Algebra Examples

$5 \frac{2}{5} - 4 \div 1 \frac{2}{3}$

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

$5 \cdot \frac{5}{5} + \frac{2}{5} - 4 \div 1 \frac{2}{3}$

Step 1.2.2

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

$\frac{5 \cdot 5}{5} + \frac{2}{5} - 4 \div 1 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 2}{5} - 4 \div 1 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $5$ .

$\frac{25 + 2}{5} - 4 \div 1 \frac{2}{3}$

Step 1.2.4.2

Add $25$ and $2$ .

$\frac{27}{5} - 4 \div 1 \frac{2}{3}$

Step 2

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

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Step 2.1

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

$\frac{27}{5} - 4 \div (1 + \frac{2}{3})$

Step 2.2

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

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Step 2.2.1

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

$\frac{27}{5} - 4 \div (\frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{27}{5} - 4 \div \frac{3 + 2}{3}$

Step 2.2.3

Add $3$ and $2$ .

$\frac{27}{5} - 4 \div \frac{5}{3}$

Step 3

Simplify each term.

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Step 3.1

To divide by a fraction, multiply by its reciprocal.

$\frac{27}{5} - (4 (\frac{3}{5}))$

Step 3.2

Multiply $4 (\frac{3}{5})$ .

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Step 3.2.1

Combine $4$ and $\frac{3}{5}$ .

$\frac{27}{5} - \frac{4 \cdot 3}{5}$

Step 3.2.2

Multiply $4$ by $3$ .

$\frac{27}{5} - \frac{12}{5}$

Step 4

Combine fractions.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{27 - 12}{5}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Subtract $12$ from $27$ .

$\frac{15}{5}$

Step 4.2.2

Divide $15$ by $5$ .

$3$