Basic Math Examples

$\frac{7}{27} + \frac{5}{18} + \frac{1}{10}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{7}{27}$ by $\frac{10}{10}$ .

$\frac{7}{27} \cdot \frac{10}{10} + \frac{5}{18} + \frac{1}{10}$

Step 1.2

Multiply $\frac{7}{27}$ by $\frac{10}{10}$ .

$\frac{7 \cdot 10}{27 \cdot 10} + \frac{5}{18} + \frac{1}{10}$

Step 1.3

Multiply $\frac{5}{18}$ by $\frac{15}{15}$ .

$\frac{7 \cdot 10}{27 \cdot 10} + \frac{5}{18} \cdot \frac{15}{15} + \frac{1}{10}$

Step 1.4

Multiply $\frac{5}{18}$ by $\frac{15}{15}$ .

$\frac{7 \cdot 10}{27 \cdot 10} + \frac{5 \cdot 15}{18 \cdot 15} + \frac{1}{10}$

Step 1.5

Multiply $\frac{1}{10}$ by $\frac{27}{27}$ .

$\frac{7 \cdot 10}{27 \cdot 10} + \frac{5 \cdot 15}{18 \cdot 15} + \frac{1}{10} \cdot \frac{27}{27}$

Step 1.6

Multiply $\frac{1}{10}$ by $\frac{27}{27}$ .

$\frac{7 \cdot 10}{27 \cdot 10} + \frac{5 \cdot 15}{18 \cdot 15} + \frac{27}{10 \cdot 27}$

Step 1.7

Reorder the factors of $27 \cdot 10$ .

$\frac{7 \cdot 10}{10 \cdot 27} + \frac{5 \cdot 15}{18 \cdot 15} + \frac{27}{10 \cdot 27}$

Step 1.8

Multiply $10$ by $27$ .

$\frac{7 \cdot 10}{270} + \frac{5 \cdot 15}{18 \cdot 15} + \frac{27}{10 \cdot 27}$

Step 1.9

Reorder the factors of $18 \cdot 15$ .

$\frac{7 \cdot 10}{270} + \frac{5 \cdot 15}{15 \cdot 18} + \frac{27}{10 \cdot 27}$

Step 1.10

Multiply $15$ by $18$ .

$\frac{7 \cdot 10}{270} + \frac{5 \cdot 15}{270} + \frac{27}{10 \cdot 27}$

Step 1.11

Multiply $10$ by $27$ .

$\frac{7 \cdot 10}{270} + \frac{5 \cdot 15}{270} + \frac{27}{270}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 \cdot 10 + 5 \cdot 15 + 27}{270}$

Step 3

Simplify each term.

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Step 3.1

Multiply $7$ by $10$ .

$\frac{70 + 5 \cdot 15 + 27}{270}$

Step 3.2

Multiply $5$ by $15$ .

$\frac{70 + 75 + 27}{270}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $70$ and $75$ .

$\frac{145 + 27}{270}$

Step 4.2

Add $145$ and $27$ .

$\frac{172}{270}$

Step 4.3

Cancel the common factor of $172$ and $270$ .

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Step 4.3.1

Factor $2$ out of $172$ .

$\frac{2 (86)}{270}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $270$ .

$\frac{2 \cdot 86}{2 \cdot 135}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 86}{2 \cdot 135}$

Step 4.3.2.3

Rewrite the expression.

$\frac{86}{135}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{86}{135}$

Decimal Form:

$0.6\overline{370}$