Mathematics Appendix 1
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
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
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
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
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
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
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