➕ Addition & Subtraction

Grade 5 · Number · Cambridge Primary Stage 5

Column Addition

Adding up to 6-digit numbers with carrying

Column Subtraction

Subtracting with borrowing/regrouping

Mental Strategies

Rounding, near doubles, bridging

Checking Answers

Using inverse operations

Word Problems

Multi-step problems and estimation

1. Column Addition (with Carrying)

To add large numbers, line them up by place value and add each column from right to left (ones first).

If a column adds up to 10 or more → write the units digit and carry 1 to the next column on the left.
Example: 47,382 + 25,619
Ones: 2 + 9 = 11 → write 1, carry 1
Tens: 8 + 1 + 1(carried) = 10 → write 0, carry 1
Hundreds: 3 + 6 + 1(carried) = 10 → write 0, carry 1
Thousands: 7 + 5 + 1(carried) = 13 → write 3, carry 1
Ten-thousands: 4 + 2 + 1(carried) = 7 → write 7
Answer: 73,001
💡 Always write carries in small digits above the next column. Never forget them!

2. Column Subtraction (Borrowing)

To subtract, line up the digits by place value and subtract each column from right to left. If the top digit is smaller, you must borrow from the next column.

Borrowing: take 1 from the next column to the left. That column loses 1, but your current column gains 10.
Example: 80,000 − 34,785
You need to borrow all the way from the 8 (ten-thousands). This is called a chain of borrowing.
Work carefully from right to left, borrowing as needed.
Answer: 45,215
💡 Check your subtraction by adding: 45,215 + 34,785 = 80,000 ✓

3. Mental Strategies

Sometimes it is faster to use a mental method than to write it out.

Round & Adjust: add or subtract a round number, then adjust.
Near multiples of 10/100:
47 + 99 = 47 + 100 − 1 = 146
263 + 198 = 263 + 200 − 2 = 461

Near doubles:
34 + 36 = double 35 = 70
48 + 46 = double 47 = 94

Bridging through 10 or 100:
76 + 28: 76 + 24 = 100, then + 4 = 104
💡 Choose the method that makes the calculation easiest. You don't always need to write it out!

4. Checking with Inverse Operations

Addition and subtraction are inverse operations — they undo each other. You can use this to check your work.

If A + B = C, then C − B = A and C − A = B
You calculated: 34,256 + 18,743 = 53,999
Check: 53,999 − 18,743 = 34,256 ✓

You calculated: 72,400 − 35,180 = 37,220
Check: 37,220 + 35,180 = 72,400 ✓
💡 Always estimate first, then calculate, then check with the inverse. Three steps to a reliable answer!

5. Estimation & Word Problems

Before you calculate exactly, estimate by rounding each number to the nearest 100 or 1,000. This tells you roughly what to expect.

Round each number first → add/subtract the rounded numbers → then do the exact calculation.
Example: 4,872 + 3,145
Estimate: 4,900 + 3,100 = 8,000
Exact: 4,872 + 3,145 = 8,017 (close to 8,000 ✓)

Word problem tip:
1. Read carefully — what are you asked to find?
2. Decide: do you need to add or subtract?
3. Write the calculation.
4. Solve, then check your answer makes sense.
💡 "How many more?" and "difference" usually mean subtract. "Total" and "altogether" usually mean add.

Example 1 — Column Addition with Carrying

Write the sum: 47,382 + 25,619
Line up by place value. Add ones: 2 + 9 = 11 → write 1, carry 1.
Tens: 8 + 1 + 1(carry) = 10 → write 0, carry 1. Hundreds: 3 + 6 + 1 = 10 → write 0, carry 1.
Thousands: 7 + 5 + 1 = 13 → write 3, carry 1. Ten-thousands: 4 + 2 + 1 = 7.
Answer: 73,001

Example 2 — Column Subtraction with Borrowing

Write the sum: 80,000 − 34,785
Ones: 0 − 5 — can't do it! Borrow from tens. But tens is 0 too, keep borrowing all the way to the 8.
After borrowing chain: ones column becomes 10 − 5 = 5. Tens: 9 − 8 = 1. Hundreds: 9 − 7 = 2. Thousands: 9 − 4 = 5. Ten-thousands: 7 − 3 = 4.
Answer: 45,215
Check: 45,215 + 34,785 = 80,000 ✓

Example 3 — Mental Strategy: Round & Adjust

Calculate 263 + 198 mentally.
198 is close to 200. So add 200 instead: 263 + 200 = 463.
But we added 2 too many, so subtract 2: 463 − 2 = 461.
Answer: 461

Example 4 — Word Problem with Estimation

A school library has 34,256 books. They buy 8,975 more. How many books in total?
Estimate: 34,000 + 9,000 = 43,000
Exact: 34,256 + 8,975 = 43,231
Answer: 43,231 books (close to estimate ✓)

🔬 Visualizer 1 — Column Addition Animator

Enter two numbers and see the column addition worked out step by step.

🔬 Visualizer 2 — Estimation Checker

Enter two numbers. See their rounded values and compare the estimate to the exact answer.

Exercise 1 — Column Addition

1. 23,415 + 14,382 = ?

2. 45,267 + 31,524 = ?

3. 38,456 + 47,382 = ?

4. 123,456 + 234,321 = ?

5. 47,382 + 25,619 = ?

6. 56,748 + 38,593 = ?

7. 349,276 + 185,447 = ?

8. 476,835 + 278,496 = ?

9. 273,648 + 364,897 = ?

10. 528,374 + 394,857 = ?

Exercise 2 — Column Subtraction (with Borrowing)

1. 7,500 − 3,248 = ?

2. 50,000 − 17,436 = ?

3. 80,000 − 34,785 = ?

4. 63,400 − 28,756 = ?

5. 100,000 − 46,382 = ?

6. 500,000 − 183,746 = ?

7. 724,000 − 385,647 = ?

8. 400,050 − 167,384 = ?

9. 300,100 − 145,673 = ?

10. 900,000 − 467,382 = ?

Exercise 3 — Mental Strategies

1. 47 + 99 = ? (add 100, subtract 1)

2. 263 + 198 = ? (add 200, subtract 2)

3. 345 + 299 = ? (add 300, subtract 1)

4. 76 + 28 = ? (bridge through 100)

5. 34 + 36 = ? (near double: double 35)

6. 48 + 46 = ? (near double: double 47)

7. 504 − 99 = ? (subtract 100, add 1)

8. 752 − 198 = ? (subtract 200, add 2)

9. 1,000 − 1 = ? (quick mental)

10. 2,500 + 1,999 = ? (add 2,000, subtract 1)

Exercise 4 — Estimation (Round to Nearest 100, then Add)

Round each number to the nearest 100, then add the rounded numbers. Enter the estimated total.

1. Estimate 4,872 + 3,145 (round to nearest 100)

2. Estimate 7,356 + 2,248 (round to nearest 100)

3. Estimate 12,463 + 8,724 (round to nearest 100)

4. Estimate 35,182 + 14,850 (round to nearest 100)

5. Estimate 6,345 − 2,178 (round to nearest 100)

6. Estimate 48,632 + 23,489 (round to nearest 100)

7. Estimate 71,846 − 29,373 (round to nearest 100)

8. Estimate 3,456 + 6,892 (round to nearest 100)

9. Estimate 22,748 + 37,162 (round to nearest 100)

10. Estimate 94,327 − 48,651 (round to nearest 100)

Exercise 5 — Word Problems

1. A shop sold 12,350 items in January and 15,480 in February. How many items in total?

2. A stadium holds 45,000 people. 27,348 are seated. How many empty seats?

3. A school raised £3,456 in term 1 and £2,875 in term 2. Total raised?

4. A train travels 324 km on Monday and 487 km on Tuesday. Total km?

5. Sarah has £100. She spends £37.45. How much does she have left? (Enter in pence: answer × 100)

6. A factory made 246,000 cars. 87,354 were sold. How many remain?

7. Town A has 34,782 people. Town B has 28,456 people. How many more in Town A?

8. A swimmer swims 1,250 m on day 1, 1,380 m on day 2, and 1,175 m on day 3. Total metres?

9. 500,000 people visited a park this year. Last year 374,285 visited. How many more this year?

10. A book has 348 pages. Mia has read 127 pages. How many pages left?

🏋️ Practice — 20 Questions

1. 34,256 + 18,743 = ?

2. 72,400 − 35,180 = ?

3. 245,378 + 164,822 = ?

4. 60,000 − 27,543 = ?

5. 57 + 99 = ?

6. 448 + 198 = ?

7. Estimate 5,384 + 2,716 (round to nearest 100)

8. 400,000 − 258,347 = ?

9. 63 + 58 = ?

10. A town has 85,000 residents. 36,742 are adults. How many are not adults?

11. 138,475 + 296,348 = ?

12. 700,000 − 384,952 = ?

13. 82 + 78 = ? (near double)

14. Estimate 24,356 + 35,847 (round to nearest 100)

15. 604 − 198 = ?

16. A school library had 47,320 books. They donated 8,475 and bought 12,300 new ones. How many now?

17. 573,846 + 284,957 = ?

18. 1,000,000 − 437,856 = ?

19. 3,750 + 2,999 = ? (add 3,000, subtract 1)

20. If 34,856 + 27,144 = 82,000 ... wait, is this true? Enter 1 for yes, 0 for no. (34,856 + 27,144 = 62,000?)

🏆 Challenge — 8 Questions

1. Find the missing digit: 4□,387 + 23,614 = 72,001. What is □?

2. The sum of two numbers is 150,000. One number is 87,346. What is the other?

3. A number subtracted from 200,000 gives 83,754. What is the number?

4. Three towns have populations 34,256; 47,839; and 28,075. What is the total population?

5. A journey is 500 km total. Sam drives 187 km, then 234 km. How far is left?

6. What must be added to 364,875 to make 500,000?

7. The difference between two numbers is 37,482. The larger number is 100,000. What is the smaller?

8. A factory produces 8,500 items per day. In 5 days they made 42,500. They sold 27,648. How many remain?