Multiplication & Division Methods for SATs

Multiplication and division make up a huge chunk of the arithmetic paper. Your child needs reliable written methods they can use quickly and accurately under timed conditions. Here are the methods the SATs expect, plus the number properties that come up on reasoning papers.

Short Multiplication

Used when multiplying by a single digit. Line up the numbers, multiply each digit from right to left, and carry as needed.

346

× 7

------

2422

(6×7=42, write 2 carry 4; 4×7=28+4=32, write 2 carry 3; 3×7=21+3=24)

Long Multiplication

Used when multiplying by a two-digit number. Multiply by the ones digit first, then by the tens digit (remembering the placeholder zero), then add.

243

× 36

-------

1458 (243 × 6)

7290 (243 × 30)

-------

8748

The most common error is forgetting the placeholder zero on the second line. Drilling this method until it’s automatic is well worth the time.

Short Division (Bus Stop Method)

Dividing by a single digit. Work from left to right, dividing each digit and carrying remainders.

432 ÷ 5

4 ÷ 5 = 0 remainder 4 → carry 4 to make 43

43 ÷ 5 = 8 remainder 3 → carry 3 to make 32

32 ÷ 5 = 6 remainder 2

Answer: 86 remainder 2 (or 86.4)

Long Division

Used when dividing by a two-digit number. The method is the same as short division, but you need to estimate how many times the divisor goes into each chunk.

756 ÷ 18

18 into 75 = 4 (4 × 18 = 72), remainder 3

Bring down 6 → 36

18 into 36 = 2 (2 × 18 = 36), remainder 0

Answer: 42

For more detail, see our long division step-by-step guide.

Factors, Multiples, Primes, Squares & Cubes

These crop up on the reasoning papers. Make sure your child knows:

Factors — numbers that divide exactly into another. Factors of 12: 1, 2, 3, 4, 6, 12.
Multiples — the times table results. Multiples of 6: 6, 12, 18, 24…
Prime numbers — only divisible by 1 and themselves. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29… (note: 1 is NOT prime).
Square numbers — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Cube numbers — 1, 8, 27, 64, 125.

SATs-Style Example Question

“A school orders 1,248 exercise books. They come in packs of 24. How many packs does the school need?”

1248 ÷ 24

24 into 124 = 5 (5 × 24 = 120), remainder 4

Bring down 8 → 48

24 into 48 = 2

Answer: 52 packs

Common Mistakes to Watch For

Forgetting the placeholder zero in long multiplication — the second partial product must start one column to the left.
Carrying errors — writing the carried digit in the wrong column or forgetting to add it.
Thinking 1 is prime — it isn’t. This comes up almost every year.
Confusing factors and multiples — factors are smaller (or equal), multiples are bigger (or equal).

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