Simplify 1 2/3-(-5 2/3)

$1 \frac{2}{3} - (- 5 \frac{2}{3})$

Step 1

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

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

$1 + \frac{2}{3} - (- 5 \frac{2}{3})$

Add $1$ and $\frac{2}{3}$ .

Write $1$ as a fraction with a common denominator.

$\frac{3}{3} + \frac{2}{3} - (- 5 \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{3 + 2}{3} - (- 5 \frac{2}{3})$

Add $3$ and $2$ .

$\frac{5}{3} - (- 5 \frac{2}{3})$

Step 2

Convert $5 \frac{2}{3}$ to an improper fraction.

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

$\frac{5}{3} - - (5 + \frac{2}{3})$

Add $5$ and $\frac{2}{3}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} - - (5 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $5$ and $\frac{3}{3}$ .

$\frac{5}{3} - - (\frac{5 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{5}{3} - - \frac{15 + 2}{3}$

Add $15$ and $2$ .

$\frac{5}{3} - - \frac{17}{3}$

Step 3

Multiply $- - \frac{17}{3}$ .

Multiply $- 1$ by $- 1$ .

$\frac{5}{3} + 1 (\frac{17}{3})$

Multiply $\frac{17}{3}$ by $1$ .

$\frac{5}{3} + \frac{17}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 + 17}{3}$

Step 5

Add $5$ and $17$ .

$\frac{22}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{3}$

Decimal Form:

$7.\overline{3}$

Mixed Number Form:

$7 \frac{1}{3}$

Simplify 1 2/3-(-5 2/3)

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