Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $2$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Add $2$ and $5$ .

$\frac{1}{2} + \frac{7}{3} + \frac{1}{5}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{1}{2} \cdot \frac{15}{15} + \frac{7}{3} + \frac{1}{5}$

Step 4.2

Multiply $\frac{1}{2}$ by $\frac{15}{15}$ .

$\frac{15}{2 \cdot 15} + \frac{7}{3} + \frac{1}{5}$

Step 4.3

Multiply $\frac{7}{3}$ by $\frac{10}{10}$ .

$\frac{15}{2 \cdot 15} + \frac{7}{3} \cdot \frac{10}{10} + \frac{1}{5}$

Step 4.4

Multiply $\frac{7}{3}$ by $\frac{10}{10}$ .

$\frac{15}{2 \cdot 15} + \frac{7 \cdot 10}{3 \cdot 10} + \frac{1}{5}$

Step 4.5

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{15}{2 \cdot 15} + \frac{7 \cdot 10}{3 \cdot 10} + \frac{1}{5} \cdot \frac{6}{6}$

Step 4.6

Multiply $\frac{1}{5}$ by $\frac{6}{6}$ .

$\frac{15}{2 \cdot 15} + \frac{7 \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6}$

Step 4.7

Multiply $2$ by $15$ .

$\frac{15}{30} + \frac{7 \cdot 10}{3 \cdot 10} + \frac{6}{5 \cdot 6}$

Step 4.8

Multiply $3$ by $10$ .

$\frac{15}{30} + \frac{7 \cdot 10}{30} + \frac{6}{5 \cdot 6}$

Step 4.9

Multiply $5$ by $6$ .

$\frac{15}{30} + \frac{7 \cdot 10}{30} + \frac{6}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{15 + 7 \cdot 10 + 6}{30}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $7$ by $10$ .

$\frac{15 + 70 + 6}{30}$

Step 6.2

Add $15$ and $70$ .

$\frac{85 + 6}{30}$

Step 6.3

Add $85$ and $6$ .

$\frac{91}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{30}$

Decimal Form:

$3.0\overline{3}$

Mixed Number Form:

$3 \frac{1}{30}$