Question

Describe how you can use number relationships to tell whether the equation from question 3 (also below) is true or false without having to find the answer on both sides.

67 × 18 = (67 × 20) − (67 × 2)

Answer 1

The equation 67 × 18 = (67 × 20) − (67 × 2) is true because it correctly applies the distributive property of multiplication over subtraction, confirming that the original equation and the expanded form are equivalent.

Step-by-step explanation:

To determine whether the equation 67 × 18 = (67 × 20) − (67 × 2) is true, you can use the distributive property of multiplication over subtraction. This property implies that multiplying the same number to a difference gives the same result as if you multiplied the number by each of the terms individually and then found the difference of the products. Therefore, according to the distributive property:

67 × (20 - 2) = (67 × 20) - (67 × 2)

So we simplify the term inside the parentheses:

67 × 18 = (67 × 20) - (67 × 2)

Since the equation represents the distributive property accurately, the equation given is true.