Question

yani is making a cake. the recipe calls for \\(\frac{3}{4}\\) a cup of sugar total. \\(\frac{2}{3}\\) of the sugar goes into the frosting. how much sugar goes into the cake batter?

evaluate the expression:

\\\frac{3}{4} - \frac{2}{3}\\

• \\(\frac{1}{12}\\)
• \\(\frac{1}{4}\\)
• \\(\frac{1}{8}\\)
• \\(\frac{1}{7}\\)

Explanation:

Find a common denominator

$$ \text{LCD}(4, 3) = 12 $$

Convert fractions to equivalent fractions

$$ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $$

$$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $$

Subtract the numerators

$$ \frac{9}{12} - \frac{8}{12} = \frac{9 - 8}{12} = \frac{1}{12} $$

Answer:

• (A) \(\frac{1}{12}\) (Correct answer)
• (B) \(\frac{1}{4}\)
• (C) \(\frac{1}{8}\)
• (D) \(\frac{1}{7}\)