Basic Math Examples

$5 \frac{9}{16} - 1 \frac{1}{2}$

Step 1

Convert

$5 \frac{9}{16}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$5 + \frac{9}{16} - 1 \frac{1}{2}$

Step 1.2

Add

$5$ and

$\frac{9}{16}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{16}{16}$ .

$5 \cdot \frac{16}{16} + \frac{9}{16} - 1 \frac{1}{2}$

Step 1.2.2

Combine

$5$ and

$\frac{16}{16}$ .

$\frac{5 \cdot 16}{16} + \frac{9}{16} - 1 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 16 + 9}{16} - 1 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$16$ .

$\frac{80 + 9}{16} - 1 \frac{1}{2}$

Step 1.2.4.2

Add

$80$ and

$9$ .

$\frac{89}{16} - 1 \frac{1}{2}$

Step 2

Convert

$1 \frac{1}{2}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{89}{16} - (1 + \frac{1}{2})$

Step 2.2

Add

$1$ and

$\frac{1}{2}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{89}{16} - (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{89}{16} - \frac{2 + 1}{2}$

Step 2.2.3

Add

$2$ and

$1$ .

$\frac{89}{16} - \frac{3}{2}$

Step 3

To write

$- \frac{3}{2}$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{89}{16} - \frac{3}{2} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of

$16$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{3}{2}$ by

$\frac{8}{8}$ .

$\frac{89}{16} - \frac{3 \cdot 8}{2 \cdot 8}$

Step 4.2

Multiply

$2$ by

$8$ .

$\frac{89}{16} - \frac{3 \cdot 8}{16}$

Step 5

Combine the numerators over the common denominator.

$\frac{89 - 3 \cdot 8}{16}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$- 3$ by

$8$ .

$\frac{89 - 24}{16}$

Step 6.2

Subtract

$24$ from

$89$ .

$\frac{65}{16}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{16}$

Decimal Form:

$4.0625$

Mixed Number Form:

$4 \frac{1}{16}$