Simplify 4 2/3-1 1/2

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

Step 1

Convert

$4 \frac{2}{3}$ to an improper fraction.

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

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

Add

$4$ and

$\frac{2}{3}$ .

To write

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

$\frac{3}{3}$ .

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

Combine

$4$ and

$\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$3$ .

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

Add

$12$ and

$2$ .

$\frac{14}{3} - 1 \frac{1}{2}$

Step 2

Convert

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

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

$\frac{14}{3} - (1 + \frac{1}{2})$

Add

$1$ and

$\frac{1}{2}$ .

Write

$1$ as a fraction with a common denominator.

$\frac{14}{3} - (\frac{2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{14}{3} - \frac{2 + 1}{2}$

Add

$2$ and

$1$ .

$\frac{14}{3} - \frac{3}{2}$

Step 3

To write

$\frac{14}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{14}{3} \cdot \frac{2}{2} - \frac{3}{2}$

Step 4

To write

$- \frac{3}{2}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{14}{3} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{14}{3}$ by

$\frac{2}{2}$ .

$\frac{14 \cdot 2}{3 \cdot 2} - \frac{3}{2} \cdot \frac{3}{3}$

Multiply

$3$ by

$2$ .

$\frac{14 \cdot 2}{6} - \frac{3}{2} \cdot \frac{3}{3}$

Multiply

$\frac{3}{2}$ by

$\frac{3}{3}$ .

$\frac{14 \cdot 2}{6} - \frac{3 \cdot 3}{2 \cdot 3}$

Multiply

$2$ by

$3$ .

$\frac{14 \cdot 2}{6} - \frac{3 \cdot 3}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{14 \cdot 2 - 3 \cdot 3}{6}$

Step 7

Simplify the numerator.

Multiply

$14$ by

$2$ .

$\frac{28 - 3 \cdot 3}{6}$

Multiply

$- 3$ by

$3$ .

$\frac{28 - 9}{6}$

Subtract

$9$ from

$28$ .

$\frac{19}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{6}$

Decimal Form:

$3.1\overline{6}$

Mixed Number Form:

$3 \frac{1}{6}$

Simplify 4 2/3-1 1/2

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