Basic Math Examples

$3 \frac{3}{4} \div 1 \frac{1}{8}$

Step 1

Convert

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

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Step 1.1

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

$(3 + \frac{3}{4}) \div 1 \frac{1}{8}$

Step 1.2

Add

$3$ and

$\frac{3}{4}$ .

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Step 1.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$(3 \cdot \frac{4}{4} + \frac{3}{4}) \div 1 \frac{1}{8}$

Step 1.2.2

Combine

$3$ and

$\frac{4}{4}$ .

$(\frac{3 \cdot 4}{4} + \frac{3}{4}) \div 1 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 3}{4} \div 1 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$4$ .

$\frac{12 + 3}{4} \div 1 \frac{1}{8}$

Step 1.2.4.2

Add

$12$ and

$3$ .

$\frac{15}{4} \div 1 \frac{1}{8}$

Step 2

Convert

$1 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{15}{4} \div (1 + \frac{1}{8})$

Step 2.2

Add

$1$ and

$\frac{1}{8}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{15}{4} \div (\frac{8}{8} + \frac{1}{8})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{15}{4} \div \frac{8 + 1}{8}$

Step 2.2.3

Add

$8$ and

$1$ .

$\frac{15}{4} \div \frac{9}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{4} \cdot \frac{8}{9}$

Step 4

Cancel the common factor of

$3$ .

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Step 4.1

Factor

$3$ out of

$15$ .

$\frac{3 (5)}{4} \cdot \frac{8}{9}$

Step 4.2

Factor

$3$ out of

$9$ .

$\frac{3 \cdot 5}{4} \cdot \frac{8}{3 \cdot 3}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot 5}{4} \cdot \frac{8}{3 \cdot 3}$

Step 4.4

Rewrite the expression.

$\frac{5}{4} \cdot \frac{8}{3}$

Step 5

Cancel the common factor of

$4$ .

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Step 5.1

Factor

$4$ out of

$8$ .

$\frac{5}{4} \cdot \frac{4 (2)}{3}$

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$5 (\frac{2}{3})$

Step 6

Combine

$5$ and

$\frac{2}{3}$ .

$\frac{5 \cdot 2}{3}$

Step 7

Multiply

$5$ by

$2$ .

$\frac{10}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$