Basic Math Examples

$\frac{9 \frac{3}{4}}{5 \frac{5}{14}}$

Step 1

Convert $9 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{9 + \frac{3}{4}}{5 \frac{5}{14}}$

Step 1.2

Add $9$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9 \cdot \frac{4}{4} + \frac{3}{4}}{5 \frac{5}{14}}$

Step 1.2.2

Combine $9$ and $\frac{4}{4}$ .

$\frac{\frac{9 \cdot 4}{4} + \frac{3}{4}}{5 \frac{5}{14}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{9 \cdot 4 + 3}{4}}{5 \frac{5}{14}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $9$ by $4$ .

$\frac{\frac{36 + 3}{4}}{5 \frac{5}{14}}$

Step 1.2.4.2

Add $36$ and $3$ .

$\frac{\frac{39}{4}}{5 \frac{5}{14}}$

Step 2

Convert $5 \frac{5}{14}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{\frac{39}{4}}{5 + \frac{5}{14}}$

Step 2.2

Add $5$ and $\frac{5}{14}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$\frac{\frac{39}{4}}{5 \cdot \frac{14}{14} + \frac{5}{14}}$

Step 2.2.2

Combine $5$ and $\frac{14}{14}$ .

$\frac{\frac{39}{4}}{\frac{5 \cdot 14}{14} + \frac{5}{14}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{39}{4}}{\frac{5 \cdot 14 + 5}{14}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $14$ .

$\frac{\frac{39}{4}}{\frac{70 + 5}{14}}$

Step 2.2.4.2

Add $70$ and $5$ .

$\frac{\frac{39}{4}}{\frac{75}{14}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{39}{4} \cdot \frac{14}{75}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $39$ .

$\frac{3 (13)}{4} \cdot \frac{14}{75}$

Step 4.2

Factor $3$ out of $75$ .

$\frac{3 \cdot 13}{4} \cdot \frac{14}{3 \cdot 25}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot 13}{4} \cdot \frac{14}{3 \cdot 25}$

Step 4.4

Rewrite the expression.

$\frac{13}{4} \cdot \frac{14}{25}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $4$ .

$\frac{13}{2 (2)} \cdot \frac{14}{25}$

Step 5.2

Factor $2$ out of $14$ .

$\frac{13}{2 \cdot 2} \cdot \frac{2 \cdot 7}{25}$

Step 5.3

Cancel the common factor.

$\frac{13}{2 \cdot 2} \cdot \frac{2 \cdot 7}{25}$

Step 5.4

Rewrite the expression.

$\frac{13}{2} \cdot \frac{7}{25}$

Step 6

Multiply $\frac{13}{2}$ by $\frac{7}{25}$ .

$\frac{13 \cdot 7}{2 \cdot 25}$

Step 7

Multiply.

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Step 7.1

Multiply $13$ by $7$ .

$\frac{91}{2 \cdot 25}$

Step 7.2

Multiply $2$ by $25$ .

$\frac{91}{50}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{50}$

Decimal Form:

$1.82$

Mixed Number Form:

$1 \frac{41}{50}$