Basic Math Examples

$\frac{\frac{5}{35}}{\frac{4}{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}}$

Step 1

Cancel the common factor of $5$ and $35$ .

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Step 1.1

Factor $5$ out of $5$ .

$\frac{\frac{5 (1)}{35}}{\frac{4}{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $35$ .

$\frac{\frac{5 \cdot 1}{5 \cdot 7}}{\frac{4}{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{5 \cdot 1}{5 \cdot 7}}{\frac{4}{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{1}{7}}{\frac{4}{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} \cdot \frac{\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}}}{4}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} (\frac{9}{\frac{3}{\frac{10}{\frac{7}{4}}}} \cdot \frac{1}{4})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} (9 \frac{\frac{10}{\frac{7}{4}}}{3} \frac{1}{4})$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $9$ .

$\frac{1}{7} (3 (3) \frac{\frac{10}{\frac{7}{4}}}{3} \frac{1}{4})$

Step 5.2

Cancel the common factor.

$\frac{1}{7} (3 \cdot 3 \frac{\frac{10}{\frac{7}{4}}}{3} \frac{1}{4})$

Step 5.3

Rewrite the expression.

$\frac{1}{7} (3 \frac{10}{\frac{7}{4}} \frac{1}{4})$

Step 6

Combine $3$ and $\frac{10}{\frac{7}{4}}$ .

$\frac{1}{7} (\frac{3 \cdot 10}{\frac{7}{4}} \cdot \frac{1}{4})$

Step 7

Multiply $3$ by $10$ .

$\frac{1}{7} (\frac{30}{\frac{7}{4}} \cdot \frac{1}{4})$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $30$ .

$\frac{1}{7} (\frac{2 (15)}{\frac{7}{4}} \cdot \frac{1}{4})$

Step 8.2

Factor $2$ out of $4$ .

$\frac{1}{7} (\frac{2 \cdot 15}{\frac{7}{4}} \cdot \frac{1}{2 \cdot 2})$

Step 8.3

Cancel the common factor.

$\frac{1}{7} (\frac{2 \cdot 15}{\frac{7}{4}} \cdot \frac{1}{2 \cdot 2})$

Step 8.4

Rewrite the expression.

$\frac{1}{7} (\frac{15}{\frac{7}{4}} \cdot \frac{1}{2})$

Step 9

Multiply $\frac{15}{\frac{7}{4}}$ by $\frac{1}{2}$ .

$\frac{1}{7} \cdot \frac{15}{\frac{7}{4} \cdot 2}$

Step 10

Combine $\frac{7}{4}$ and $2$ .

$\frac{1}{7} \cdot \frac{15}{\frac{7 \cdot 2}{4}}$

Step 11

Multiply $7$ by $2$ .

$\frac{1}{7} \cdot \frac{15}{\frac{14}{4}}$

Step 12

Cancel the common factor of $14$ and $4$ .

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Step 12.1

Factor $2$ out of $14$ .

$\frac{1}{7} \cdot \frac{15}{\frac{2 (7)}{4}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $2$ out of $4$ .

$\frac{1}{7} \cdot \frac{15}{\frac{2 \cdot 7}{2 \cdot 2}}$

Step 12.2.2

Cancel the common factor.

$\frac{1}{7} \cdot \frac{15}{\frac{2 \cdot 7}{2 \cdot 2}}$

Step 12.2.3

Rewrite the expression.

$\frac{1}{7} \cdot \frac{15}{\frac{7}{2}}$

Step 13

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} (15 (\frac{2}{7}))$

Step 14

Multiply $15 (\frac{2}{7})$ .

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Step 14.1

Combine $15$ and $\frac{2}{7}$ .

$\frac{1}{7} \cdot \frac{15 \cdot 2}{7}$

Step 14.2

Multiply $15$ by $2$ .

$\frac{1}{7} \cdot \frac{30}{7}$

Step 15

Multiply $\frac{1}{7} \cdot \frac{30}{7}$ .

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Step 15.1

Multiply $\frac{1}{7}$ by $\frac{30}{7}$ .

$\frac{30}{7 \cdot 7}$

Step 15.2

Multiply $7$ by $7$ .

$\frac{30}{49}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$\frac{30}{49}$

Decimal Form:

$0.61224489 \dots$