Basic Math Examples

$1 \frac{1}{3} \div 1 \frac{1}{4} \cdot 2 \div \frac{2}{3}$

Step 1

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{1}{3}) \div 1 \frac{1}{4} \cdot 2 \div \frac{2}{3}$

Step 1.2

Add $1$ and $\frac{1}{3}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{3}{3} + \frac{1}{3}) \div 1 \frac{1}{4} \cdot 2 \div \frac{2}{3}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3 + 1}{3} \div 1 \frac{1}{4} \cdot 2 \div \frac{2}{3}$

Step 1.2.3

Add $3$ and $1$ .

$\frac{4}{3} \div 1 \frac{1}{4} \cdot 2 \div \frac{2}{3}$

Step 2

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{4}{3} \div (1 + \frac{1}{4}) \cdot 2 \div \frac{2}{3}$

Step 2.2

Add $1$ and $\frac{1}{4}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{4}{3} \div (\frac{4}{4} + \frac{1}{4}) \cdot 2 \div \frac{2}{3}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{4}{3} \div \frac{4 + 1}{4} \cdot 2 \div \frac{2}{3}$

Step 2.2.3

Add $4$ and $1$ .

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

Step 3

To divide by a fraction, multiply by its reciprocal.

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $\frac{4}{3} \div \frac{5}{4} \cdot 2$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Combine $\frac{\frac{2}{3}}{\frac{5}{4}}$ and $2$ .

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

Step 6

Combine $\frac{2}{3}$ and $2$ .

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

Step 7

Multiply $2$ by $2$ .

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

Step 8

Combine $\frac{\frac{4}{3}}{\frac{5}{4}}$ and $3$ .

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

Step 9

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

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

Step 10

Multiply $4$ by $3$ .

$\frac{\frac{12}{3}}{\frac{5}{4}}$

Step 11

Cancel the common factor of $12$ and $3$ .

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Step 11.1

Factor $3$ out of $12$ .

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3$ .

$\frac{\frac{3 \cdot 4}{3 (1)}}{\frac{5}{4}}$

Step 11.2.2

Cancel the common factor.

$\frac{\frac{3 \cdot 4}{3 \cdot 1}}{\frac{5}{4}}$

Step 11.2.3

Rewrite the expression.

$\frac{\frac{4}{1}}{\frac{5}{4}}$

Step 11.2.4

Divide $4$ by $1$ .

$\frac{4}{\frac{5}{4}}$

Step 12

Multiply the numerator by the reciprocal of the denominator.

$4 (\frac{4}{5})$

Step 13

Multiply $4 (\frac{4}{5})$ .

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Step 13.1

Combine $4$ and $\frac{4}{5}$ .

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

Step 13.2

Multiply $4$ by $4$ .

$\frac{16}{5}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{5}$

Decimal Form:

$3.2$

Mixed Number Form:

$3 \frac{1}{5}$