Question

Simplify the expression. $$ \frac{48 a-56 b}{16} $$

Short answer

The simplified expression is \(3a - 7b\).

Step-by-step solution

Factorize the numerator and denominator

Factorize 48a and 56b separately. The factor for 48 can be written as 16 * 3 and for 56 it can be written as 16 * 7. Hence 48a-56b can be written as \(16 * 3a - 16 * 7b\). The denominator 16 is already factorized.

Factorize the entire fraction

Rewrite the expression, and then factor 16 out of the entire fraction. Since both terms in the numerator are being divided by 16, we get \(\frac{16 * 3a - 16 * 7b}{16} = 16 * \left(\frac{3a - 7b}{16}\right)\).

Simplify the expression

The factor of 16 in the numerator and denominator cancel out. What we are left with is \(3a - 7b\).