Algebra Examples

$\frac{\frac{3}{16} \cdot \frac{2}{5}}{\frac{7}{4} \cdot \frac{3}{2}}$

Step 1

Multiply $\frac{3}{16}$ by $\frac{2}{5}$ .

$\frac{\frac{3 \cdot 2}{16 \cdot 5}}{\frac{7}{4} \cdot \frac{3}{2}}$

Step 2

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

$\frac{\frac{3 \cdot 2}{16 \cdot 5}}{\frac{7 \cdot 3}{4 \cdot 2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $3$ by $2$ .

$\frac{\frac{6}{16 \cdot 5}}{\frac{7 \cdot 3}{4 \cdot 2}}$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $16$ by $5$ .

$\frac{\frac{6}{80}}{\frac{7 \cdot 3}{4 \cdot 2}}$

Step 3.2.2

Multiply $7$ by $3$ .

$\frac{\frac{6}{80}}{\frac{21}{4 \cdot 2}}$

Step 3.2.3

Multiply $4$ by $2$ .

$\frac{\frac{6}{80}}{\frac{21}{8}}$

Step 3.3

Cancel the common factor of $6$ and $80$ .

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Step 3.3.1

Factor $2$ out of $6$ .

$\frac{\frac{2 (3)}{80}}{\frac{21}{8}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $2$ out of $80$ .

$\frac{\frac{2 \cdot 3}{2 \cdot 40}}{\frac{21}{8}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 3}{2 \cdot 40}}{\frac{21}{8}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{\frac{3}{40}}{\frac{21}{8}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{40} \cdot \frac{8}{21}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $21$ .

$\frac{3}{40} \cdot \frac{8}{3 (7)}$

Step 5.2

Cancel the common factor.

$\frac{3}{40} \cdot \frac{8}{3 \cdot 7}$

Step 5.3

Rewrite the expression.

$\frac{1}{40} \cdot \frac{8}{7}$

Step 6

Cancel the common factor of $8$ .

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Step 6.1

Factor $8$ out of $40$ .

$\frac{1}{8 (5)} \cdot \frac{8}{7}$

Step 6.2

Cancel the common factor.

$\frac{1}{8 \cdot 5} \cdot \frac{8}{7}$

Step 6.3

Rewrite the expression.

$\frac{1}{5} \cdot \frac{1}{7}$

Step 7

Multiply $\frac{1}{5}$ by $\frac{1}{7}$ .

$\frac{1}{5 \cdot 7}$

Step 8

Multiply $5$ by $7$ .

$\frac{1}{35}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{35}$

Decimal Form:

$0.0\overline{285714}$