Basic Math Examples

2 \frac{2}{3} - \frac{1}{4}

$2 \frac{2}{3} - \frac{1}{4}$

Step 1

Convert

2 \frac{2}{3}

$2 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

2 + \frac{2}{3} - \frac{1}{4}

$2 + \frac{2}{3} - \frac{1}{4}$

Step 1.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

2 \cdot \frac{3}{3} + \frac{2}{3} - \frac{1}{4}

$2 \cdot \frac{3}{3} + \frac{2}{3} - \frac{1}{4}$

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 \cdot 3}{3} + \frac{2}{3} - \frac{1}{4}

$\frac{2 \cdot 3}{3} + \frac{2}{3} - \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 3 + 2}{3} - \frac{1}{4}

$\frac{2 \cdot 3 + 2}{3} - \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 2}{3} - \frac{1}{4}

$\frac{6 + 2}{3} - \frac{1}{4}$

Step 1.2.4.2

Add

6

$6$ and

2

$2$ .

\frac{8}{3} - \frac{1}{4}

$\frac{8}{3} - \frac{1}{4}$

\frac{8}{3} - \frac{1}{4}

$\frac{8}{3} - \frac{1}{4}$

\frac{8}{3} - \frac{1}{4}

$\frac{8}{3} - \frac{1}{4}$

\frac{8}{3} - \frac{1}{4}

$\frac{8}{3} - \frac{1}{4}$

Step 2

To write

\frac{8}{3}

$\frac{8}{3}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 3

To write

- \frac{1}{4}

$- \frac{1}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4

Write each expression with a common denominator of

12

$12$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{8}{3}

$\frac{8}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 4.2

Multiply

3

$3$ by

4

$4$ .

\frac{8 \cdot 4}{12} - \frac{1}{4} \cdot \frac{3}{3}

$\frac{8 \cdot 4}{12} - \frac{1}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{8 \cdot 4}{12} - \frac{3}{4 \cdot 3}

$\frac{8 \cdot 4}{12} - \frac{3}{4 \cdot 3}$

Step 4.4

Multiply

4

$4$ by

3

$3$ .

\frac{8 \cdot 4}{12} - \frac{3}{12}

$\frac{8 \cdot 4}{12} - \frac{3}{12}$

\frac{8 \cdot 4}{12} - \frac{3}{12}

$\frac{8 \cdot 4}{12} - \frac{3}{12}$

Step 5

Combine the numerators over the common denominator.

\frac{8 \cdot 4 - 3}{12}

$\frac{8 \cdot 4 - 3}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

8

$8$ by

4

$4$ .

\frac{32 - 3}{12}

$\frac{32 - 3}{12}$

Step 6.2

Subtract

3

$3$ from

32

$32$ .

\frac{29}{12}

$\frac{29}{12}$

\frac{29}{12}

$\frac{29}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{29}{12}

$\frac{29}{12}$

Decimal Form:

2.41 ¯ 6

$2.41\overline{6}$

Mixed Number Form:

2 \frac{5}{12}

$2 \frac{5}{12}$