Basic Math Examples

\frac{1}{6} - 6 \frac{7}{8}

$\frac{1}{6} - 6 \frac{7}{8}$

Step 1

Convert

6 \frac{7}{8}

$6 \frac{7}{8}$ to an improper fraction.

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Step 1.1

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

\frac{1}{6} - (6 + \frac{7}{8})

$\frac{1}{6} - (6 + \frac{7}{8})$

Step 1.2

Add

6

$6$ and

\frac{7}{8}

$\frac{7}{8}$ .

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Step 1.2.1

To write

6

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

\frac{8}{8}

$\frac{8}{8}$ .

\frac{1}{6} - (6 \cdot \frac{8}{8} + \frac{7}{8})

$\frac{1}{6} - (6 \cdot \frac{8}{8} + \frac{7}{8})$

Step 1.2.2

Combine

6

$6$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{1}{6} - (\frac{6 \cdot 8}{8} + \frac{7}{8})

$\frac{1}{6} - (\frac{6 \cdot 8}{8} + \frac{7}{8})$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{1}{6} - \frac{6 \cdot 8 + 7}{8}

$\frac{1}{6} - \frac{6 \cdot 8 + 7}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

8

$8$ .

\frac{1}{6} - \frac{48 + 7}{8}

$\frac{1}{6} - \frac{48 + 7}{8}$

Step 1.2.4.2

Add

48

$48$ and

7

$7$ .

\frac{1}{6} - \frac{55}{8}

$\frac{1}{6} - \frac{55}{8}$

\frac{1}{6} - \frac{55}{8}

$\frac{1}{6} - \frac{55}{8}$

\frac{1}{6} - \frac{55}{8}

$\frac{1}{6} - \frac{55}{8}$

\frac{1}{6} - \frac{55}{8}

$\frac{1}{6} - \frac{55}{8}$

Step 2

To write

\frac{1}{6}

$\frac{1}{6}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{1}{6} \cdot \frac{4}{4} - \frac{55}{8}

$\frac{1}{6} \cdot \frac{4}{4} - \frac{55}{8}$

Step 3

To write

- \frac{55}{8}

$- \frac{55}{8}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{6} \cdot \frac{4}{4} - \frac{55}{8} \cdot \frac{3}{3}

$\frac{1}{6} \cdot \frac{4}{4} - \frac{55}{8} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of

24

$24$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{4}{6 \cdot 4} - \frac{55}{8} \cdot \frac{3}{3}

$\frac{4}{6 \cdot 4} - \frac{55}{8} \cdot \frac{3}{3}$

Step 4.2

Multiply

6

$6$ by

4

$4$ .

\frac{4}{24} - \frac{55}{8} \cdot \frac{3}{3}

$\frac{4}{24} - \frac{55}{8} \cdot \frac{3}{3}$

Step 4.3

Multiply

\frac{55}{8}

$\frac{55}{8}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{4}{24} - \frac{55 \cdot 3}{8 \cdot 3}

$\frac{4}{24} - \frac{55 \cdot 3}{8 \cdot 3}$

Step 4.4

Multiply

8

$8$ by

3

$3$ .

\frac{4}{24} - \frac{55 \cdot 3}{24}

$\frac{4}{24} - \frac{55 \cdot 3}{24}$

\frac{4}{24} - \frac{55 \cdot 3}{24}

$\frac{4}{24} - \frac{55 \cdot 3}{24}$

Step 5

Combine the numerators over the common denominator.

\frac{4 - 55 \cdot 3}{24}

$\frac{4 - 55 \cdot 3}{24}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 55

$- 55$ by

3

$3$ .

\frac{4 - 165}{24}

$\frac{4 - 165}{24}$

Step 6.2

Subtract

165

$165$ from

4

$4$ .

\frac{- 161}{24}

$\frac{- 161}{24}$

\frac{- 161}{24}

$\frac{- 161}{24}$

Step 7

Move the negative in front of the fraction.

- \frac{161}{24}

$- \frac{161}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

- \frac{161}{24}

$- \frac{161}{24}$

Decimal Form:

- 6.708 ¯ 3

$- 6.708\overline{3}$

Mixed Number Form:

- 6 \frac{17}{24}

$- 6 \frac{17}{24}$