The Distributive Property of Multiplication
Concept
Multiplication is adding a number (the multiplicand) to itself a specified number of times. Instead of adding, multi-digit multiplication can be found by expanding the numbers and using the distributive property. The distributive property can be used to multiply a sum/difference by multiplying each addend/subtrahend separately and then adding the products.
Rules
1. Expand the multi-digit number.
2. Multiply
a (b + c + d) = ab + ac + ad
3. Add the products.
Example
Use the distributive property to multiply.
6 x 34
Solution
Use the distributive property to multiply.
6 × 34 = 6 × (30 + 4) Multiplying can be seen as 6 sets of 34
6 × 30 = 180 which can be broken down into 6 sets of 30 = 180
+6 × 4 = 24 plus 6 sets of 4 = 24
6 × 34 = 180 + 24
6 × 34 = 204
Practice Distributive Property
Practice Problem 1
Use the distributive property to multiply.
5 x 29 = 5 x (30 – 1)
Practice Problem 2
Use the distributive property to multiply.
9 x 33
Hint: 9 x (30 + 3)
Practice Problem 3
Use the distributive property to multiply.
8 x 88
Practice Problem 4
Use the distributive property to multiply.
9 x 62
Practice Problem 5
Maria is shopping for fruit. She wants to buy 6 bananas for $4.15 each and 6 apples for $0.35 each.
Write an expression using the distributive property to represent the total cost. Then simplify the expression.
Distributive Property – to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses.
Pre-requisite Skill
Multiplying Using Basic Facts and Patterns
Related Skill
The Distributive Property