Basic Math Examples

(\frac{2}{5} + \frac{2}{3}) \div (\frac{4}{5} + 1 \frac{2}{3})

$(\frac{2}{5} + \frac{2}{3}) \div (\frac{4}{5} + 1 \frac{2}{3})$

Step 1

Convert

1 \frac{2}{3}

$1 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

(\frac{2}{5} + \frac{2}{3}) \div (\frac{4}{5} + 1 + \frac{2}{3})

$(\frac{2}{5} + \frac{2}{3}) \div (\frac{4}{5} + 1 + \frac{2}{3})$

Step 1.2

Add

1

$1$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

3

$3$ and

2

$2$ .

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

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

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

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

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

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

Step 2

Rewrite the division as a fraction.

\frac{\frac{2}{5} + \frac{2}{3}}{\frac{4}{5} + \frac{5}{3}}

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

Step 3

Multiply the numerator and denominator of the fraction by

15

$15$ .

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Step 3.1

Multiply

\frac{\frac{2}{5} + \frac{2}{3}}{\frac{4}{5} + \frac{5}{3}}

$\frac{\frac{2}{5} + \frac{2}{3}}{\frac{4}{5} + \frac{5}{3}}$ by

\frac{15}{15}

$\frac{15}{15}$ .

\frac{15}{15} \cdot \frac{\frac{2}{5} + \frac{2}{3}}{\frac{4}{5} + \frac{5}{3}}

$\frac{15}{15} \cdot \frac{\frac{2}{5} + \frac{2}{3}}{\frac{4}{5} + \frac{5}{3}}$

Step 3.2

Combine.

\frac{15 (\frac{2}{5} + \frac{2}{3})}{15 (\frac{4}{5} + \frac{5}{3})}

$\frac{15 (\frac{2}{5} + \frac{2}{3})}{15 (\frac{4}{5} + \frac{5}{3})}$

\frac{15 (\frac{2}{5} + \frac{2}{3})}{15 (\frac{4}{5} + \frac{5}{3})}

$\frac{15 (\frac{2}{5} + \frac{2}{3})}{15 (\frac{4}{5} + \frac{5}{3})}$

Step 4

Apply the distributive property.

\frac{15 (\frac{2}{5}) + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}

$\frac{15 (\frac{2}{5}) + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5

Simplify by cancelling.

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Step 5.1

Cancel the common factor of

5

$5$ .

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Step 5.1.1

Factor

5

$5$ out of

15

$15$ .

\frac{5 (3) \frac{2}{5} + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}

$\frac{5 (3) \frac{2}{5} + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.1.2

Cancel the common factor.

$\frac{5 \cdot 3 \frac{2}{5} + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.1.3

Rewrite the expression.

$\frac{3 \cdot 2 + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.2

Multiply

$3$ by

$2$ .

$\frac{6 + 15 (\frac{2}{3})}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.3

Cancel the common factor of

$3$ .

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Step 5.3.1

Factor

$3$ out of

$15$ .

$\frac{6 + 3 (5) \frac{2}{3}}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.3.2

Cancel the common factor.

$\frac{6 + 3 \cdot 5 \frac{2}{3}}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.3.3

Rewrite the expression.

$\frac{6 + 5 \cdot 2}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.4

Multiply

$5$ by

$2$ .

$\frac{6 + 10}{15 (\frac{4}{5}) + 15 (\frac{5}{3})}$

Step 5.5

Cancel the common factor of

$5$ .

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Step 5.5.1

Factor

$5$ out of

$15$ .

$\frac{6 + 10}{5 (3) \frac{4}{5} + 15 (\frac{5}{3})}$

Step 5.5.2

Cancel the common factor.

$\frac{6 + 10}{5 \cdot 3 \frac{4}{5} + 15 (\frac{5}{3})}$

Step 5.5.3

Rewrite the expression.

$\frac{6 + 10}{3 \cdot 4 + 15 (\frac{5}{3})}$

Step 5.6

Multiply

$3$ by

$4$ .

$\frac{6 + 10}{12 + 15 (\frac{5}{3})}$

Step 5.7

Cancel the common factor of

$3$ .

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Step 5.7.1

Factor

$3$ out of

$15$ .

$\frac{6 + 10}{12 + 3 (5) \frac{5}{3}}$

Step 5.7.2

Cancel the common factor.

$\frac{6 + 10}{12 + 3 \cdot 5 \frac{5}{3}}$

Step 5.7.3

Rewrite the expression.

$\frac{6 + 10}{12 + 5 \cdot 5}$

Step 5.8

Multiply

$5$ by

$5$ .

$\frac{6 + 10}{12 + 25}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add

$6$ and

$10$ .

$\frac{16}{12 + 25}$

Step 6.2

Add

$12$ and

$25$ .

$\frac{16}{37}$