# Question #9ac69

Jan 2, 2018

#### Explanation:

$42 = 2 \cdot 3 \cdot 7$ and $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$

$G C F = 2 \cdot 3 = 6$

Note that $42 = 6 \times 7$ and $48 = 6 \times 8$, so

$42 + 48 = 6 \times 7 + 6 \times 8 = 6 \times \left(7 + 8\right) = 6 \times 15$

As long as we're here let's finish.

Method 1: (using the distributuve property)
$6 \times \left(15\right) = 6 \times \left(10 + 5\right) = 6 \times 10 + 6 \times 5 = 60 + 30 = 90$

Method 2: (using factoring and the associative property of multiplication)
$6 \times 15 = \left(3 \times 2\right) \times 15 = 3 \times \left(2 \times 15\right) = 3 \times 30 = 90$