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
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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