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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Jaylen Fountain
Answered 2021-06-16 Author has 7197 answers
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content_user
Answered 2021-09-30 Author has 1944 answers

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

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