Year 6 Arithmetic (SATs): Adding and subtracting large numbers mentally
Part of the Year 6 Arithmetic (SATs) mental arithmetic chapter. Chapter overview · whole chapter on one page
Adding and subtracting large numbers mentally
Rule
To add in your head, split each number into its big part and its small part. Add the big parts, then the small parts, and put them together.
To subtract, you can round the number taken away to a friendly number, subtract that, then correct the answer.
Practice guide: work out each answer in your head, then write only the number. Do not use a calculator or paper for the mental parts.
Key ideas
- Split large numbers into thousands and the rest.
- Round a number to a friendly number, then correct the answer.
- Estimate first: an answer far from the estimate has gone wrong.
Method. Split the numbers into thousands and the rest, then add.
- Split each number into thousands and the rest. 12,500 is 12,000 and 500; 8,700 is 8,000 and 700.12,000 + 500 and 8,000 + 700
- Add the thousands. The thousands add first.12,000 + 8,000 = 20,000
- Add the rest. Add the smaller parts.500 + 700 = 1200
- Put the parts together. Add the two totals.20,000 + 1200 = 21,200
- Write the answer. 21,200
Check. About 13,000 + 9,000 = 22,000, close to 21,200. ✓
Method. Subtract a friendly number, then correct the answer.
- Round the number taken away to the nearest thousand. 4,300 is close to 4,000.4,300 ≈ 4,000
- Subtract the rounded number. This is easier to work out.9,000 - 4,000 = 5,000
- Correct the answer. 4,000 is 300 less than 4,300, so take 300 away.5,000 - 300 = 4,700
- Write the answer. 4,700
Check. 4,700 + 4,300 = 9,000. ✓
Watch out. Check by adding the answer back to 4,300.
Method. Add the thousands, then the rest.
- Split each number into thousands and the rest. 45,000 is 45,000 and 0; 8,900 is 8,000 and 900.45,000 + 0 and 8,000 + 900
- Add the thousands. The thousands add first.45,000 + 8,000 = 53,000
- Add the rest. Add the smaller parts.0 + 900 = 900
- Put the parts together. Add the two totals.53,000 + 900 = 53,900
- Write the answer. 53,900
Check. About 45,000 + 9,000 = 54,000, close to 53,900. ✓
Exercise 7A Practice: adding and subtracting large numbers
Non-calculatorMethod. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 3,400 is 3,000 and 400; 2,800 is 2,000 and 800.3,000 + 400 and 2,000 + 800
- Add the thousands. The thousands add first.3,000 + 2,000 = 5,000
- Add the rest. Add the smaller parts.400 + 800 = 1200
- Put the parts together. Add the two totals.5,000 + 1200 = 6,200
- Write the answer. 6,200
Check. 6,200 - 2,800 = 3,400. ✓
Method. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 56,000 is 56,000 and 0; 7,000 is 7,000 and 0.56,000 + 0 and 7,000 + 0
- Add the thousands. The thousands add first.56,000 + 7,000 = 63,000
- Add the rest. Add the smaller parts.0 + 0 = 0
- Put the parts together. Add the two totals.63,000 + 0 = 63,000
- Write the answer. 63,000
Check. 63,000 - 7,000 = 56,000. ✓
Method. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 1,200,000 is 1,200,000 and 0; 350,000 is 350,000 and 0.1,200,000 + 0 and 350,000 + 0
- Add the thousands. The thousands add first.1,200,000 + 350,000 = 1,550,000
- Add the rest. Add the smaller parts.0 + 0 = 0
- Put the parts together. Add the two totals.1,550,000 + 0 = 1,550,000
- Write the answer. 1,550,000
Check. 1,550,000 - 350,000 = 1,200,000. ✓
Method. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 45,000 is 45,000 and 0; 8,900 is 8,000 and 900.45,000 + 0 and 8,000 + 900
- Add the thousands. The thousands add first.45,000 + 8,000 = 53,000
- Add the rest. Add the smaller parts.0 + 900 = 900
- Put the parts together. Add the two totals.53,000 + 900 = 53,900
- Write the answer. 53,900
Check. 53,900 - 8,900 = 45,000. ✓
Method. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 6,700 is 6,000 and 700; 1,500 is 1,000 and 500.6,000 + 700 and 1,000 + 500
- Add the thousands. The thousands add first.6,000 + 1,000 = 7,000
- Add the rest. Add the smaller parts.700 + 500 = 1200
- Put the parts together. Add the two totals.7,000 + 1200 = 8,200
- Write the answer. 8,200
Check. 8,200 - 1,500 = 6,700. ✓
Method. Split into thousands and the rest, then add.
- Split each number into thousands and the rest. 23,000 is 23,000 and 0; 9,900 is 9,000 and 900.23,000 + 0 and 9,000 + 900
- Add the thousands. The thousands add first.23,000 + 9,000 = 32,000
- Add the rest. Add the smaller parts.0 + 900 = 900
- Put the parts together. Add the two totals.32,000 + 900 = 32,900
- Write the answer. 32,900
Check. 32,900 - 9,900 = 23,000. ✓
Method. Round the number taken away, subtract, then correct.
- Round the number taken away to the nearest thousand. 4,300 is close to 4,000.4,300 ≈ 4,000
- Subtract the rounded number. This is easier to work out.9,000 - 4,000 = 5,000
- Correct the answer. 4,000 is 300 less than 4,300, so take 300 away.5,000 - 300 = 4,700
- Write the answer. 4,700
Check. 4,700 + 4,300 = 9,000. ✓
Method. Round the number taken away, subtract, then correct.
- Round the number taken away to the nearest thousand. 9,500 is close to 10,000.9,500 ≈ 10,000
- Subtract the rounded number. This is easier to work out.72,000 - 10,000 = 62,000
- Correct the answer. 10,000 is 500 more than 9,500, so add 500 back.62,000 + 500 = 62,500
- Write the answer. 62,500
Check. 62,500 + 9,500 = 72,000. ✓
Method. Round the number taken away, subtract, then correct.
- Round the number taken away to the nearest thousand. 85,000 is close to 85,000.85,000 ≈ 85,000
- Subtract the rounded number. This is easier to work out.640,000 - 85,000 = 555,000
- Correct the answer. 85,000 is 0 more than 85,000, so add 0 back.555,000 + 0 = 555,000
- Write the answer. 555,000
Check. 555,000 + 85,000 = 640,000. ✓
Method. Round the number taken away, subtract, then correct.
- Round the number taken away to the nearest thousand. 1,250,000 is close to 1,250,000.1,250,000 ≈ 1,250,000
- Subtract the rounded number. This is easier to work out.3,000,000 - 1,250,000 = 1,750,000
- Correct the answer. 1,250,000 is 0 more than 1,250,000, so add 0 back.1,750,000 + 0 = 1,750,000
- Write the answer. 1,750,000
Check. 1,750,000 + 1,250,000 = 3,000,000. ✓
Method. Round the number taken away, subtract, then correct.
- Round the number taken away to the nearest thousand. 2,600 is close to 3,000.2,600 ≈ 3,000
- Subtract the rounded number. This is easier to work out.8,100 - 3,000 = 5,100
- Correct the answer. 3,000 is 400 more than 2,600, so add 400 back.5,100 + 400 = 5,500
- Write the answer. 5,500
Check. 5,500 + 2,600 = 8,100. ✓
Method. Add the two amounts.
- Split each number into thousands and the rest. 12,500 is 12,000 and 500; 8,700 is 8,000 and 700.12,000 + 500 and 8,000 + 700
- Add the thousands. The thousands add first.12,000 + 8,000 = 20,000
- Add the rest. Add the smaller parts.500 + 700 = 1200
- Put the parts together. Add the two totals.20,000 + 1200 = 21,200
- Write the answer. £21,200
Check. About £13,000 + £9,000 = £22,000; £21,200 is close. ✓
Method. Add the two distances.
- Add the thousands. 6,000 + 3,000 = 9,000.9,000
- Add the rest. 450 + 800 = 1,250.1,250
- Put together. 9,000 + 1,250 = 10,250.10,250
- Write the answer. 10,250 km
Check. 10,250 - 3,800 = 6,450. ✓
Method. Round 1,850 to 2,000, subtract, then correct.
- Round. 1,850 is about 2,000.2,000
- Subtract. 5,000 - 2,000 = 3,000.3,000
- Correct. 2,000 is 150 more than 1,850, so add 150.3,150
- Write the answer. 3,150
Check. 3,150 + 1,850 = 5,000. ✓
Method. Round 375,000 to 400,000, then correct by 25,000.
- Round. 375,000 is about 400,000.400,000
- Subtract. 1,000,000 - 400,000 = 600,000.600,000
- Correct. 400,000 is 25,000 more, so add 25,000.625,000
- Write the answer. 625,000
Check. 625,000 + 375,000 = 1,000,000. ✓
Method. Check the subtraction by adding back.
- Add. 7,000 + 6,000 = 13,000.13,000
- Check. 13,000 - 6,000 = 7,000, the same as the start.7,000
- Write the answer. Yes, because subtracting 6,000 undoes adding 6,000, so the answer goes back to 7,000.
Check. The check works. ✓
Method. Use the number just below 50,000.
- Add 50,000 and 49,999. That is 50,000 + 50,000 - 1.100,000 - 1
- Write the answer. 100,000 - 1 = 99,999.99,999
- Write the answer. 99,999
Check. 99,999 is one less than 100,000. ✓
Method. Count on from 1,999,998 to 2,000,000.
- Count on. From 1,999,998 to 2,000,000 is 2 steps.2 steps
- Write the answer. 2
Check. 1,999,998 + 2 = 2,000,000. ✓