Expand 7/10(5d+6)

Question

A. 5d+21/5
B. 35d+6
C. 7/2 d+21/5
D. 35d+42

Answer 1

To expand the algebraic expression \( \frac{7}{10}(5d+6) \), we need to distribute the \( \frac{7}{10} \) to both terms inside the parentheses:

\[ \frac{7}{10} \times 5d + \frac{7}{10} \times 6 \]

First, multiply the coefficient \( \frac{7}{10} \) by \( 5d \):

\[ \frac{7}{10} \times 5d = \frac{7 \times 5}{10} d = \frac{35}{10} d \]

Now, simplify the fraction \( \frac{35}{10} \):

\[ \frac{35}{10} d = \frac{35 \div 5}{10 \div 5} d = \frac{7}{2} d \]

Next, multiply \( \frac{7}{10} \) by \( 6 \):

\[ \frac{7}{10} \times 6 = \frac{7 \times 6}{10} = \frac{42}{10} \]

Simplify the fraction \( \frac{42}{10} \):

\[ \frac{42}{10} = \frac{42 \div 2}{10 \div 2} = \frac{21}{5} \]

Therefore, the expanded expression is:

\[ \frac{7}{2} d + \frac{21}{5} \]

So the correct answer is:

C. \( \frac{7}{2} d + \frac{21}{5} \)