Simplify 6 3/5-1 2/3

$6 \frac{3}{5} - 1 \frac{2}{3}$

Step 1

Convert $6 \frac{3}{5}$ to an improper fraction.

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

$6 + \frac{3}{5} - 1 \frac{2}{3}$

Add $6$ and $\frac{3}{5}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 \cdot \frac{5}{5} + \frac{3}{5} - 1 \frac{2}{3}$

Combine $6$ and $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} + \frac{3}{5} - 1 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 + 3}{5} - 1 \frac{2}{3}$

Simplify the numerator.

Multiply $6$ by $5$ .

$\frac{30 + 3}{5} - 1 \frac{2}{3}$

Add $30$ and $3$ .

$\frac{33}{5} - 1 \frac{2}{3}$

Step 2

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

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

$\frac{33}{5} - (1 + \frac{2}{3})$

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

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

$\frac{33}{5} - (\frac{3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{33}{5} - \frac{3 + 2}{3}$

Add $3$ and $2$ .

$\frac{33}{5} - \frac{5}{3}$

Step 3

To write $\frac{33}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{33}{5} \cdot \frac{3}{3} - \frac{5}{3}$

Step 4

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

$\frac{33}{5} \cdot \frac{3}{3} - \frac{5}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{33}{5}$ by $\frac{3}{3}$ .

$\frac{33 \cdot 3}{5 \cdot 3} - \frac{5}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$\frac{33 \cdot 3}{15} - \frac{5}{3} \cdot \frac{5}{5}$

Multiply $\frac{5}{3}$ by $\frac{5}{5}$ .

$\frac{33 \cdot 3}{15} - \frac{5 \cdot 5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{33 \cdot 3}{15} - \frac{5 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{33 \cdot 3 - 5 \cdot 5}{15}$

Step 7

Simplify the numerator.

Multiply $33$ by $3$ .

$\frac{99 - 5 \cdot 5}{15}$

Multiply $- 5$ by $5$ .

$\frac{99 - 25}{15}$

Subtract $25$ from $99$ .

$\frac{74}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{74}{15}$

Decimal Form:

$4.9\overline{3}$

Mixed Number Form:

$4 \frac{14}{15}$

Simplify 6 3/5-1 2/3

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