Basic Math Examples

\frac{23}{30} - \frac{11}{20}

$\frac{23}{30} - \frac{11}{20}$

Step 1

To write

\frac{23}{30}

$\frac{23}{30}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{30} \cdot \frac{2}{2} - \frac{11}{20}

$\frac{23}{30} \cdot \frac{2}{2} - \frac{11}{20}$

Step 2

To write

- \frac{11}{20}

$- \frac{11}{20}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{23}{30} \cdot \frac{2}{2} - \frac{11}{20} \cdot \frac{3}{3}

$\frac{23}{30} \cdot \frac{2}{2} - \frac{11}{20} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

60

$60$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{23}{30}

$\frac{23}{30}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23 \cdot 2}{30 \cdot 2} - \frac{11}{20} \cdot \frac{3}{3}

$\frac{23 \cdot 2}{30 \cdot 2} - \frac{11}{20} \cdot \frac{3}{3}$

Step 3.2

Multiply

30

$30$ by

2

$2$ .

\frac{23 \cdot 2}{60} - \frac{11}{20} \cdot \frac{3}{3}

$\frac{23 \cdot 2}{60} - \frac{11}{20} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{11}{20}

$\frac{11}{20}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{20 \cdot 3}

$\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{20 \cdot 3}$

Step 3.4

Multiply

20

$20$ by

3

$3$ .

\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{60}

$\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{60}$

\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{60}

$\frac{23 \cdot 2}{60} - \frac{11 \cdot 3}{60}$

Step 4

Combine the numerators over the common denominator.

\frac{23 \cdot 2 - 11 \cdot 3}{60}

$\frac{23 \cdot 2 - 11 \cdot 3}{60}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

23

$23$ by

2

$2$ .

\frac{46 - 11 \cdot 3}{60}

$\frac{46 - 11 \cdot 3}{60}$

Step 5.2

Multiply

- 11

$- 11$ by

3

$3$ .

\frac{46 - 33}{60}

$\frac{46 - 33}{60}$

Step 5.3

Subtract

33

$33$ from

46

$46$ .

\frac{13}{60}

$\frac{13}{60}$

\frac{13}{60}

$\frac{13}{60}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{13}{60}

$\frac{13}{60}$

Decimal Form:

0.21 ¯ 6

$0.21\overline{6}$