Math can be full of interesting properties and rules that make solving problems easier. One such rule is the distributive law, which helps us simplify expressions and make calculations simpler. Let's dive into the world of distributive law!
A × ( B + C) = A × B + A × C
Let's solve the expression 5×(2 + 3) using the distributive property of multiplication over addition.
5 × (2 + 3) = 5 × 2 + 5 × 3
5 × (2 + 3) = 10 + 15 = 25
Using the distributive property, we first multiply every addend by 5. This is known as distributing the number 5 among the two addends and then we can add the products. This means that the multiplication of 5 × 2 and 5 × 3 will be performed before the addition. This leads to 5 × 2 + 5 × 3 = 25
A × (B − C) = A × B − A × C
Let's solve the expression 2 × (4 − 1) using the distributive law of multiplication over subtraction.
2 × (4 − 1) = (2 × 4) − (2 × 1)
2 × (4 − 1) = 8 − 2 = 6
Example: You have 5 boxes of toys, and each box contains 2 bats and 3 balls. We can use the distributive law to find out how many bats and balls you have in total.
5 × (2 bats + 3 balls)
Applying the distributive law, we can multiply 5 by each term inside the parentheses:
= (5 × 2 bats) + (5 × 3 balls)
= 10 bats + 15 balls = 25 toys in total
We can divide larger numbers using the distributive property by breaking those numbers into smaller factors.
Let us understand this using an example, Divide 108 by 12
108 can also be expressed as 96 + 12, therefore, 108 ÷ 12 can also be written as (96 + 12) ÷ 12
Now distributing division operation for each factor in the bracket we get:
(96 ÷ 12) + (12 ÷ 12)
⇒ 8 + 1 = 9
