Basic Math Examples

$\frac{15}{8} \div \frac{1}{4} - \frac{2}{7} \cdot \frac{6}{3}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{8} \cdot 4 - \frac{2}{7} \cdot \frac{6}{3}$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $8$ .

$\frac{15}{4 (2)} \cdot 4 - \frac{2}{7} \cdot \frac{6}{3}$

Step 1.2.2

Cancel the common factor.

$\frac{15}{4 \cdot 2} \cdot 4 - \frac{2}{7} \cdot \frac{6}{3}$

Step 1.2.3

Rewrite the expression.

$\frac{15}{2} - \frac{2}{7} \cdot \frac{6}{3}$

Step 1.3

Divide $6$ by $3$ .

$\frac{15}{2} - \frac{2}{7} \cdot 2$

Step 1.4

Multiply $- \frac{2}{7} \cdot 2$ .

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Step 1.4.1

Multiply $2$ by $- 1$ .

$\frac{15}{2} - 2 (\frac{2}{7})$

Step 1.4.2

Combine $- 2$ and $\frac{2}{7}$ .

$\frac{15}{2} + \frac{- 2 \cdot 2}{7}$

Step 1.4.3

Multiply $- 2$ by $2$ .

$\frac{15}{2} + \frac{- 4}{7}$

Step 1.5

Move the negative in front of the fraction.

$\frac{15}{2} - \frac{4}{7}$

Step 2

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{15}{2} \cdot \frac{7}{7} - \frac{4}{7}$

Step 3

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15}{2} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{15}{2}$ by $\frac{7}{7}$ .

$\frac{15 \cdot 7}{2 \cdot 7} - \frac{4}{7} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $7$ .

$\frac{15 \cdot 7}{14} - \frac{4}{7} \cdot \frac{2}{2}$

Step 4.3

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

$\frac{15 \cdot 7}{14} - \frac{4 \cdot 2}{7 \cdot 2}$

Step 4.4

Multiply $7$ by $2$ .

$\frac{15 \cdot 7}{14} - \frac{4 \cdot 2}{14}$

Step 5

Combine the numerators over the common denominator.

$\frac{15 \cdot 7 - 4 \cdot 2}{14}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $15$ by $7$ .

$\frac{105 - 4 \cdot 2}{14}$

Step 6.2

Multiply $- 4$ by $2$ .

$\frac{105 - 8}{14}$

Step 6.3

Subtract $8$ from $105$ .

$\frac{97}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{97}{14}$

Decimal Form:

$6.92857142 \dots$

Mixed Number Form:

$6 \frac{13}{14}$