Simplify 4 1/2-3 2/3

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

Step 1

Convert

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

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

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

Add

$4$ and

$\frac{1}{2}$ .

To write

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

$\frac{2}{2}$ .

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

Combine

$4$ and

$\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$2$ .

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

Add

$8$ and

$1$ .

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

Step 2

Convert

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

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

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

Add

$3$ and

$\frac{2}{3}$ .

To write

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

$\frac{3}{3}$ .

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

Combine

$3$ and

$\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$3$ by

$3$ .

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

Add

$9$ and

$2$ .

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

Step 3

To write

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

$\frac{3}{3}$ .

$\frac{9}{2} \cdot \frac{3}{3} - \frac{11}{3}$

Step 4

To write

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

$\frac{2}{2}$ .

$\frac{9}{2} \cdot \frac{3}{3} - \frac{11}{3} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{9}{2}$ by

$\frac{3}{3}$ .

$\frac{9 \cdot 3}{2 \cdot 3} - \frac{11}{3} \cdot \frac{2}{2}$

Multiply

$2$ by

$3$ .

$\frac{9 \cdot 3}{6} - \frac{11}{3} \cdot \frac{2}{2}$

Multiply

$\frac{11}{3}$ by

$\frac{2}{2}$ .

$\frac{9 \cdot 3}{6} - \frac{11 \cdot 2}{3 \cdot 2}$

Multiply

$3$ by

$2$ .

$\frac{9 \cdot 3}{6} - \frac{11 \cdot 2}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - 11 \cdot 2}{6}$

Step 7

Simplify the numerator.

Multiply

$9$ by

$3$ .

$\frac{27 - 11 \cdot 2}{6}$

Multiply

$- 11$ by

$2$ .

$\frac{27 - 22}{6}$

Subtract

$22$ from

$27$ .

$\frac{5}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$

Simplify 4 1/2-3 2/3

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