Pre-Algebra Examples

$\frac{1}{10} + \frac{3}{10} + \frac{1}{5} + \frac{1}{4} + \frac{3}{10}$

Step 1

Combine the numerators over the common denominator.

$\frac{1 + 3 + 3}{10} + \frac{1}{5} + \frac{1}{4}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $1$ and $3$ .

$\frac{4 + 3}{10} + \frac{1}{5} + \frac{1}{4}$

Step 2.2

Add $4$ and $3$ .

$\frac{7}{10} + \frac{1}{5} + \frac{1}{4}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{7}{10}$ by $\frac{2}{2}$ .

$\frac{7}{10} \cdot \frac{2}{2} + \frac{1}{5} + \frac{1}{4}$

Step 3.2

Multiply $\frac{7}{10}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 2}{10 \cdot 2} + \frac{1}{5} + \frac{1}{4}$

Step 3.3

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 2}{10 \cdot 2} + \frac{1}{5} \cdot \frac{4}{4} + \frac{1}{4}$

Step 3.4

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 2}{10 \cdot 2} + \frac{4}{5 \cdot 4} + \frac{1}{4}$

Step 3.5

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 2}{10 \cdot 2} + \frac{4}{5 \cdot 4} + \frac{1}{4} \cdot \frac{5}{5}$

Step 3.6

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 2}{10 \cdot 2} + \frac{4}{5 \cdot 4} + \frac{5}{4 \cdot 5}$

Step 3.7

Reorder the factors of $10 \cdot 2$ .

$\frac{7 \cdot 2}{2 \cdot 10} + \frac{4}{5 \cdot 4} + \frac{5}{4 \cdot 5}$

Step 3.8

Multiply $2$ by $10$ .

$\frac{7 \cdot 2}{20} + \frac{4}{5 \cdot 4} + \frac{5}{4 \cdot 5}$

Step 3.9

Reorder the factors of $5 \cdot 4$ .

$\frac{7 \cdot 2}{20} + \frac{4}{4 \cdot 5} + \frac{5}{4 \cdot 5}$

Step 3.10

Multiply $4$ by $5$ .

$\frac{7 \cdot 2}{20} + \frac{4}{20} + \frac{5}{4 \cdot 5}$

Step 3.11

Multiply $4$ by $5$ .

$\frac{7 \cdot 2}{20} + \frac{4}{20} + \frac{5}{20}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 4 + 5}{20}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $7$ by $2$ .

$\frac{14 + 4 + 5}{20}$

Step 5.2

Add $14$ and $4$ .

$\frac{18 + 5}{20}$

Step 5.3

Add $18$ and $5$ .

$\frac{23}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{20}$

Decimal Form:

$1.15$

Mixed Number Form:

$1 \frac{3}{20}$