Basic Math Examples

5 \frac{3}{5} - 3 \frac{5}{6}

$5 \frac{3}{5} - 3 \frac{5}{6}$

Step 1

Convert

5 \frac{3}{5}

$5 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

5 + \frac{3}{5} - 3 \frac{5}{6}

$5 + \frac{3}{5} - 3 \frac{5}{6}$

Step 1.2

Add

5

$5$ and

\frac{3}{5}

$\frac{3}{5}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

5 \cdot \frac{5}{5} + \frac{3}{5} - 3 \frac{5}{6}

$5 \cdot \frac{5}{5} + \frac{3}{5} - 3 \frac{5}{6}$

Step 1.2.2

Combine

5

$5$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{5} + \frac{3}{5} - 3 \frac{5}{6}

$\frac{5 \cdot 5}{5} + \frac{3}{5} - 3 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 5 + 3}{5} - 3 \frac{5}{6}

$\frac{5 \cdot 5 + 3}{5} - 3 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 + 3}{5} - 3 \frac{5}{6}

$\frac{25 + 3}{5} - 3 \frac{5}{6}$

Step 1.2.4.2

Add

25

$25$ and

3

$3$ .

\frac{28}{5} - 3 \frac{5}{6}

$\frac{28}{5} - 3 \frac{5}{6}$

\frac{28}{5} - 3 \frac{5}{6}

$\frac{28}{5} - 3 \frac{5}{6}$

\frac{28}{5} - 3 \frac{5}{6}

$\frac{28}{5} - 3 \frac{5}{6}$

\frac{28}{5} - 3 \frac{5}{6}

$\frac{28}{5} - 3 \frac{5}{6}$

Step 2

Convert

3 \frac{5}{6}

$3 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

\frac{28}{5} - (3 + \frac{5}{6})

$\frac{28}{5} - (3 + \frac{5}{6})$

Step 2.2

Add

3

$3$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 2.2.1

To write

3

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{28}{5} - (3 \cdot \frac{6}{6} + \frac{5}{6})

$\frac{28}{5} - (3 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

3

$3$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{28}{5} - (\frac{3 \cdot 6}{6} + \frac{5}{6})

$\frac{28}{5} - (\frac{3 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{28}{5} - \frac{3 \cdot 6 + 5}{6}

$\frac{28}{5} - \frac{3 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

6

$6$ .

\frac{28}{5} - \frac{18 + 5}{6}

$\frac{28}{5} - \frac{18 + 5}{6}$

Step 2.2.4.2

Add

18

$18$ and

5

$5$ .

\frac{28}{5} - \frac{23}{6}

$\frac{28}{5} - \frac{23}{6}$

\frac{28}{5} - \frac{23}{6}

$\frac{28}{5} - \frac{23}{6}$

\frac{28}{5} - \frac{23}{6}

$\frac{28}{5} - \frac{23}{6}$

\frac{28}{5} - \frac{23}{6}

$\frac{28}{5} - \frac{23}{6}$

Step 3

To write

\frac{28}{5}

$\frac{28}{5}$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{28}{5} \cdot \frac{6}{6} - \frac{23}{6}

$\frac{28}{5} \cdot \frac{6}{6} - \frac{23}{6}$

Step 4

To write

- \frac{23}{6}

$- \frac{23}{6}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{28}{5} \cdot \frac{6}{6} - \frac{23}{6} \cdot \frac{5}{5}

$\frac{28}{5} \cdot \frac{6}{6} - \frac{23}{6} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

30

$30$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{28}{5}

$\frac{28}{5}$ by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{28 \cdot 6}{5 \cdot 6} - \frac{23}{6} \cdot \frac{5}{5}

$\frac{28 \cdot 6}{5 \cdot 6} - \frac{23}{6} \cdot \frac{5}{5}$

Step 5.2

Multiply

5

$5$ by

6

$6$ .

\frac{28 \cdot 6}{30} - \frac{23}{6} \cdot \frac{5}{5}

$\frac{28 \cdot 6}{30} - \frac{23}{6} \cdot \frac{5}{5}$

Step 5.3

Multiply

\frac{23}{6}

$\frac{23}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{6 \cdot 5}

$\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{6 \cdot 5}$

Step 5.4

Multiply

6

$6$ by

5

$5$ .

\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{30}

$\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{30}$

\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{30}

$\frac{28 \cdot 6}{30} - \frac{23 \cdot 5}{30}$

Step 6

Combine the numerators over the common denominator.

\frac{28 \cdot 6 - 23 \cdot 5}{30}

$\frac{28 \cdot 6 - 23 \cdot 5}{30}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

28

$28$ by

6

$6$ .

\frac{168 - 23 \cdot 5}{30}

$\frac{168 - 23 \cdot 5}{30}$

Step 7.2

Multiply

- 23

$- 23$ by

5

$5$ .

\frac{168 - 115}{30}

$\frac{168 - 115}{30}$

Step 7.3

Subtract

115

$115$ from

168

$168$ .

\frac{53}{30}

$\frac{53}{30}$

\frac{53}{30}

$\frac{53}{30}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{53}{30}

$\frac{53}{30}$

Decimal Form:

1.7\overline{6}

$1.7\overline{6}$

Mixed Number Form:

1 \frac{23}{30}

$1 \frac{23}{30}$