Basic Math Examples

6 \frac{1}{6} - 6 \frac{3}{10}

$6 \frac{1}{6} - 6 \frac{3}{10}$

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} - 6 \frac{3}{10}

$6 + \frac{1}{6} - 6 \frac{3}{10}$

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} - 6 \frac{3}{10}

$6 \cdot \frac{6}{6} + \frac{1}{6} - 6 \frac{3}{10}$

Step 1.2.2

Combine

6

$6$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{6 \cdot 6}{6} + \frac{1}{6} - 6 \frac{3}{10}

$\frac{6 \cdot 6}{6} + \frac{1}{6} - 6 \frac{3}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 6 + 1}{6} - 6 \frac{3}{10}

$\frac{6 \cdot 6 + 1}{6} - 6 \frac{3}{10}$

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} - 6 \frac{3}{10}

$\frac{36 + 1}{6} - 6 \frac{3}{10}$

Step 1.2.4.2

Add

36

$36$ and

1

$1$ .

\frac{37}{6} - 6 \frac{3}{10}

$\frac{37}{6} - 6 \frac{3}{10}$

\frac{37}{6} - 6 \frac{3}{10}

$\frac{37}{6} - 6 \frac{3}{10}$

\frac{37}{6} - 6 \frac{3}{10}

$\frac{37}{6} - 6 \frac{3}{10}$

\frac{37}{6} - 6 \frac{3}{10}

$\frac{37}{6} - 6 \frac{3}{10}$

Step 2

Convert

6 \frac{3}{10}

$6 \frac{3}{10}$ 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} - (6 + \frac{3}{10})

$\frac{37}{6} - (6 + \frac{3}{10})$

Step 2.2

Add

6

$6$ and

\frac{3}{10}

$\frac{3}{10}$ .

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Step 2.2.1

To write

6

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

\frac{10}{10}

$\frac{10}{10}$ .

\frac{37}{6} - (6 \cdot \frac{10}{10} + \frac{3}{10})

$\frac{37}{6} - (6 \cdot \frac{10}{10} + \frac{3}{10})$

Step 2.2.2

Combine

6

$6$ and

\frac{10}{10}

$\frac{10}{10}$ .

\frac{37}{6} - (\frac{6 \cdot 10}{10} + \frac{3}{10})

$\frac{37}{6} - (\frac{6 \cdot 10}{10} + \frac{3}{10})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{37}{6} - \frac{6 \cdot 10 + 3}{10}

$\frac{37}{6} - \frac{6 \cdot 10 + 3}{10}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

6

$6$ by

10

$10$ .

\frac{37}{6} - \frac{60 + 3}{10}

$\frac{37}{6} - \frac{60 + 3}{10}$

Step 2.2.4.2

Add

60

$60$ and

3

$3$ .

\frac{37}{6} - \frac{63}{10}

$\frac{37}{6} - \frac{63}{10}$

\frac{37}{6} - \frac{63}{10}

$\frac{37}{6} - \frac{63}{10}$

\frac{37}{6} - \frac{63}{10}

$\frac{37}{6} - \frac{63}{10}$

\frac{37}{6} - \frac{63}{10}

$\frac{37}{6} - \frac{63}{10}$

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{63}{10}

$\frac{37}{6} \cdot \frac{5}{5} - \frac{63}{10}$

Step 4

To write

- \frac{63}{10}

$- \frac{63}{10}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{37}{6} \cdot \frac{5}{5} - \frac{63}{10} \cdot \frac{3}{3}

$\frac{37}{6} \cdot \frac{5}{5} - \frac{63}{10} \cdot \frac{3}{3}$

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{63}{10} \cdot \frac{3}{3}

$\frac{37 \cdot 5}{6 \cdot 5} - \frac{63}{10} \cdot \frac{3}{3}$

Step 5.2

Multiply

6

$6$ by

5

$5$ .

\frac{37 \cdot 5}{30} - \frac{63}{10} \cdot \frac{3}{3}

$\frac{37 \cdot 5}{30} - \frac{63}{10} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{63}{10}

$\frac{63}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{10 \cdot 3}

$\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{10 \cdot 3}$

Step 5.4

Multiply

10

$10$ by

3

$3$ .

\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{30}

$\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{30}$

\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{30}

$\frac{37 \cdot 5}{30} - \frac{63 \cdot 3}{30}$

Step 6

Combine the numerators over the common denominator.

\frac{37 \cdot 5 - 63 \cdot 3}{30}

$\frac{37 \cdot 5 - 63 \cdot 3}{30}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

37

$37$ by

5

$5$ .

\frac{185 - 63 \cdot 3}{30}

$\frac{185 - 63 \cdot 3}{30}$

Step 7.2

Multiply

- 63

$- 63$ by

3

$3$ .

\frac{185 - 189}{30}

$\frac{185 - 189}{30}$

Step 7.3

Subtract

189

$189$ from

185

$185$ .

\frac{- 4}{30}

$\frac{- 4}{30}$

\frac{- 4}{30}

$\frac{- 4}{30}$

Step 8

Cancel the common factor of

- 4

$- 4$ and

30

$30$ .

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Step 8.1

Factor

2

$2$ out of

- 4

$- 4$ .

\frac{2 (- 2)}{30}

$\frac{2 (- 2)}{30}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor

2

$2$ out of

30

$30$ .

\frac{2 \cdot - 2}{2 \cdot 15}

$\frac{2 \cdot - 2}{2 \cdot 15}$

Step 8.2.2

Cancel the common factor.

$\frac{2 \cdot - 2}{2 \cdot 15}$

Step 8.2.3

Rewrite the expression.

$\frac{- 2}{15}$

Step 9

Move the negative in front of the fraction.

$- \frac{2}{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{15}$

Decimal Form:

$- 0.1\overline{3}$