Pre-Algebra Examples

$\frac{3}{5} + \frac{2}{15} \div \frac{1}{5} - \frac{4}{5}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{3 - 4}{5} + \frac{\frac{2}{15}}{\frac{1}{5}}$

Step 1.2

Subtract $4$ from $3$ .

$\frac{- 1}{5} + \frac{\frac{2}{15}}{\frac{1}{5}}$

Step 2

Simplify each term.

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Step 2.1

Move the negative in front of the fraction.

$- \frac{1}{5} + \frac{\frac{2}{15}}{\frac{1}{5}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{5} + \frac{2}{15} \cdot 5$

Step 2.3

Cancel the common factor of $5$ .

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Step 2.3.1

Factor $5$ out of $15$ .

$- \frac{1}{5} + \frac{2}{5 (3)} \cdot 5$

Step 2.3.2

Cancel the common factor.

$- \frac{1}{5} + \frac{2}{5 \cdot 3} \cdot 5$

Step 2.3.3

Rewrite the expression.

$- \frac{1}{5} + \frac{2}{3}$

Step 3

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{1}{5} \cdot \frac{3}{3} + \frac{2}{3}$

Step 4

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{1}{5} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$- \frac{3}{5 \cdot 3} + \frac{2}{3} \cdot \frac{5}{5}$

Step 5.2

Multiply $5$ by $3$ .

$- \frac{3}{15} + \frac{2}{3} \cdot \frac{5}{5}$

Step 5.3

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$- \frac{3}{15} + \frac{2 \cdot 5}{3 \cdot 5}$

Step 5.4

Multiply $3$ by $5$ .

$- \frac{3}{15} + \frac{2 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 3 + 2 \cdot 5}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $2$ by $5$ .

$\frac{- 3 + 10}{15}$

Step 7.2

Add $- 3$ and $10$ .

$\frac{7}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{15}$

Decimal Form:

$0.4\overline{6}$