Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $24$ .

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Multiply $11$ by $11$ .

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

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.6

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

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

Step 1.7

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.8

Cancel the common factor of $8$ .

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Step 1.8.1

Factor $8$ out of $32$ .

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

Step 1.8.2

Cancel the common factor.

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

Step 1.8.3

Rewrite the expression.

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

Step 1.9

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

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

Step 1.10

Multiply $15$ by $4$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $72$ by $5$ .

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

Step 4.3

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

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

Step 4.4

Multiply $60$ by $6$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $121$ by $5$ .

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

Step 6.2

Add $605$ and $6$ .

$\frac{611}{360}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{611}{360}$

Decimal Form:

$1.697\overline{2}$

Mixed Number Form:

$1 \frac{251}{360}$