Evaluate 11/(24/(11/3))+1/(32/(8/15))

$\frac{11}{\frac{24}{\frac{11}{3}}} + \frac{1}{\frac{32}{\frac{8}{15}}}$

Simplify each term.

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Multiply the numerator by the reciprocal of the denominator.

$11 \frac{\frac{11}{3}}{24} + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$11 (\frac{11}{3} \cdot \frac{1}{24}) + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply $\frac{11}{3} \cdot \frac{1}{24}$ .

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Multiply $\frac{11}{3}$ and $\frac{1}{24}$ .

$11 \frac{11}{3 \cdot 24} + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply $3$ by $24$ .

$11 (\frac{11}{72}) + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply $11 (\frac{11}{72})$ .

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Combine $11$ and $\frac{11}{72}$ .

$\frac{11 \cdot 11}{72} + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply $11$ by $11$ .

$\frac{121}{72} + \frac{1}{\frac{32}{\frac{8}{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{121}{72} + 1 \frac{\frac{8}{15}}{32}$

Multiply $\frac{\frac{8}{15}}{32}$ by $1$ .

$\frac{121}{72} + \frac{\frac{8}{15}}{32}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{121}{72} + \frac{8}{15} \cdot \frac{1}{32}$

Cancel the common factor of $8$ .

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Factor $8$ out of $32$ .

$\frac{121}{72} + \frac{8}{15} \cdot \frac{1}{8 (4)}$

Cancel the common factor.

$\frac{121}{72} + \frac{8}{15} \cdot \frac{1}{8 \cdot 4}$

Rewrite the expression.

$\frac{121}{72} + \frac{1}{15} \cdot \frac{1}{4}$

Multiply $\frac{1}{15}$ and $\frac{1}{4}$ .

$\frac{121}{72} + \frac{1}{15 \cdot 4}$

Multiply $15$ by $4$ .

$\frac{121}{72} + \frac{1}{60}$

To write $\frac{121}{72}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{121}{72} \cdot \frac{5}{5} + \frac{1}{60}$

To write $\frac{1}{60}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{121}{72} \cdot \frac{5}{5} + \frac{1}{60} \cdot \frac{6}{6}$

Write each expression with a common denominator of $360$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{121}{72}$ and $\frac{5}{5}$ .

$\frac{121 \cdot 5}{72 \cdot 5} + \frac{1}{60} \cdot \frac{6}{6}$

Multiply $72$ by $5$ .

$\frac{121 \cdot 5}{360} + \frac{1}{60} \cdot \frac{6}{6}$

Multiply $\frac{1}{60}$ and $\frac{6}{6}$ .

$\frac{121 \cdot 5}{360} + \frac{6}{60 \cdot 6}$

Multiply $60$ by $6$ .

$\frac{121 \cdot 5}{360} + \frac{6}{360}$

Combine the numerators over the common denominator.

$\frac{121 \cdot 5 + 6}{360}$

Simplify the numerator.

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Multiply $121$ by $5$ .

$\frac{605 + 6}{360}$

Add $605$ and $6$ .

$\frac{611}{360}$

The result can be shown in multiple forms.

Exact Form:

$\frac{611}{360}$

Decimal Form:

$1.697\overline{2}$

Mixed Number Form:

$1 \frac{251}{360}$

Evaluate 11/(24/(11/3))+1/(32/(8/15))

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