Basic Math Examples

$(- \frac{7}{5} + \frac{21}{8}) \cdot (- \frac{4}{7}) \div (- \frac{4}{15})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(- \frac{7}{5} + \frac{21}{8}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 2

To write $- \frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(- \frac{7}{5} \cdot \frac{8}{8} + \frac{21}{8}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 3

To write $\frac{21}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(- \frac{7}{5} \cdot \frac{8}{8} + \frac{21}{8} \cdot \frac{5}{5}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{5}$ by $\frac{8}{8}$ .

$(- \frac{7 \cdot 8}{5 \cdot 8} + \frac{21}{8} \cdot \frac{5}{5}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 4.2

Multiply $5$ by $8$ .

$(- \frac{7 \cdot 8}{40} + \frac{21}{8} \cdot \frac{5}{5}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 4.3

Multiply $\frac{21}{8}$ by $\frac{5}{5}$ .

$(- \frac{7 \cdot 8}{40} + \frac{21 \cdot 5}{8 \cdot 5}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 4.4

Multiply $8$ by $5$ .

$(- \frac{7 \cdot 8}{40} + \frac{21 \cdot 5}{40}) \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 5

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 8 + 21 \cdot 5}{40} \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 7$ by $8$ .

$\frac{- 56 + 21 \cdot 5}{40} \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 6.2

Multiply $21$ by $5$ .

$\frac{- 56 + 105}{40} \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 6.3

Add $- 56$ and $105$ .

$\frac{49}{40} \cdot (- \frac{4}{7}) (- \frac{15}{4})$

Step 7

Cancel the common factor of $7$ .

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Step 7.1

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$\frac{49}{40} \cdot \frac{- 4}{7} (- \frac{15}{4})$

Step 7.2

Factor $7$ out of $49$ .

$\frac{7 (7)}{40} \cdot \frac{- 4}{7} (- \frac{15}{4})$

Step 7.3

Cancel the common factor.

$\frac{7 \cdot 7}{40} \cdot \frac{- 4}{7} (- \frac{15}{4})$

Step 7.4

Rewrite the expression.

$\frac{7}{40} \cdot - 4 (- \frac{15}{4})$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $40$ .

$\frac{7}{4 (10)} \cdot - 4 (- \frac{15}{4})$

Step 8.2

Factor $4$ out of $- 4$ .

$\frac{7}{4 \cdot 10} \cdot (4 \cdot - 1) (- \frac{15}{4})$

Step 8.3

Cancel the common factor.

$\frac{7}{4 \cdot 10} \cdot (4 \cdot - 1) (- \frac{15}{4})$

Step 8.4

Rewrite the expression.

$\frac{7}{10} \cdot - 1 (- \frac{15}{4})$

Step 9

Combine $\frac{7}{10}$ and $- 1$ .

$\frac{7 \cdot - 1}{10} (- \frac{15}{4})$

Step 10

Multiply $7$ by $- 1$ .

$\frac{- 7}{10} (- \frac{15}{4})$

Step 11

Cancel the common factor of $5$ .

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Step 11.1

Move the leading negative in $- \frac{15}{4}$ into the numerator.

$\frac{- 7}{10} \cdot \frac{- 15}{4}$

Step 11.2

Factor $5$ out of $10$ .

$\frac{- 7}{5 (2)} \cdot \frac{- 15}{4}$

Step 11.3

Factor $5$ out of $- 15$ .

$\frac{- 7}{5 \cdot 2} \cdot \frac{5 \cdot - 3}{4}$

Step 11.4

Cancel the common factor.

$\frac{- 7}{5 \cdot 2} \cdot \frac{5 \cdot - 3}{4}$

Step 11.5

Rewrite the expression.

$\frac{- 7}{2} \cdot \frac{- 3}{4}$

Step 12

Multiply $\frac{- 7}{2}$ by $\frac{- 3}{4}$ .

$\frac{- 7 \cdot - 3}{2 \cdot 4}$

Step 13

Multiply.

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Step 13.1

Multiply $- 7$ by $- 3$ .

$\frac{21}{2 \cdot 4}$

Step 13.2

Multiply $2$ by $4$ .

$\frac{21}{8}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{8}$

Decimal Form:

$2.625$

Mixed Number Form:

$2 \frac{5}{8}$