Basic Math Examples

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

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

Step 1

Convert

2 \frac{3}{4}

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

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

Step 1.2

Add

2

$2$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{8 + 3}{4} - 3 \frac{2}{3}

$\frac{8 + 3}{4} - 3 \frac{2}{3}$

Step 1.2.4.2

Add

8

$8$ and

3

$3$ .

\frac{11}{4} - 3 \frac{2}{3}

$\frac{11}{4} - 3 \frac{2}{3}$

\frac{11}{4} - 3 \frac{2}{3}

$\frac{11}{4} - 3 \frac{2}{3}$

\frac{11}{4} - 3 \frac{2}{3}

$\frac{11}{4} - 3 \frac{2}{3}$

\frac{11}{4} - 3 \frac{2}{3}

$\frac{11}{4} - 3 \frac{2}{3}$

Step 2

Convert

3 \frac{2}{3}

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

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Step 2.1

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

\frac{11}{4} - (3 + \frac{2}{3})

$\frac{11}{4} - (3 + \frac{2}{3})$

Step 2.2

Add

3

$3$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11}{4} - (3 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{11}{4} - (3 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11}{4} - (\frac{3 \cdot 3}{3} + \frac{2}{3})

$\frac{11}{4} - (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{11}{4} - \frac{3 \cdot 3 + 2}{3}

$\frac{11}{4} - \frac{3 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{11}{4} - \frac{9 + 2}{3}

$\frac{11}{4} - \frac{9 + 2}{3}$

Step 2.2.4.2

Add

9

$9$ and

2

$2$ .

\frac{11}{4} - \frac{11}{3}

$\frac{11}{4} - \frac{11}{3}$

\frac{11}{4} - \frac{11}{3}

$\frac{11}{4} - \frac{11}{3}$

\frac{11}{4} - \frac{11}{3}

$\frac{11}{4} - \frac{11}{3}$

\frac{11}{4} - \frac{11}{3}

$\frac{11}{4} - \frac{11}{3}$

Step 3

To write

\frac{11}{4}

$\frac{11}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11}{4} \cdot \frac{3}{3} - \frac{11}{3}

$\frac{11}{4} \cdot \frac{3}{3} - \frac{11}{3}$

Step 4

To write

- \frac{11}{3}

$- \frac{11}{3}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11}{4} \cdot \frac{3}{3} - \frac{11}{3} \cdot \frac{4}{4}

$\frac{11}{4} \cdot \frac{3}{3} - \frac{11}{3} \cdot \frac{4}{4}$

Step 5

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 5.1

Multiply

\frac{11}{4}

$\frac{11}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{11 \cdot 3}{4 \cdot 3} - \frac{11}{3} \cdot \frac{4}{4}

$\frac{11 \cdot 3}{4 \cdot 3} - \frac{11}{3} \cdot \frac{4}{4}$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

\frac{11 \cdot 3}{12} - \frac{11}{3} \cdot \frac{4}{4}

$\frac{11 \cdot 3}{12} - \frac{11}{3} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{11}{3}

$\frac{11}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{3 \cdot 4}

$\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{3 \cdot 4}$

Step 5.4

Multiply

3

$3$ by

4

$4$ .

\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{12}

$\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{12}$

\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{12}

$\frac{11 \cdot 3}{12} - \frac{11 \cdot 4}{12}$

Step 6

Combine the numerators over the common denominator.

\frac{11 \cdot 3 - 11 \cdot 4}{12}

$\frac{11 \cdot 3 - 11 \cdot 4}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

11

$11$ by

3

$3$ .

\frac{33 - 11 \cdot 4}{12}

$\frac{33 - 11 \cdot 4}{12}$

Step 7.2

Multiply

- 11

$- 11$ by

4

$4$ .

\frac{33 - 44}{12}

$\frac{33 - 44}{12}$

Step 7.3

Subtract

44

$44$ from

33

$33$ .

\frac{- 11}{12}

$\frac{- 11}{12}$

\frac{- 11}{12}

$\frac{- 11}{12}$

Step 8

Move the negative in front of the fraction.

- \frac{11}{12}

$- \frac{11}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

- \frac{11}{12}

$- \frac{11}{12}$

Decimal Form:

- 0.91\overline{6}

$- 0.91\overline{6}$