Skip to content
MathAnvil
§ Arithmetic

Addition

§ Arithmetic

Addition

CCSS.1.OACCSS.2.NBT3 min read

Addition combines two or more numbers to find their total sum. The process follows a systematic approach of aligning digits by place value and working from right to left, carrying over when column totals exceed 9. Addition forms the foundation for all arithmetic operations and appears throughout the UK National Curriculum from Reception through GCSE level.

§ 01

Why it matters

Addition underpins everyday financial calculations, from working out shopping totals to calculating change at the tuck shop. In Year 6 SATs, pupils encounter multi-step problems requiring addition of amounts like £47.50 + £23.75. Beyond primary school, addition becomes essential for algebraic manipulation in GCSE Mathematics, where students combine like terms such as 3x + 7x = 10x. Engineering applications rely on addition for measurements — architects add dimensions like 2.5m + 1.8m + 3.2m to calculate total room lengths. Statistics courses use addition to find means, where adding scores like 85 + 92 + 78 then dividing by 3 gives the average. Even computer programming uses addition algorithms, making this fundamental skill relevant across STEM subjects and daily life situations involving money, time, and measurement.

§ 02

How to solve addition

Addition — how to

  • Line up digits by place value (ones under ones, tens under tens).
  • Add each column starting from the right.
  • If a column sum is 10+, carry the tens digit to the next column.

Example: 27 + 38: 7+8=15, write 5 carry 1. 2+3+1=6. Answer: 65.

§ 03

Worked examples

Beginner§ 01

Mom gives you 3 coins. Dad gives you 4 coins. How many do you have?

Answer: 7

  1. Figure out what to add 3 + 4 You got 3 from Mom and 4 from Dad. Adding tells us the total.
  2. Add the numbers 3 + 4 = 7 Put them together: 3 and 4 makes 7.
  3. Say the answer 7 You have 7 coins altogether.
Easy§ 02

A pencil costs £14.00 and an eraser costs £12.00. How much for both?

Answer: 26

  1. Find the two prices £14.00 + £12.00 The pencil is £14.00 and the eraser is £12.00. To find the total cost, we add them.
  2. Add the prices 14 + 12 = 26 Adding 14 and 12 gives 26.
  3. Write the answer with the unit £26.00 Both items together cost £26.00.
Medium§ 03

_______ + 51 = 78

Answer: 27

  1. Read the problem ? + 51 = 78 We know one number (51) and the total (78). We need the missing one.
  2. Use subtraction to find the missing number 78 - 51 = 27 Since addition and subtraction are opposites, take the total and subtract 51.
  3. Check our answer 27 + 51 = 78 ✓ Put 27 back in: 27 + 51 = 78. Correct!
§ 04

Common mistakes

  • Misaligning digits leads to errors like adding 24 + 17 as 2+1=3 and 4+7=11, giving 311 instead of 41
  • Forgetting to carry results in mistakes such as 58 + 37 = 85 instead of 95, missing the carried 1 from 8+7=15
  • Adding incorrectly from left to right produces errors like 146 + 28 = 166 instead of 174, ignoring place value rules
§ 05

Frequently asked questions

What is the difference between addition and subtraction?
Addition combines numbers to find a total, whilst subtraction removes one number from another to find the difference. They are inverse operations — if 15 + 8 = 23, then 23 - 8 = 15. Both follow place value alignment rules but work in opposite directions.
How do you check if an addition answer is correct?
Reverse the calculation using subtraction. For 47 + 29 = 76, check by calculating 76 - 29 = 47 or 76 - 47 = 29. Alternatively, add the numbers in reverse order — since addition is commutative, 29 + 47 should also equal 76.
When should children learn carrying in addition?
The National Curriculum introduces carrying in Year 2, typically after mastering single-digit addition and two-digit addition without regrouping. Children usually learn this concept around age 6-7, progressing from concrete manipulatives to formal column methods over several months of practice.
What does 'sum' mean in addition?
The sum is the final answer when adding numbers together. In the calculation 12 + 15 = 27, the number 27 is the sum. This term distinguishes the result from the addends (12 and 15), which are the numbers being combined.
How is mental addition different from written methods?
Mental addition uses strategies like rounding, partitioning, or counting on, whilst written methods follow formal algorithms with place value columns. For 47 + 35, mental methods might calculate 47 + 30 + 5 = 82, whereas column addition aligns digits vertically and carries systematically.
§ 06

See also

§ 06

Where to next?

Share this article