Basic Math Examples

6 \frac{1}{6} - 1 \frac{4}{15}

$6 \frac{1}{6} - 1 \frac{4}{15}$

Step 1

Convert

6 \frac{1}{6}

$6 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

6 + \frac{1}{6} - 1 \frac{4}{15}

$6 + \frac{1}{6} - 1 \frac{4}{15}$

Step 1.2

Add

6

$6$ and

\frac{1}{6}

$\frac{1}{6}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

6 \cdot \frac{6}{6} + \frac{1}{6} - 1 \frac{4}{15}

$6 \cdot \frac{6}{6} + \frac{1}{6} - 1 \frac{4}{15}$

Step 1.2.2

Combine

6

$6$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{6 \cdot 6}{6} + \frac{1}{6} - 1 \frac{4}{15}

$\frac{6 \cdot 6}{6} + \frac{1}{6} - 1 \frac{4}{15}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 6 + 1}{6} - 1 \frac{4}{15}

$\frac{6 \cdot 6 + 1}{6} - 1 \frac{4}{15}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

6

$6$ .

\frac{36 + 1}{6} - 1 \frac{4}{15}

$\frac{36 + 1}{6} - 1 \frac{4}{15}$

Step 1.2.4.2

Add

36

$36$ and

1

$1$ .

\frac{37}{6} - 1 \frac{4}{15}

$\frac{37}{6} - 1 \frac{4}{15}$

\frac{37}{6} - 1 \frac{4}{15}

$\frac{37}{6} - 1 \frac{4}{15}$

\frac{37}{6} - 1 \frac{4}{15}

$\frac{37}{6} - 1 \frac{4}{15}$

\frac{37}{6} - 1 \frac{4}{15}

$\frac{37}{6} - 1 \frac{4}{15}$

Step 2

Convert

1 \frac{4}{15}

$1 \frac{4}{15}$ to an improper fraction.

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Step 2.1

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

\frac{37}{6} - (1 + \frac{4}{15})

$\frac{37}{6} - (1 + \frac{4}{15})$

Step 2.2

Add

1

$1$ and

\frac{4}{15}

$\frac{4}{15}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{37}{6} - (\frac{15}{15} + \frac{4}{15})

$\frac{37}{6} - (\frac{15}{15} + \frac{4}{15})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{37}{6} - \frac{15 + 4}{15}

$\frac{37}{6} - \frac{15 + 4}{15}$

Step 2.2.3

Add

15

$15$ and

4

$4$ .

\frac{37}{6} - \frac{19}{15}

$\frac{37}{6} - \frac{19}{15}$

\frac{37}{6} - \frac{19}{15}

$\frac{37}{6} - \frac{19}{15}$

\frac{37}{6} - \frac{19}{15}

$\frac{37}{6} - \frac{19}{15}$

Step 3

To write

\frac{37}{6}

$\frac{37}{6}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{37}{6} \cdot \frac{5}{5} - \frac{19}{15}

$\frac{37}{6} \cdot \frac{5}{5} - \frac{19}{15}$

Step 4

To write

- \frac{19}{15}

$- \frac{19}{15}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{37}{6} \cdot \frac{5}{5} - \frac{19}{15} \cdot \frac{2}{2}

$\frac{37}{6} \cdot \frac{5}{5} - \frac{19}{15} \cdot \frac{2}{2}$

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{37}{6}

$\frac{37}{6}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{37 \cdot 5}{6 \cdot 5} - \frac{19}{15} \cdot \frac{2}{2}

$\frac{37 \cdot 5}{6 \cdot 5} - \frac{19}{15} \cdot \frac{2}{2}$

Step 5.2

Multiply

6

$6$ by

5

$5$ .

\frac{37 \cdot 5}{30} - \frac{19}{15} \cdot \frac{2}{2}

$\frac{37 \cdot 5}{30} - \frac{19}{15} \cdot \frac{2}{2}$

Step 5.3

Multiply

\frac{19}{15}

$\frac{19}{15}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{15 \cdot 2}

$\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{15 \cdot 2}$

Step 5.4

Multiply

15

$15$ by

2

$2$ .

\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{30}

$\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{30}$

\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{30}

$\frac{37 \cdot 5}{30} - \frac{19 \cdot 2}{30}$

Step 6

Combine the numerators over the common denominator.

\frac{37 \cdot 5 - 19 \cdot 2}{30}

$\frac{37 \cdot 5 - 19 \cdot 2}{30}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

37

$37$ by

5

$5$ .

\frac{185 - 19 \cdot 2}{30}

$\frac{185 - 19 \cdot 2}{30}$

Step 7.2

Multiply

- 19

$- 19$ by

2

$2$ .

\frac{185 - 38}{30}

$\frac{185 - 38}{30}$

Step 7.3

Subtract

38

$38$ from

185

$185$ .

\frac{147}{30}

$\frac{147}{30}$

\frac{147}{30}

$\frac{147}{30}$

Step 8

Cancel the common factor of

147

$147$ and

30

$30$ .

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Step 8.1

Factor

3

$3$ out of

147

$147$ .

\frac{3 (49)}{30}

$\frac{3 (49)}{30}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor

3

$3$ out of

30

$30$ .

\frac{3 \cdot 49}{3 \cdot 10}

$\frac{3 \cdot 49}{3 \cdot 10}$

Step 8.2.2

Cancel the common factor.

\frac{3 \cdot 49}{3 \cdot 10}

$\frac{3 \cdot 49}{3 \cdot 10}$

Step 8.2.3

Rewrite the expression.

\frac{49}{10}

$\frac{49}{10}$

\frac{49}{10}

$\frac{49}{10}$

\frac{49}{10}

$\frac{49}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

\frac{49}{10}

$\frac{49}{10}$

Decimal Form:

4.9

$4.9$

Mixed Number Form:

4 \frac{9}{10}

$4 \frac{9}{10}$