies between 740,000 and 750,000.
   740,000 < 743,526 < 750,000
2. Look at the digit just to the right of the rounding column. It shows which multiple is nearer.
   digit 3
3. Round to the nearest ten thousand. The digit is 3, which is less than 5, so round down.
   743,526 rounds to 740,000
4. Write the answer.
   740,000

Check. 740,000 is 3,526 less; 750,000 is 6,474 more. ✓

Method. Add column by column from the right.

1. Add the ones column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   2 + 8 + 0 = 10, write 0, carry 1
2. Add the tens column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   0 + 5 + 1 = 6, write 6
3. Add the hundreds column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   6 + 4 + 0 = 10, write 0, carry 1
4. Add the thousands column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   5 + 7 + 1 = 13, write 3, carry 1
5. Add the ten thousands column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   0 + 3 + 1 = 4, write 4
6. Add the hundred thousands column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   8 + 9 + 0 = 17, write 7, carry 1
7. Add the millions column. Write the ones digit of the total in this column, and carry the tens digit to the next column.
   4 + 1 + 1 = 6, write 6
8. Write the answer.
   6,743,060

Check. 1,937,458 + 4,805,602 = 6,743,060. ✓

Method. Subtract column by column, borrowing.

1. Subtract the ones column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 0 = 0
2. Subtract the tens column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 0 = 0, which is less than 5, so borrow 10: 10 - 5 = 5
3. Subtract the hundreds column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 1 = -1, which is less than 7, so borrow 10: 9 - 7 = 2
4. Subtract the thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 1 = -1, which is less than 6, so borrow 10: 9 - 6 = 3
5. Subtract the ten thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 1 = -1, which is less than 8, so borrow 10: 9 - 8 = 1
6. Subtract the hundred thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 1 = -1, which is less than 4, so borrow 10: 9 - 4 = 5
7. Subtract the millions column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   2 - 1 = 1
8. Write the answer.
   1,513,250

Check. 1,513,250 + 1,486,750 = 3,000,000. ✓

Method. Count up 11 from -8.

1. Count up. -8 up to 0 is 8 steps; 3 more steps reach 3.
   -8 + 11 = 3
2. Write the answer.
   3°C

Check. Count back 11 from 3 to reach -8. ✓

Method. Multiply first, then go left to right.

1. Multiply. 2 × 6 = 12.
   9 + 12 - 4
2. Add and subtract. 9 + 12 = 21, then 21 - 4 = 17.
   17
3. Write the answer.
   17

Check. Working left to right without the rule gives 11 × 6 - 4 = 62, which is wrong. ✓

Method. Brackets, then multiply, then add.

1. Brackets. 14 - 6 = 8.
   8 × 3 + 2
2. Multiply. 8 × 3 = 24.
   24 + 2
3. Add. 24 + 2 = 26.
   26
4. Write the answer.
   26

Check. 26 - 2 = 24 = 8 × 3. ✓

Method. Multiply to find the total seats, then subtract the broken seats.

1. Total seats. 30 × 22 = 660.
   30 × 22 = 660
2. Usable seats. 660 - 68 = 592.
   660 - 68 = 592
3. Write the answer.
   592

Check. 592 + 68 = 660. ✓

Method. Round each number, then add.

1. Round. 6,197 → 6,000 and 2,806 → 3,000.
   6,000 + 3,000
2. Add. 6,000 + 3,000 = 9,000.
   9,000
3. Write the answer.
   9,000

Check. The exact answer is 9,003, which is close to 9,000. ✓

Method. Work out both calculations.

1. Work out 7,000 - 5. The answer is 6,995.
   7,000 - 5 = 6,995
2. Work out 7,000 - 50 - 5. The answer is 6,945.
   7,000 - 50 - 5 = 6,945
3. Write the answer.
   Because they are different calculations, so the answers are different.

Check. 6,995 and 6,945 are different. ✓

Method. Find the column of the 8.

1. Find the column. The 8 is in the ten thousands column.
   8 × 10,000
2. Multiply. 8 × 10,000 = 80,000.
   80,000
3. Write the answer.
   80,000

Check. 80,000 is the value. ✓

Method. Write each part in its column.

1. Write the millions. 2 million is 2,000,000.
   2,000,000
2. Write the thousands and the ones. 7 thousands is 7,000 and 45 is 45.
   2,000,000 + 7,000 + 45 = 2,007,045
3. Write the answer.
   2,007,045

Check. The hundreds column is zero. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what you need to find or check.
2. Test the choice. 4,000,000 has 4 millions, which is more than 3 millions.
   4,000,000 is right
3. Reject the other choices. 3,999,999, 3,900,000 and 3,990,000 all have 3 millions.
   3,999,999 and 3,900,000 and 3,990,000 are not right
4. Write the answer.
   4,000,000

Check. 4,000,000 is right. ✓

Method. Look at the hundreds digit.

1. Find the two multiples of the rounding amount either side of the number. The number lies between 582,000 and 583,000.
   582,000 < 582,500 < 583,000
2. Look at the digit just to the right of the rounding column. It shows which multiple is nearer.
   digit 5
3. Round to the nearest thousand. The digit is 5, which is 5 or more, so round up.
   582,500 rounds to 583,000
4. Write the answer.
   583,000

Check. 582,500 is halfway, and halves round up to 583,000. ✓

Method. Subtract column by column, borrowing.

1. Subtract the ones column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   9 - 4 = 5
2. Subtract the tens column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   1 - 0 = 1, which is less than 8, so borrow 10: 11 - 8 = 3
3. Subtract the hundreds column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   2 - 1 = 1, which is less than 3, so borrow 10: 11 - 3 = 8
4. Subtract the thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   5 - 0 = 5
5. Subtract the ten thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   0 - 0 = 0, which is less than 7, so borrow 10: 10 - 7 = 3
6. Subtract the hundred thousands column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   4 - 1 = 3, which is less than 8, so borrow 10: 13 - 8 = 5
7. Subtract the millions column. Take the bottom digit from the top digit. If the top is too small, borrow 10 from the column on the left.
   4 - 2 = 2
8. Write the answer.
   2,535,835

Check. 2,535,835 + 2,870,384 = 5,406,219. ✓

Method. Multiply first, then add and subtract from left to right.

1. Multiply. 4 × 6 = 24.
   15 + 24 - 9
2. Add and subtract. 15 + 24 = 39, then 39 - 9 = 30.
   30
3. Write the answer.
   30

Check. The answer is 30. ✓

Method. Count down 5 from -3.

1. Count down. -3 → -4 → -5 → -6 → -7 → -8.
   -3 - 5 = -8
2. Write the answer.
   -8°C

Check. Count up 5 from -8 to reach -3. ✓

Method. Add the two weekly totals.

1. Add. 1,250 + 180 = 1,430.
   1,250 + 180 = 1,430
2. Write the answer.
   1,430

Check. 1,430 - 180 = 1,250. ✓

Method. Brackets, then divide, then add.

1. Brackets. 25 - 9 = 16.
   16 ÷ 4 + 3
2. Divide. 16 ÷ 4 = 4.
   4 + 3
3. Add. 4 + 3 = 7.
   7
4. Write the answer.
   7

Check. The answer is 7. ✓

Method. Take away 1,000,000 and add back 1.

1. Take away 1,000,000. 6,000,000 - 1,000,000 = 5,000,000.
   5,000,000
2. Add back 1. 999,999 is 1 less than 1,000,000, so add 1 back.
   5,000,001
3. Write the answer.
   5,000,001, because 999,999 is one less than 1,000,000, so 6,000,000 - 999,999 is 5,000,001.

Check. 5,000,001 + 999,999 = 6,000,000. ✓