Basic Math Examples

$4 \frac{2}{3} \div 7 \frac{5}{8}$

Step 1

Convert $4 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$(4 + \frac{2}{3}) \div 7 \frac{5}{8}$

Step 1.2

Add $4$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(4 \cdot \frac{3}{3} + \frac{2}{3}) \div 7 \frac{5}{8}$

Step 1.2.2

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

$(\frac{4 \cdot 3}{3} + \frac{2}{3}) \div 7 \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 2}{3} \div 7 \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $3$ .

$\frac{12 + 2}{3} \div 7 \frac{5}{8}$

Step 1.2.4.2

Add $12$ and $2$ .

$\frac{14}{3} \div 7 \frac{5}{8}$

Step 2

Convert $7 \frac{5}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{14}{3} \div (7 + \frac{5}{8})$

Step 2.2

Add $7$ and $\frac{5}{8}$ .

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Step 2.2.1

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

$\frac{14}{3} \div (7 \cdot \frac{8}{8} + \frac{5}{8})$

Step 2.2.2

Combine $7$ and $\frac{8}{8}$ .

$\frac{14}{3} \div (\frac{7 \cdot 8}{8} + \frac{5}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{14}{3} \div \frac{7 \cdot 8 + 5}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $8$ .

$\frac{14}{3} \div \frac{56 + 5}{8}$

Step 2.2.4.2

Add $56$ and $5$ .

$\frac{14}{3} \div \frac{61}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{14}{3} \cdot \frac{8}{61}$

Step 4

Multiply $\frac{14}{3} \cdot \frac{8}{61}$ .

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Step 4.1

Multiply $\frac{14}{3}$ by $\frac{8}{61}$ .

$\frac{14 \cdot 8}{3 \cdot 61}$

Step 4.2

Multiply $14$ by $8$ .

$\frac{112}{3 \cdot 61}$

Step 4.3

Multiply $3$ by $61$ .

$\frac{112}{183}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{112}{183}$

Decimal Form:

$0.61202185 \dots$