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:

$1 \frac{3}{20}$