Basic Math Examples

(\frac{7}{16} + \frac{5}{16}) \cdot (\frac{5}{8} \div \frac{1}{10})

$(\frac{7}{16} + \frac{5}{16}) \cdot (\frac{5}{8} \div \frac{1}{10})$

Step 1

Combine the numerators over the common denominator.

\frac{7 + 5}{16} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{7 + 5}{16} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 2

Add

7

$7$ and

5

$5$ .

\frac{12}{16} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{12}{16} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 3

Cancel the common factor of

12

$12$ and

16

$16$ .

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Step 3.1

Factor

4

$4$ out of

12

$12$ .

\frac{4 (3)}{16} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{4 (3)}{16} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

4

$4$ out of

16

$16$ .

\frac{4 \cdot 3}{4 \cdot 4} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{4 \cdot 3}{4 \cdot 4} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 3.2.2

Cancel the common factor.

\frac{4 \cdot 3}{4 \cdot 4} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{4 \cdot 3}{4 \cdot 4} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 3.2.3

Rewrite the expression.

\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}$

\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}$

\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}

$\frac{3}{4} \cdot \frac{5}{8} \div \frac{1}{10}$

Step 4

To divide by a fraction, multiply by its reciprocal.

\frac{3}{4} \cdot (\frac{5}{8} \cdot 10)

$\frac{3}{4} \cdot (\frac{5}{8} \cdot 10)$

Step 5

Cancel the common factor of

2

$2$ .

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Step 5.1

Factor

2

$2$ out of

4

$4$ .

\frac{3}{2 (2)} \cdot (\frac{5}{8} \cdot 10)

$\frac{3}{2 (2)} \cdot (\frac{5}{8} \cdot 10)$

Step 5.2

Factor

2

$2$ out of

\frac{5}{8} \cdot 10

$\frac{5}{8} \cdot 10$ .

\frac{3}{2 (2)} \cdot (2 (\frac{5}{8} \cdot 5))

$\frac{3}{2 (2)} \cdot (2 (\frac{5}{8} \cdot 5))$

Step 5.3

Cancel the common factor.

\frac{3}{2 \cdot 2} \cdot (2 (\frac{5}{8} \cdot 5))

$\frac{3}{2 \cdot 2} \cdot (2 (\frac{5}{8} \cdot 5))$

Step 5.4

Rewrite the expression.

\frac{3}{2} \cdot (\frac{5}{8} \cdot 5)

$\frac{3}{2} \cdot (\frac{5}{8} \cdot 5)$

\frac{3}{2} \cdot (\frac{5}{8} \cdot 5)

$\frac{3}{2} \cdot (\frac{5}{8} \cdot 5)$

Step 6

Combine

\frac{5}{8}

$\frac{5}{8}$ and

5

$5$ .

\frac{3}{2} \cdot \frac{5 \cdot 5}{8}

$\frac{3}{2} \cdot \frac{5 \cdot 5}{8}$

Step 7

Multiply

5

$5$ by

5

$5$ .

\frac{3}{2} \cdot \frac{25}{8}

$\frac{3}{2} \cdot \frac{25}{8}$

Step 8

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{25}{8}

$\frac{25}{8}$ .

\frac{3 \cdot 25}{2 \cdot 8}

$\frac{3 \cdot 25}{2 \cdot 8}$

Step 9

Multiply.

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Step 9.1

Multiply

3

$3$ by

25

$25$ .

\frac{75}{2 \cdot 8}

$\frac{75}{2 \cdot 8}$

Step 9.2

Multiply

2

$2$ by

8

$8$ .

\frac{75}{16}

$\frac{75}{16}$

\frac{75}{16}

$\frac{75}{16}$

Step 10

The result can be shown in multiple forms.

Exact Form:

\frac{75}{16}

$\frac{75}{16}$

Decimal Form:

4.6875

$4.6875$

Mixed Number Form:

4 \frac{11}{16}

$4 \frac{11}{16}$