Basic Math Examples

\frac{5}{7} - \frac{1}{5}

$\frac{5}{7} - \frac{1}{5}$

Step 1

To write

\frac{5}{7}

$\frac{5}{7}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{7} \cdot \frac{5}{5} - \frac{1}{5}

$\frac{5}{7} \cdot \frac{5}{5} - \frac{1}{5}$

Step 2

To write

- \frac{1}{5}

$- \frac{1}{5}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5}{7} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{7}{7}

$\frac{5}{7} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of

35

$35$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{7}

$\frac{5}{7}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{7 \cdot 5} - \frac{1}{5} \cdot \frac{7}{7}

$\frac{5 \cdot 5}{7 \cdot 5} - \frac{1}{5} \cdot \frac{7}{7}$

Step 3.2

Multiply

7

$7$ by

5

$5$ .

\frac{5 \cdot 5}{35} - \frac{1}{5} \cdot \frac{7}{7}

$\frac{5 \cdot 5}{35} - \frac{1}{5} \cdot \frac{7}{7}$

Step 3.3

Multiply

\frac{1}{5}

$\frac{1}{5}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5 \cdot 5}{35} - \frac{7}{5 \cdot 7}

$\frac{5 \cdot 5}{35} - \frac{7}{5 \cdot 7}$

Step 3.4

Multiply

5

$5$ by

7

$7$ .

\frac{5 \cdot 5}{35} - \frac{7}{35}

$\frac{5 \cdot 5}{35} - \frac{7}{35}$

\frac{5 \cdot 5}{35} - \frac{7}{35}

$\frac{5 \cdot 5}{35} - \frac{7}{35}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 5 - 7}{35}

$\frac{5 \cdot 5 - 7}{35}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 - 7}{35}

$\frac{25 - 7}{35}$

Step 5.2

Subtract

7

$7$ from

25

$25$ .

\frac{18}{35}

$\frac{18}{35}$

\frac{18}{35}

$\frac{18}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{18}{35}

$\frac{18}{35}$

Decimal Form:

0.5 ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 142857

$0.5\overline{142857}$