Basic Math Examples

5 \frac{11}{12} - 4 \frac{1}{8}

$5 \frac{11}{12} - 4 \frac{1}{8}$

Step 1

Convert

5 \frac{11}{12}

$5 \frac{11}{12}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

5 + \frac{11}{12} - 4 \frac{1}{8}

$5 + \frac{11}{12} - 4 \frac{1}{8}$

Step 1.2

Add

5

$5$ and

\frac{11}{12}

$\frac{11}{12}$ .

Tap for more steps...

Step 1.2.1

To write

5

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

\frac{12}{12}

$\frac{12}{12}$ .

5 \cdot \frac{12}{12} + \frac{11}{12} - 4 \frac{1}{8}

$5 \cdot \frac{12}{12} + \frac{11}{12} - 4 \frac{1}{8}$

Step 1.2.2

Combine

5

$5$ and

\frac{12}{12}

$\frac{12}{12}$ .

\frac{5 \cdot 12}{12} + \frac{11}{12} - 4 \frac{1}{8}

$\frac{5 \cdot 12}{12} + \frac{11}{12} - 4 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 12 + 11}{12} - 4 \frac{1}{8}

$\frac{5 \cdot 12 + 11}{12} - 4 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

5

$5$ by

12

$12$ .

\frac{60 + 11}{12} - 4 \frac{1}{8}

$\frac{60 + 11}{12} - 4 \frac{1}{8}$

Step 1.2.4.2

Add

60

$60$ and

11

$11$ .

\frac{71}{12} - 4 \frac{1}{8}

$\frac{71}{12} - 4 \frac{1}{8}$

\frac{71}{12} - 4 \frac{1}{8}

$\frac{71}{12} - 4 \frac{1}{8}$

\frac{71}{12} - 4 \frac{1}{8}

$\frac{71}{12} - 4 \frac{1}{8}$

\frac{71}{12} - 4 \frac{1}{8}

$\frac{71}{12} - 4 \frac{1}{8}$

Step 2

Convert

4 \frac{1}{8}

$4 \frac{1}{8}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

\frac{71}{12} - (4 + \frac{1}{8})

$\frac{71}{12} - (4 + \frac{1}{8})$

Step 2.2

Add

4

$4$ and

\frac{1}{8}

$\frac{1}{8}$ .

Tap for more steps...

Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{71}{12} - (4 \cdot \frac{8}{8} + \frac{1}{8})

$\frac{71}{12} - (4 \cdot \frac{8}{8} + \frac{1}{8})$

Step 2.2.2

Combine

4

$4$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{71}{12} - (\frac{4 \cdot 8}{8} + \frac{1}{8})

$\frac{71}{12} - (\frac{4 \cdot 8}{8} + \frac{1}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{71}{12} - \frac{4 \cdot 8 + 1}{8}

$\frac{71}{12} - \frac{4 \cdot 8 + 1}{8}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

4

$4$ by

8

$8$ .

\frac{71}{12} - \frac{32 + 1}{8}

$\frac{71}{12} - \frac{32 + 1}{8}$

Step 2.2.4.2

Add

32

$32$ and

1

$1$ .

\frac{71}{12} - \frac{33}{8}

$\frac{71}{12} - \frac{33}{8}$

\frac{71}{12} - \frac{33}{8}

$\frac{71}{12} - \frac{33}{8}$

\frac{71}{12} - \frac{33}{8}

$\frac{71}{12} - \frac{33}{8}$

\frac{71}{12} - \frac{33}{8}

$\frac{71}{12} - \frac{33}{8}$

Step 3

To write

\frac{71}{12}

$\frac{71}{12}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{71}{12} \cdot \frac{2}{2} - \frac{33}{8}

$\frac{71}{12} \cdot \frac{2}{2} - \frac{33}{8}$

Step 4

To write

- \frac{33}{8}

$- \frac{33}{8}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{71}{12} \cdot \frac{2}{2} - \frac{33}{8} \cdot \frac{3}{3}

$\frac{71}{12} \cdot \frac{2}{2} - \frac{33}{8} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

24

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

1

$1$ .

Tap for more steps...

Step 5.1

Multiply

\frac{71}{12}

$\frac{71}{12}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{71 \cdot 2}{12 \cdot 2} - \frac{33}{8} \cdot \frac{3}{3}

$\frac{71 \cdot 2}{12 \cdot 2} - \frac{33}{8} \cdot \frac{3}{3}$

Step 5.2

Multiply

12

$12$ by

2

$2$ .

\frac{71 \cdot 2}{24} - \frac{33}{8} \cdot \frac{3}{3}

$\frac{71 \cdot 2}{24} - \frac{33}{8} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{33}{8}

$\frac{33}{8}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{8 \cdot 3}

$\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{8 \cdot 3}$

Step 5.4

Multiply

8

$8$ by

3

$3$ .

\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{24}

$\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{24}$

\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{24}

$\frac{71 \cdot 2}{24} - \frac{33 \cdot 3}{24}$

Step 6

Combine the numerators over the common denominator.

\frac{71 \cdot 2 - 33 \cdot 3}{24}

$\frac{71 \cdot 2 - 33 \cdot 3}{24}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply

71

$71$ by

2

$2$ .

\frac{142 - 33 \cdot 3}{24}

$\frac{142 - 33 \cdot 3}{24}$

Step 7.2

Multiply

- 33

$- 33$ by

3

$3$ .

\frac{142 - 99}{24}

$\frac{142 - 99}{24}$

Step 7.3

Subtract

99

$99$ from

142

$142$ .

\frac{43}{24}

$\frac{43}{24}$

\frac{43}{24}

$\frac{43}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{43}{24}

$\frac{43}{24}$

Decimal Form:

1.791 ¯ 6

$1.791\overline{6}$

Mixed Number Form:

1 \frac{19}{24}

$1 \frac{19}{24}$