Basic Math Examples

8 \frac{7}{8} - 3 \frac{5}{6}

$8 \frac{7}{8} - 3 \frac{5}{6}$

Step 1

Convert

8 \frac{7}{8}

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

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Step 1.1

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

8 + \frac{7}{8} - 3 \frac{5}{6}

$8 + \frac{7}{8} - 3 \frac{5}{6}$

Step 1.2

Add

8

$8$ and

\frac{7}{8}

$\frac{7}{8}$ .

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Step 1.2.1

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

8 \cdot \frac{8}{8} + \frac{7}{8} - 3 \frac{5}{6}

$8 \cdot \frac{8}{8} + \frac{7}{8} - 3 \frac{5}{6}$

Step 1.2.2

Combine

8

$8$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{8 \cdot 8}{8} + \frac{7}{8} - 3 \frac{5}{6}

$\frac{8 \cdot 8}{8} + \frac{7}{8} - 3 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{8 \cdot 8 + 7}{8} - 3 \frac{5}{6}

$\frac{8 \cdot 8 + 7}{8} - 3 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

8

$8$ by

8

$8$ .

\frac{64 + 7}{8} - 3 \frac{5}{6}

$\frac{64 + 7}{8} - 3 \frac{5}{6}$

Step 1.2.4.2

Add

64

$64$ and

7

$7$ .

\frac{71}{8} - 3 \frac{5}{6}

$\frac{71}{8} - 3 \frac{5}{6}$

\frac{71}{8} - 3 \frac{5}{6}

$\frac{71}{8} - 3 \frac{5}{6}$

\frac{71}{8} - 3 \frac{5}{6}

$\frac{71}{8} - 3 \frac{5}{6}$

\frac{71}{8} - 3 \frac{5}{6}

$\frac{71}{8} - 3 \frac{5}{6}$

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{71}{8} - (3 + \frac{5}{6})

$\frac{71}{8} - (3 + \frac{5}{6})$

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{71}{8} - (3 \cdot \frac{6}{6} + \frac{5}{6})

$\frac{71}{8} - (3 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

3

$3$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{71}{8} - (\frac{3 \cdot 6}{6} + \frac{5}{6})

$\frac{71}{8} - (\frac{3 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{71}{8} - \frac{3 \cdot 6 + 5}{6}

$\frac{71}{8} - \frac{3 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

6

$6$ .

\frac{71}{8} - \frac{18 + 5}{6}

$\frac{71}{8} - \frac{18 + 5}{6}$

Step 2.2.4.2

Add

18

$18$ and

5

$5$ .

\frac{71}{8} - \frac{23}{6}

$\frac{71}{8} - \frac{23}{6}$

\frac{71}{8} - \frac{23}{6}

$\frac{71}{8} - \frac{23}{6}$

\frac{71}{8} - \frac{23}{6}

$\frac{71}{8} - \frac{23}{6}$

\frac{71}{8} - \frac{23}{6}

$\frac{71}{8} - \frac{23}{6}$

Step 3

To write

\frac{71}{8}

$\frac{71}{8}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{71}{8} \cdot \frac{3}{3} - \frac{23}{6}

$\frac{71}{8} \cdot \frac{3}{3} - \frac{23}{6}$

Step 4

To write

- \frac{23}{6}

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{71}{8} \cdot \frac{3}{3} - \frac{23}{6} \cdot \frac{4}{4}

$\frac{71}{8} \cdot \frac{3}{3} - \frac{23}{6} \cdot \frac{4}{4}$

Step 5

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 5.1

Multiply

\frac{71}{8}

$\frac{71}{8}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{71 \cdot 3}{8 \cdot 3} - \frac{23}{6} \cdot \frac{4}{4}

$\frac{71 \cdot 3}{8 \cdot 3} - \frac{23}{6} \cdot \frac{4}{4}$

Step 5.2

Multiply

8

$8$ by

3

$3$ .

\frac{71 \cdot 3}{24} - \frac{23}{6} \cdot \frac{4}{4}

$\frac{71 \cdot 3}{24} - \frac{23}{6} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{23}{6}

$\frac{23}{6}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{6 \cdot 4}

$\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{6 \cdot 4}$

Step 5.4

Multiply

6

$6$ by

4

$4$ .

\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{24}

$\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{24}$

\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{24}

$\frac{71 \cdot 3}{24} - \frac{23 \cdot 4}{24}$

Step 6

Combine the numerators over the common denominator.

\frac{71 \cdot 3 - 23 \cdot 4}{24}

$\frac{71 \cdot 3 - 23 \cdot 4}{24}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

71

$71$ by

3

$3$ .

\frac{213 - 23 \cdot 4}{24}

$\frac{213 - 23 \cdot 4}{24}$

Step 7.2

Multiply

- 23

$- 23$ by

4

$4$ .

\frac{213 - 92}{24}

$\frac{213 - 92}{24}$

Step 7.3

Subtract

92

$92$ from

213

$213$ .

\frac{121}{24}

$\frac{121}{24}$

\frac{121}{24}

$\frac{121}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{121}{24}

$\frac{121}{24}$

Decimal Form:

5.041 ¯ 6

$5.041\overline{6}$

Mixed Number Form:

5 \frac{1}{24}

$5 \frac{1}{24}$