Parent guide · 5 min read
The distributive property for kids: multiplying across a bracket
The distributive property is the rule that lets a child multiply a number by a bracket: 3 × (x + 5) becomes 3x + 15. It shows up first with plain numbers, as a mental maths trick, and then reappears in algebra, where it is used constantly. Children who learned it as a memorised rule tend to drop half of it, writing 3x + 5, while children who saw why it works rarely do.
Try this tonight
4 things you can do at home
Start with numbers, using a mental maths problem
Ask "what is 6 × 14?" and let your child split 14 into 10 + 4: 6 × 10 = 60, 6 × 4 = 24, and 60 + 24 = 84. This is the distributive property in disguise, and it shows the rule as something they already do.
Draw the rectangle
Draw a rectangle 6 tall and 14 wide, then a line splitting the width into 10 and 4. The whole area is the two smaller areas added together. This picture works for letters too: a rectangle 3 tall and (x + 5) wide has area 3x + 15.
Draw an arrow to every term inside the bracket
When working with 3(x + 5), draw one arrow from the 3 to the x and a second arrow from the 3 to the 5. It is a small habit, but it stops the "forgot the second term" mistake before it starts.
Check with a number
Pick x = 2. Then 3(x + 5) = 3 × 7 = 21, and 3x + 15 = 6 + 15 = 21. Both match. Try the same check on the wrong answer 3x + 5: 6 + 5 = 11, which does not match, so it is wrong.
What the rule says, in plain terms
A bracket is a package of terms that will be dealt with together. Multiplying the package by a number means multiplying every item in it. Writing this as a rule: a(b + c) = ab + ac.
It also works for subtraction: a(b − c) = ab − ac. The rule is the same, and the sign of each term stays with it.
A worked example: 4(2x − 3)
Multiply the 4 by the first term: 4 × 2x = 8x. Multiply the 4 by the second term: 4 × (−3) = −12. Put the results together: 4(2x − 3) = 8x − 12.
Check with x = 5: 4(2 × 5 − 3) = 4 × 7 = 28, and 8 × 5 − 12 = 40 − 12 = 28. They match, so the expansion is correct.
The traps: the forgotten term, and the negative outside
The forgotten term: 3(x + 5) written as 3x + 5. The 3 was applied only to the x. Testing with x = 2 shows it fails: 3(2 + 5) = 21 but 3 × 2 + 5 = 11.
The negative outside: −2(x − 4) means multiplying both terms by −2, giving −2x + 8. Many children get −2x − 8, because they write the minus sign from the bracket without noticing that −2 × −4 is positive. Slow down on the second term and say the signs out loud.
Signs it’s time for outside help
When home help has done what it can
- Writes 3x + 5 for 3(x + 5), multiplying only the first term.
- Gets the sign wrong when the number outside the bracket is negative.
- Cannot explain why 6 × 14 can be worked out as 60 + 24.
- Can do the rule with numbers but freezes when letters appear.
- Guesses whether to add or multiply when a bracket appears in a problem.
Questions parents ask
FAQ
What age do children usually learn the distributive property?
The number version appears around ages 8–10 (US Grade 3, when multiplication is taught), and the algebra version around ages 11–13 (US Grades 6–7, England Key Stage 3, Australian Years 7–8).
Is expanding brackets the same as the distributive property?
Yes. "Expanding brackets" is the usual name for applying the distributive property to an expression with letters in it.
Does it work with division too?
Yes, when dividing a bracket by a number: (12 + 8) ÷ 4 = 12 ÷ 4 + 8 ÷ 4 = 5. It does not work when the bracket is the divisor, so 12 ÷ (4 + 2) is not 12 ÷ 4 + 12 ÷ 2.
Why does my child get the right answer with numbers but not with letters?
Usually because letters feel abstract and the picture is lost. Going back to a rectangle with a number in place of the letter, then switching the number for the letter, tends to reconnect the two.
Further reading
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