Simplify (2/5+2/3)÷(4/5)+1 2/3

$(\frac{2}{5} + \frac{2}{3}) \div \frac{4}{5} + 1 \frac{2}{3}$

Step 1

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

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

$(\frac{2}{5} + \frac{2}{3}) \div \frac{4}{5} + 1 + \frac{2}{3}$

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

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

$(\frac{2}{5} + \frac{2}{3}) \div \frac{4}{5} + \frac{3}{3} + \frac{2}{3}$

Combine the numerators over the common denominator.

$(\frac{2}{5} + \frac{2}{3}) \div \frac{4}{5} + \frac{3 + 2}{3}$

Add $3$ and $2$ .

$(\frac{2}{5} + \frac{2}{3}) \div \frac{4}{5} + \frac{5}{3}$

Step 2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{2}{5} \cdot \frac{3}{3} + \frac{2}{3}) \div \frac{4}{5} + \frac{5}{3}$

Step 3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{2}{5} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{5}{5}) \div \frac{4}{5} + \frac{5}{3}$

Step 4

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

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$(\frac{2 \cdot 3}{5 \cdot 3} + \frac{2}{3} \cdot \frac{5}{5}) \div \frac{4}{5} + \frac{5}{3}$

Multiply $5$ by $3$ .

$(\frac{2 \cdot 3}{15} + \frac{2}{3} \cdot \frac{5}{5}) \div \frac{4}{5} + \frac{5}{3}$

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$(\frac{2 \cdot 3}{15} + \frac{2 \cdot 5}{3 \cdot 5}) \div \frac{4}{5} + \frac{5}{3}$

Multiply $3$ by $5$ .

$(\frac{2 \cdot 3}{15} + \frac{2 \cdot 5}{15}) \div \frac{4}{5} + \frac{5}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 2 \cdot 5}{15} \div \frac{4}{5} + \frac{5}{3}$

Step 6

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 + 2 \cdot 5}{15} \div \frac{4}{5} + \frac{5}{3}$

Multiply $2$ by $5$ .

$\frac{6 + 10}{15} \div \frac{4}{5} + \frac{5}{3}$

Add $6$ and $10$ .

$\frac{16}{15} \div \frac{4}{5} + \frac{5}{3}$

Step 7

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{16}{15} \cdot \frac{5}{4} + \frac{5}{3}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{4 (4)}{15} \cdot \frac{5}{4} + \frac{5}{3}$

Cancel the common factor.

$\frac{4 \cdot 4}{15} \cdot \frac{5}{4} + \frac{5}{3}$

Rewrite the expression.

$\frac{4}{15} \cdot 5 + \frac{5}{3}$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{4}{5 (3)} \cdot 5 + \frac{5}{3}$

Cancel the common factor.

$\frac{4}{5 \cdot 3} \cdot 5 + \frac{5}{3}$

Rewrite the expression.

$\frac{4}{3} + \frac{5}{3}$

Step 8

Combine fractions.

Combine the numerators over the common denominator.

$\frac{4 + 5}{3}$

Simplify the expression.

Add $4$ and $5$ .

$\frac{9}{3}$

Divide $9$ by $3$ .

$3$

Simplify (2/5+2/3)÷(4/5)+1 2/3

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