Algebra Examples

\frac{7}{10} - \frac{1}{5}

$\frac{7}{10} - \frac{1}{5}$

Step 1

To write

- \frac{1}{5}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{10} - \frac{1}{5} \cdot \frac{2}{2}

$\frac{7}{10} - \frac{1}{5} \cdot \frac{2}{2}$

Step 2

Write each expression with a common denominator of

10

$10$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.1

Multiply

\frac{1}{5}

$\frac{1}{5}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{10} - \frac{2}{5 \cdot 2}

$\frac{7}{10} - \frac{2}{5 \cdot 2}$

Step 2.2

Multiply

5

$5$ by

2

$2$ .

\frac{7}{10} - \frac{2}{10}

$\frac{7}{10} - \frac{2}{10}$

\frac{7}{10} - \frac{2}{10}

$\frac{7}{10} - \frac{2}{10}$

Step 3

Simplify the expression.

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Step 3.1

Combine the numerators over the common denominator.

\frac{7 - 2}{10}

$\frac{7 - 2}{10}$

Step 3.2

Subtract

2

$2$ from

7

$7$ .

\frac{5}{10}

$\frac{5}{10}$

\frac{5}{10}

$\frac{5}{10}$

Step 4

Cancel the common factor of

5

$5$ and

10

$10$ .

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Step 4.1

Factor

5

$5$ out of

5

$5$ .

\frac{5 (1)}{10}

$\frac{5 (1)}{10}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

5

$5$ out of

10

$10$ .

\frac{5 \cdot 1}{5 \cdot 2}

$\frac{5 \cdot 1}{5 \cdot 2}$

Step 4.2.2

Cancel the common factor.

\frac{5 \cdot 1}{5 \cdot 2}

$\frac{5 \cdot 1}{5 \cdot 2}$

Step 4.2.3

Rewrite the expression.

\frac{1}{2}

$\frac{1}{2}$

\frac{1}{2}

$\frac{1}{2}$

\frac{1}{2}

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{1}{2}

$\frac{1}{2}$

Decimal Form:

0.5

$0.5$

\frac{7}{10} - \frac{1}{5}

$\frac{7}{10} - \frac{1}{5}$

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