Basic Math Examples

\frac{1}{5} - \frac{4}{7}

$\frac{1}{5} - \frac{4}{7}$

Step 1

To write

\frac{1}{5}

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

\frac{7}{7}

$\frac{7}{7}$ .

\frac{1}{5} \cdot \frac{7}{7} - \frac{4}{7}

$\frac{1}{5} \cdot \frac{7}{7} - \frac{4}{7}$

Step 2

To write

- \frac{4}{7}

$- \frac{4}{7}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{1}{5} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{5}{5}

$\frac{1}{5} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{5}{5}$

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{1}{5}

$\frac{1}{5}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{7}{5 \cdot 7} - \frac{4}{7} \cdot \frac{5}{5}

$\frac{7}{5 \cdot 7} - \frac{4}{7} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

7

$7$ .

\frac{7}{35} - \frac{4}{7} \cdot \frac{5}{5}

$\frac{7}{35} - \frac{4}{7} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{4}{7}

$\frac{4}{7}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{7}{35} - \frac{4 \cdot 5}{7 \cdot 5}

$\frac{7}{35} - \frac{4 \cdot 5}{7 \cdot 5}$

Step 3.4

Multiply

7

$7$ by

5

$5$ .

\frac{7}{35} - \frac{4 \cdot 5}{35}

$\frac{7}{35} - \frac{4 \cdot 5}{35}$

\frac{7}{35} - \frac{4 \cdot 5}{35}

$\frac{7}{35} - \frac{4 \cdot 5}{35}$

Step 4

Combine the numerators over the common denominator.

\frac{7 - 4 \cdot 5}{35}

$\frac{7 - 4 \cdot 5}{35}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 4

$- 4$ by

5

$5$ .

\frac{7 - 20}{35}

$\frac{7 - 20}{35}$

Step 5.2

Subtract

20

$20$ from

7

$7$ .

\frac{- 13}{35}

$\frac{- 13}{35}$

\frac{- 13}{35}

$\frac{- 13}{35}$

Step 6

Move the negative in front of the fraction.

- \frac{13}{35}

$- \frac{13}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{13}{35}

$- \frac{13}{35}$

Decimal Form:

- 0.3 ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 714285

$- 0.3\overline{714285}$