Basic Math Examples

$- \frac{9}{5} \cdot \frac{2}{3} + \frac{3}{5} \div \frac{4}{5}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{2}{3} + \frac{3}{5} \div \frac{4}{5}$

Step 1.1.2

Factor $3$ out of $- 9$ .

$\frac{3 (- 3)}{5} \cdot \frac{2}{3} + \frac{3}{5} \div \frac{4}{5}$

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Combine $\frac{- 3}{5}$ and $2$ .

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

Step 1.3

Multiply $- 3$ by $2$ .

$\frac{- 6}{5} + \frac{3}{5} \div \frac{4}{5}$

Step 1.4

Move the negative in front of the fraction.

$- \frac{6}{5} + \frac{3}{5} \div \frac{4}{5}$

Step 1.5

To divide by a fraction, multiply by its reciprocal.

$- \frac{6}{5} + \frac{3}{5} \cdot \frac{5}{4}$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Cancel the common factor.

$- \frac{6}{5} + \frac{3}{5} \cdot \frac{5}{4}$

Step 1.6.2

Rewrite the expression.

$- \frac{6}{5} + 3 (\frac{1}{4})$

Step 1.7

Combine $3$ and $\frac{1}{4}$ .

$- \frac{6}{5} + \frac{3}{4}$

Step 2

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{6}{5} \cdot \frac{4}{4} + \frac{3}{4}$

Step 3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{6}{5} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$- \frac{6 \cdot 4}{5 \cdot 4} + \frac{3}{4} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $4$ .

$- \frac{6 \cdot 4}{20} + \frac{3}{4} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$- \frac{6 \cdot 4}{20} + \frac{3 \cdot 5}{4 \cdot 5}$

Step 4.4

Multiply $4$ by $5$ .

$- \frac{6 \cdot 4}{20} + \frac{3 \cdot 5}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 6 \cdot 4 + 3 \cdot 5}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 6$ by $4$ .

$\frac{- 24 + 3 \cdot 5}{20}$

Step 6.2

Multiply $3$ by $5$ .

$\frac{- 24 + 15}{20}$

Step 6.3

Add $- 24$ and $15$ .

$\frac{- 9}{20}$

Step 7

Move the negative in front of the fraction.

$- \frac{9}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{20}$

Decimal Form:

$- 0.45$