Basic Math Examples

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

$5 \frac{3}{4} - 3 \frac{1}{2}$

Step 1

Convert

5 \frac{3}{4}

$5 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

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

$5 + \frac{3}{4} - 3 \frac{1}{2}$

Step 1.2

Add

5

$5$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

5

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

\frac{4}{4}

$\frac{4}{4}$ .

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

$5 \cdot \frac{4}{4} + \frac{3}{4} - 3 \frac{1}{2}$

Step 1.2.2

Combine

5

$5$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5 \cdot 4}{4} + \frac{3}{4} - 3 \frac{1}{2}

$\frac{5 \cdot 4}{4} + \frac{3}{4} - 3 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 4 + 3}{4} - 3 \frac{1}{2}

$\frac{5 \cdot 4 + 3}{4} - 3 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

4

$4$ .

\frac{20 + 3}{4} - 3 \frac{1}{2}

$\frac{20 + 3}{4} - 3 \frac{1}{2}$

Step 1.2.4.2

Add

20

$20$ and

3

$3$ .

\frac{23}{4} - 3 \frac{1}{2}

$\frac{23}{4} - 3 \frac{1}{2}$

\frac{23}{4} - 3 \frac{1}{2}

$\frac{23}{4} - 3 \frac{1}{2}$

\frac{23}{4} - 3 \frac{1}{2}

$\frac{23}{4} - 3 \frac{1}{2}$

\frac{23}{4} - 3 \frac{1}{2}

$\frac{23}{4} - 3 \frac{1}{2}$

Step 2

Convert

3 \frac{1}{2}

$3 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

\frac{23}{4} - (3 + \frac{1}{2})

$\frac{23}{4} - (3 + \frac{1}{2})$

Step 2.2

Add

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

3

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{4} - (3 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{23}{4} - (3 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{4} - (\frac{3 \cdot 2}{2} + \frac{1}{2})

$\frac{23}{4} - (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{23}{4} - \frac{3 \cdot 2 + 1}{2}

$\frac{23}{4} - \frac{3 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

2

$2$ .

\frac{23}{4} - \frac{6 + 1}{2}

$\frac{23}{4} - \frac{6 + 1}{2}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{23}{4} - \frac{7}{2}

$\frac{23}{4} - \frac{7}{2}$

\frac{23}{4} - \frac{7}{2}

$\frac{23}{4} - \frac{7}{2}$

\frac{23}{4} - \frac{7}{2}

$\frac{23}{4} - \frac{7}{2}$

\frac{23}{4} - \frac{7}{2}

$\frac{23}{4} - \frac{7}{2}$

Step 3

To write

- \frac{7}{2}

$- \frac{7}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{4} - \frac{7}{2} \cdot \frac{2}{2}

$\frac{23}{4} - \frac{7}{2} \cdot \frac{2}{2}$

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{7}{2}

$\frac{7}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{23}{4} - \frac{7 \cdot 2}{2 \cdot 2}

$\frac{23}{4} - \frac{7 \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply

2

$2$ by

2

$2$ .

\frac{23}{4} - \frac{7 \cdot 2}{4}

$\frac{23}{4} - \frac{7 \cdot 2}{4}$

\frac{23}{4} - \frac{7 \cdot 2}{4}

$\frac{23}{4} - \frac{7 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

\frac{23 - 7 \cdot 2}{4}

$\frac{23 - 7 \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 7

$- 7$ by

2

$2$ .

\frac{23 - 14}{4}

$\frac{23 - 14}{4}$

Step 6.2

Subtract

14

$14$ from

23

$23$ .

\frac{9}{4}

$\frac{9}{4}$

\frac{9}{4}

$\frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{9}{4}

$\frac{9}{4}$

Decimal Form:

2.25

$2.25$

Mixed Number Form:

2 \frac{1}{4}

$2 \frac{1}{4}$