Question

Rewrite an equivalent expression for the sum of 75+30
in 2 different ways using the distributive property and a common factor.

Answer 1

To use the distributive property and a common factor for the sum of \(75 + 30\), we can first identify a common factor. The common factor for both 75 and 30 is 15.

1. **Factoring out the common factor:**
\[
75 + 30 = 15 \times 5 + 15 \times 2 = 15(5 + 2)
\]

2. **Using the distributive property with a different grouping:**
\[
75 + 30 = 70 + 5 + 30 = 70 + (5 + 30) = 70 + 35 = 70 + 15 \times 2 = 15 \times 5 + 15 \times 2
\]

So, the two equivalent expressions using the distributive property and a common factor are:
1. \(15(5 + 2)\)
2. \(15(5) + 15(2)\)