Basic Math Examples

$(\frac{2}{3} - \frac{1}{5}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 1

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

$(\frac{2}{3} \cdot \frac{5}{5} - \frac{1}{5}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 2

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

$(\frac{2}{3} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{3}{3}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 3

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

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Step 3.1

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

$(\frac{2 \cdot 5}{3 \cdot 5} - \frac{1}{5} \cdot \frac{3}{3}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 3.2

Multiply $3$ by $5$ .

$(\frac{2 \cdot 5}{15} - \frac{1}{5} \cdot \frac{3}{3}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 3.3

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

$(\frac{2 \cdot 5}{15} - \frac{3}{5 \cdot 3}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 3.4

Multiply $5$ by $3$ .

$(\frac{2 \cdot 5}{15} - \frac{3}{15}) \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 - 3}{15} \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $5$ .

$\frac{10 - 3}{15} \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 5.2

Subtract $3$ from $10$ .

$\frac{7}{15} \div \frac{1}{3} - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 6

Simplify each term.

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Step 6.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{15} \cdot 3 - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 6.2

Cancel the common factor of $3$ .

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Step 6.2.1

Factor $3$ out of $15$ .

$\frac{7}{3 (5)} \cdot 3 - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 6.2.2

Cancel the common factor.

$\frac{7}{3 \cdot 5} \cdot 3 - (2 \cdot \frac{1}{10} + \frac{2}{5}) \cdot 10$

Step 6.2.3

Rewrite the expression.

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

Step 6.3

Cancel the common factor of $2$ .

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Step 6.3.1

Factor $2$ out of $10$ .

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

Step 6.3.2

Cancel the common factor.

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

Step 6.3.3

Rewrite the expression.

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

Step 6.4

Combine the numerators over the common denominator.

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

Step 6.5

Add $1$ and $2$ .

$\frac{7}{5} - \frac{3}{5} \cdot 10$

Step 6.6

Cancel the common factor of $5$ .

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Step 6.6.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{7}{5} + \frac{- 3}{5} \cdot 10$

Step 6.6.2

Factor $5$ out of $10$ .

$\frac{7}{5} + \frac{- 3}{5} \cdot (5 (2))$

Step 6.6.3

Cancel the common factor.

$\frac{7}{5} + \frac{- 3}{5} \cdot (5 \cdot 2)$

Step 6.6.4

Rewrite the expression.

$\frac{7}{5} - 3 \cdot 2$

Step 6.7

Multiply $- 3$ by $2$ .

$\frac{7}{5} - 6$

Step 7

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7}{5} - 6 \cdot \frac{5}{5}$

Step 8

Combine $- 6$ and $\frac{5}{5}$ .

$\frac{7}{5} + \frac{- 6 \cdot 5}{5}$

Step 9

Combine the numerators over the common denominator.

$\frac{7 - 6 \cdot 5}{5}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 6$ by $5$ .

$\frac{7 - 30}{5}$

Step 10.2

Subtract $30$ from $7$ .

$\frac{- 23}{5}$

Step 11

Move the negative in front of the fraction.

$- \frac{23}{5}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{23}{5}$

Decimal Form:

$- 4.6$

Mixed Number Form:

$- 4 \frac{3}{5}$