Basic Math Examples

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

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

Step 1

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

4

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

2

$2$ .

\frac{8 + 1}{2} - 3 \frac{3}{4}

$\frac{8 + 1}{2} - 3 \frac{3}{4}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 2

Convert

3 \frac{3}{4}

$3 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

\frac{9}{2} - (3 + \frac{3}{4})

$\frac{9}{2} - (3 + \frac{3}{4})$

Step 2.2

Add

3

$3$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9}{2} - (3 \cdot \frac{4}{4} + \frac{3}{4})

$\frac{9}{2} - (3 \cdot \frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9}{2} - (\frac{3 \cdot 4}{4} + \frac{3}{4})

$\frac{9}{2} - (\frac{3 \cdot 4}{4} + \frac{3}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

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

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{9}{2} - \frac{12 + 3}{4}

$\frac{9}{2} - \frac{12 + 3}{4}$

Step 2.2.4.2

Add

12

$12$ and

3

$3$ .

\frac{9}{2} - \frac{15}{4}

$\frac{9}{2} - \frac{15}{4}$

\frac{9}{2} - \frac{15}{4}

$\frac{9}{2} - \frac{15}{4}$

\frac{9}{2} - \frac{15}{4}

$\frac{9}{2} - \frac{15}{4}$

\frac{9}{2} - \frac{15}{4}

$\frac{9}{2} - \frac{15}{4}$

Step 3

To write

\frac{9}{2}

$\frac{9}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9}{2} \cdot \frac{2}{2} - \frac{15}{4}

$\frac{9}{2} \cdot \frac{2}{2} - \frac{15}{4}$

Step 4

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{9}{2}

$\frac{9}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{9 \cdot 2}{2 \cdot 2} - \frac{15}{4}

$\frac{9 \cdot 2}{2 \cdot 2} - \frac{15}{4}$

Step 4.2

Multiply

2

$2$ by

2

$2$ .

\frac{9 \cdot 2}{4} - \frac{15}{4}

$\frac{9 \cdot 2}{4} - \frac{15}{4}$

\frac{9 \cdot 2}{4} - \frac{15}{4}

$\frac{9 \cdot 2}{4} - \frac{15}{4}$

Step 5

Combine the numerators over the common denominator.

\frac{9 \cdot 2 - 15}{4}

$\frac{9 \cdot 2 - 15}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

9

$9$ by

2

$2$ .

\frac{18 - 15}{4}

$\frac{18 - 15}{4}$

Step 6.2

Subtract

15

$15$ from

18

$18$ .

\frac{3}{4}

$\frac{3}{4}$

\frac{3}{4}

$\frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{3}{4}

$\frac{3}{4}$

Decimal Form:

0.75

$0.75$