Distributive Property
The distributive property means multiplying the number outside the brackets by each term inside, so a × (b + c) = a × b + a × c and a × (b − c) = a × b − a × c. It works both ways to expand brackets or factorise.
Video Lesson
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Flashcards
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What is the Distributive Property?
- The distributive property means multiplying a number across brackets.
- It is written as .
Applying the Distributive Property
- Multiply the number outside the brackets by each term inside.
- This can be used to expand brackets or simplify calculations.
Distributive Property with More Than Two Terms
- The distributive property also works with more than two terms.
- For example, .
Should I Use the Distributive Property with Division?
- Do not use the distributive property when dividing.
- When there is division, it is usually better to calculate inside the brackets first.
Practice Questions
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4 × (25 + 6)
Correct! 🎉 +10 pointsNot quite right
Calculate inside the brackets first: . Then multiply: .
8 × (50 + 2)
Correct! 🎉 +10 pointsNot quite right
Apply order of operations: , then .
7 × (80 − 3)
Correct! 🎉 +20 pointsNot quite right
Subtract first: . Then multiply: .
8 × (70 − 5)
Correct! 🎉 +20 pointsNot quite right
Use brackets first: . Then multiply: .
8 × 51
Correct! 🎉 +20 pointsNot quite right
Straight multiplication: .
12 × 102
Correct! 🎉 +30 pointsNot quite right
Break it down: and . Add them: .
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Interactive Activity
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Students Also Ask
The questions students bump into most on this topic
Yes. The distributive law works with subtraction in the same way as addition. When you multiply a number by a difference in brackets, multiply the outside number by each part. Then subtract the results instead of adding them. The method does not change.
Generally no. The distributive law is mainly a property of multiplication, so avoid using it with division. It only works when the brackets sit on the left, such as (19 + 2) ÷ 3. Even then it rarely helps, so simply work out 21 ÷ 3 = 7.
It works because regrouping never changes a total. Picture 3 rows with 4 green and 2 yellow balls in each. You can count them as 3 × (4 + 2), or add (3 × 4) and (3 × 2). Both routes reach the same total, so the two methods always agree.
You use the distributive law to simplify calculations and make mental maths quicker. By breaking a tricky number into easier parts, you can multiply step by step in your head. It also works in two directions, letting you expand brackets or factorise by taking out a common number.
Break the large number into parts that are easy to multiply, then share the multiplication across all of them. To work out 5 × 221, split 221 into 200 + 20 + 1. This gives (5 × 200) + (5 × 20) + (5 × 1), which adds up to 1105.