---
title: Primary - Mathematics Appendix 1
subjects:
    - Mathematics
year_levels:
    - Stage 1
    - Stage 2
official_source_url: https://www.gov.uk/government/publications/national-curriculum-in-england-primary-curriculum
official_published_at: 11 September 2013
official_updated_at: 6 May 2015
---

# Mathematics Appendix 1 {#mathematics-appendix-1}

## Examples of formal written methods for addition, subtraction, multiplication and division {#examples-of-formal-written-methods-for-addition-subtraction-multiplication-and-division}

This appendix sets out some examples of formal written methods for all four operations to illustrate the range of methods that could be taught. It is not intended to be an exhaustive list, nor is it intended to show progression in formal written methods. For example, the exact position of intermediate calculations (superscript and subscript digits) will vary depending on the method and format used.

For multiplication, some pupils may include an addition symbol when adding partial products. For division, some pupils may include a subtraction symbol when subtracting multiples of the divisor.

##### Addition and subtraction {#addition-and-subtraction}

Four examples of addition and subtractions calculations are shown. The first is column addition with two three-digit numbers and the next three examples are column subtraction with two three-digit numbers. The last two subtraction examples use the same numbers but show two different methods for column subtraction.

789 + 642 becomes
```lua
   789
 + 642
 ----
  1431
```
Answer: 1431

---

874 − 523 becomes
```
   874
 - 523
 ----
   351
```
Answer: 351

---

932 − 457 becomes
```
   932
 - 457
 ----
   475
```
Answer: 475

---
932 − 457 becomes
```
   932
 - 457
 ----
   475
```
Answer: 475

---

##### Short multiplication {#short-multiplication}

Three examples of short multiplication are shown, with inceasingly large numbers.

24 × 6 becomes
```
   24
 ×  6
 ----
  144
```
Answer: 144

---

342 × 7 becomes
```
   342
 ×   7
 ----
  2394
```
Answer: 2394

---

2741 × 6 becomes
```
   2741
 ×    6
 ----
  16446
```
Answer: 16 446

##### Long multiplication {#long-multiplication}

Three examples of long multiplication are shown, with the examples using the same numbers to illustrate two different ways of setting out the calculation.


24 × 16 becomes
```
    24
×   16
------
   240
   144
------
   384
```
Answer: 384

---

124 × 26 becomes
```
     124
×     26
---------
    2480
     744
---------
    3224
```
Answer: 3224

---

124 × 26 becomes (alternative working shown)
```
     124
×     26
---------
     744
    2480
---------
    3224
```
Answer: 3224


##### Short division {#short-division}

Three examples of short division are shown, with different figures in each example.


98 ÷ 7 becomes
```
  14
7 ⟌ 98
```
Answer: 14

---

432 ÷ 5 becomes
```
   86 r2
5 ⟌ 432
```
Answer: 86 remainder 2

---

496 ÷ 11 becomes

```
   45 r1
11 ⟌ 496
```
This can also be written as a mixed number.

Answer: 45 1/11

##### Long division {#long-division}

Three examples of long division are shown, using the same numbers in each example. Each example shows both a different way of setting out the calculation and a different way of setting out the result (with remainder, as a mixed number and as a decimal).

432 ÷ 15 becomes
```
     28 r12
15 ⟌ 432
     300
     ----
      132
      120
      ----
       12
```
Answer: 28 remainder 12

---

432 ÷ 15 becomes (remainder written as a fraction)
```
     28
15 ⟌ 432
     300   (15 × 20)
     ----
      132
      120   (15 × 8)
      ----
       12
```
Remainder as a fraction:

```
12/15 = 4/5
```

Answer: 28 4/5

---

432 ÷ 15 becomes (decimal form)
```
     28.8
15 ⟌ 432.0
     300
     ----
      132
      120
      ----
       120
       120
       ----
         0
```
Answer: 28.8