Algebra Examples

\frac{5}{8} - \frac{1}{20}

$\frac{5}{8} - \frac{1}{20}$

Step 1

To write

\frac{5}{8}

$\frac{5}{8}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{8} \cdot \frac{5}{5} - \frac{1}{20}

$\frac{5}{8} \cdot \frac{5}{5} - \frac{1}{20}$

Step 2

To write

- \frac{1}{20}

$- \frac{1}{20}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5}{8} \cdot \frac{5}{5} - \frac{1}{20} \cdot \frac{2}{2}

$\frac{5}{8} \cdot \frac{5}{5} - \frac{1}{20} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of

40

$40$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{8}

$\frac{5}{8}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{8 \cdot 5} - \frac{1}{20} \cdot \frac{2}{2}

$\frac{5 \cdot 5}{8 \cdot 5} - \frac{1}{20} \cdot \frac{2}{2}$

Step 3.2

Multiply

8

$8$ by

5

$5$ .

\frac{5 \cdot 5}{40} - \frac{1}{20} \cdot \frac{2}{2}

$\frac{5 \cdot 5}{40} - \frac{1}{20} \cdot \frac{2}{2}$

Step 3.3

Multiply

\frac{1}{20}

$\frac{1}{20}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{5 \cdot 5}{40} - \frac{2}{20 \cdot 2}

$\frac{5 \cdot 5}{40} - \frac{2}{20 \cdot 2}$

Step 3.4

Multiply

20

$20$ by

2

$2$ .

\frac{5 \cdot 5}{40} - \frac{2}{40}

$\frac{5 \cdot 5}{40} - \frac{2}{40}$

\frac{5 \cdot 5}{40} - \frac{2}{40}

$\frac{5 \cdot 5}{40} - \frac{2}{40}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 5 - 2}{40}

$\frac{5 \cdot 5 - 2}{40}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 - 2}{40}

$\frac{25 - 2}{40}$

Step 5.2

Subtract

2

$2$ from

25

$25$ .

\frac{23}{40}

$\frac{23}{40}$

\frac{23}{40}

$\frac{23}{40}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{23}{40}

$\frac{23}{40}$

Decimal Form:

0.575

$0.575$