Basic Math Examples

4 \frac{1}{2} - 3 \frac{1}{12}

$4 \frac{1}{2} - 3 \frac{1}{12}$

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{1}{12}

$4 + \frac{1}{2} - 3 \frac{1}{12}$

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{1}{12}

$4 \cdot \frac{2}{2} + \frac{1}{2} - 3 \frac{1}{12}$

Step 1.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{4 \cdot 2}{2} + \frac{1}{2} - 3 \frac{1}{12}

$\frac{4 \cdot 2}{2} + \frac{1}{2} - 3 \frac{1}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{4 \cdot 2 + 1}{2} - 3 \frac{1}{12}

$\frac{4 \cdot 2 + 1}{2} - 3 \frac{1}{12}$

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{1}{12}

$\frac{8 + 1}{2} - 3 \frac{1}{12}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{2} - 3 \frac{1}{12}

$\frac{9}{2} - 3 \frac{1}{12}$

\frac{9}{2} - 3 \frac{1}{12}

$\frac{9}{2} - 3 \frac{1}{12}$

\frac{9}{2} - 3 \frac{1}{12}

$\frac{9}{2} - 3 \frac{1}{12}$

\frac{9}{2} - 3 \frac{1}{12}

$\frac{9}{2} - 3 \frac{1}{12}$

Step 2

Convert

3 \frac{1}{12}

$3 \frac{1}{12}$ 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{1}{12})

$\frac{9}{2} - (3 + \frac{1}{12})$

Step 2.2

Add

$3$ and

$\frac{1}{12}$ .

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Step 2.2.1

To write

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

$\frac{12}{12}$ .

$\frac{9}{2} - (3 \cdot \frac{12}{12} + \frac{1}{12})$

Step 2.2.2

Combine

$3$ and

$\frac{12}{12}$ .

$\frac{9}{2} - (\frac{3 \cdot 12}{12} + \frac{1}{12})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{3 \cdot 12 + 1}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$12$ .

$\frac{9}{2} - \frac{36 + 1}{12}$

Step 2.2.4.2

Add

$36$ and

$1$ .

$\frac{9}{2} - \frac{37}{12}$

Step 3

To write

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

$\frac{6}{6}$ .

$\frac{9}{2} \cdot \frac{6}{6} - \frac{37}{12}$

Step 4

Write each expression with a common denominator of

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

$1$ .

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Step 4.1

Multiply

$\frac{9}{2}$ by

$\frac{6}{6}$ .

$\frac{9 \cdot 6}{2 \cdot 6} - \frac{37}{12}$

Step 4.2

Multiply

$2$ by

$6$ .

$\frac{9 \cdot 6}{12} - \frac{37}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 6 - 37}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$9$ by

$6$ .

$\frac{54 - 37}{12}$

Step 6.2

Subtract

$37$ from

$54$ .

$\frac{17}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{12}$

Decimal Form:

$1.41\overline{6}$

Mixed Number Form:

$1 \frac{5}{12}$