Distributive Property Chapter Notes | Mathematics for Grade 6 PDF Download

Introduction

The distributive property is a math rule that helps you multiply a number by a sum or difference inside parentheses. Instead of solving inside the parentheses first, you multiply the number outside by each term inside and then add or subtract the results. It works for numbers, variables, and even large numbers, making calculations easier. This guide explains the distributive property with clear examples to show how it simplifies multiplication in different situations.

What is the distributive property?

• Let's say you want to find 5(6 + 8). You could use the order of operations to solve by adding the numbers in parentheses first.
  • 5(6 + 8)
  • 5(14)
  • 70
• Or you could use the distributive property. Multiply the number outside of the parentheses by each number inside of the parentheses. Then add those products. 
  Look at the steps below:
  • 5(6 + 8)
  • 5(6) + 5(8)
  • 30 + 40
  • 70
  • So, 5(6 + 8) = 70!
• The distributive property works with subtraction in the parentheses, too.
  • 8(10 – 4)
  • 8(10) – 8(4)
  • 80 – 32
  • 48
• Check your work with the order of operations:
  • 8(10 – 4)
  • 8(6)
  • 48
  • So, 8(10 – 4) = 48!

The distributive property with variables

• The distributive property is useful when simplifying expressions with variables. When using variables, you may not be able to do the operation inside the parentheses first.
• For Example: 8(y + 4z)
  The y and 4z cannot be combined. They are not like terms.
  8(y) + 8(4z)
  8y + 32z
  Remember to multiply, or distribute, the 8 to each term inside the parentheses.
  So, 8(y + 4z) = 8y + 32z!

Using the distributive property to multiply large numbers

• You can use the distributive property to help multiply large numbers.
• For Example: Let's try it with 6×57. First, split 57 up into smaller pieces.
  6 × 57
  6 × (50 + 7)
  Then use the distributive property to solve!
  6(50 + 7)
  6(50) + 6(7)
  300 + 42
  342
  You can use area models to see why this works. The model below shows 6 × 57.
  You can also show 6 × 57 as 6 × (50 + 7).
  Multiply the 6 by 50 and by 7.
  Then add to find the total area.
  300 + 42 = 342
  So, 6 × 57 = 342!