Basic Math Examples

$\frac{1}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60} \cdot \frac{1}{60} + \frac{1}{60} + \frac{1}{5} + \frac{2}{5}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{1}{60} \cdot \frac{1}{60} + \frac{1 + 1 + 2}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 1.2

Simplify by adding numbers.

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Step 1.2.1

Add $1$ and $1$ .

$\frac{1}{60} \cdot \frac{1}{60} + \frac{2 + 2}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 1.2.2

Add $2$ and $2$ .

$\frac{1}{60} \cdot \frac{1}{60} + \frac{4}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 2

Multiply $\frac{1}{60} \cdot \frac{1}{60}$ .

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Step 2.1

Multiply $\frac{1}{60}$ by $\frac{1}{60}$ .

$\frac{1}{60 \cdot 60} + \frac{4}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 2.2

Multiply $60$ by $60$ .

$\frac{1}{3600} + \frac{4}{5} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{4}{5}$ by $\frac{720}{720}$ .

$\frac{1}{3600} + \frac{4}{5} \cdot \frac{720}{720} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 3.2

Multiply $\frac{4}{5}$ by $\frac{720}{720}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{1}{10} + \frac{1}{20} + \frac{1}{60}$

Step 3.3

Multiply $\frac{1}{10}$ by $\frac{360}{360}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{1}{10} \cdot \frac{360}{360} + \frac{1}{20} + \frac{1}{60}$

Step 3.4

Multiply $\frac{1}{10}$ by $\frac{360}{360}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{360}{10 \cdot 360} + \frac{1}{20} + \frac{1}{60}$

Step 3.5

Multiply $\frac{1}{20}$ by $\frac{180}{180}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{360}{10 \cdot 360} + \frac{1}{20} \cdot \frac{180}{180} + \frac{1}{60}$

Step 3.6

Multiply $\frac{1}{20}$ by $\frac{180}{180}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{360}{10 \cdot 360} + \frac{180}{20 \cdot 180} + \frac{1}{60}$

Step 3.7

Multiply $\frac{1}{60}$ by $\frac{60}{60}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{360}{10 \cdot 360} + \frac{180}{20 \cdot 180} + \frac{1}{60} \cdot \frac{60}{60}$

Step 3.8

Multiply $\frac{1}{60}$ by $\frac{60}{60}$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{5 \cdot 720} + \frac{360}{10 \cdot 360} + \frac{180}{20 \cdot 180} + \frac{60}{60 \cdot 60}$

Step 3.9

Multiply $5$ by $720$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{3600} + \frac{360}{10 \cdot 360} + \frac{180}{20 \cdot 180} + \frac{60}{60 \cdot 60}$

Step 3.10

Multiply $10$ by $360$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{3600} + \frac{360}{3600} + \frac{180}{20 \cdot 180} + \frac{60}{60 \cdot 60}$

Step 3.11

Multiply $20$ by $180$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{3600} + \frac{360}{3600} + \frac{180}{3600} + \frac{60}{60 \cdot 60}$

Step 3.12

Multiply $60$ by $60$ .

$\frac{1}{3600} + \frac{4 \cdot 720}{3600} + \frac{360}{3600} + \frac{180}{3600} + \frac{60}{3600}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 4 \cdot 720 + 360 + 180 + 60}{3600}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $4$ by $720$ .

$\frac{1 + 2880 + 360 + 180 + 60}{3600}$

Step 5.2

Add $1$ and $2880$ .

$\frac{2881 + 360 + 180 + 60}{3600}$

Step 5.3

Add $2881$ and $360$ .

$\frac{3241 + 180 + 60}{3600}$

Step 5.4

Add $3241$ and $180$ .

$\frac{3421 + 60}{3600}$

Step 5.5

Add $3421$ and $60$ .

$\frac{3481}{3600}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3481}{3600}$

Decimal Form:

$0.9669\overline{4}$