Simplify 4 1/2-3 1/12

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

Step 1

Convert

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

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

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

Add

$4$ and

$\frac{1}{2}$ .

To write

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

$\frac{2}{2}$ .

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

Combine

$4$ and

$\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$2$ .

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

Add

$8$ and

$1$ .

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

Step 2

Convert

$3 \frac{1}{12}$ to an improper fraction.

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

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

Add

$3$ and

$\frac{1}{12}$ .

To write

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

$\frac{12}{12}$ .

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

Combine

$3$ and

$\frac{12}{12}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$3$ by

$12$ .

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

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

$1$ .

Multiply

$\frac{9}{2}$ by

$\frac{6}{6}$ .

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

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.

Multiply

$9$ by

$6$ .

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

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:

$1 \frac{5}{12}$

Simplify 4 1/2-3 1/12

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