 # One cake recipe calls for \frac{2}{3 cup of sugar. Another recipe calls for 1\frac{1}{4} cups of sugar. How many cups of sugar are needed to make both Cem Hayes 2021-06-14 Answered

One cake recipe calls for $$\displaystyle{\frac{{{2}}}{{{3}}}}$$ cup of sugar. Another recipe calls for $$\displaystyle{1}{\frac{{{1}}}{{{4}}}}$$ cups of sugar. How many cups of sugar are needed to make both cakes?

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We added the two amount of sugar:

$$\frac{2}{3}+1\frac{1}{4}$$

Write the mixed fraction as an improper fraction:

$$=\frac{2}{3}+\frac{5}{4}$$

Rewrite each fraction using the LCD which is 12:

$$=\frac{2}{3}\cdot\frac{4}{4}+\frac{5}{4}\cdot\frac{3}{3}$$

$$=\frac{8}{12}+\frac{15}{12}$$

Combine the numerators:

$$=\frac{8+15}{12}$$

$$=\frac{23}{12}$$

Write as a mixed fraction:

$$1\frac{11}{12}$$ cups of sugar are needed