Question

you are considering two potential renovations to your house to determine if you can afford both. the first renovation will consume \\(\frac{3}{8}\\) of your budget, and the other will consume \\(\frac{2}{3}\\) of it.

evaluate the following expression to determine how much of your budget will both project consume:

\\\frac{3}{8} + \frac{2}{3}\\

a.) \\(\frac{3}{4}\\)

b.) \\(1\frac{1}{24}\\)

Explanation:

Find a common denominator

The denominators are 8 and 3. The least common multiple of 8 and 3 is 24.

Convert the fractions

$$ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} $$

$$ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} $$

Add the fractions and convert to a mixed number

$$ \frac{9}{24} + \frac{16}{24} = \frac{25}{24} = 1\frac{1}{24} $$

Answer:

• a.) \(\frac{3}{4}\)
• b.) \(1\frac{1}{24}\) (Correct answer)