Basic Math Examples

$\frac{\frac{\frac{4}{35} - \frac{1}{70}}{3}}{10} + \frac{11}{20}$

Step 1

To write $\frac{4}{35}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{\frac{4}{35} \cdot \frac{2}{2} - \frac{1}{70}}{3}}{10} + \frac{11}{20}$

Step 2

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{4}{35}$ by $\frac{2}{2}$ .

$\frac{\frac{\frac{4 \cdot 2}{35 \cdot 2} - \frac{1}{70}}{3}}{10} + \frac{11}{20}$

Step 2.2

Multiply $35$ by $2$ .

$\frac{\frac{\frac{4 \cdot 2}{70} - \frac{1}{70}}{3}}{10} + \frac{11}{20}$

Step 3

Combine the numerators over the common denominator.

$\frac{\frac{\frac{4 \cdot 2 - 1}{70}}{3}}{10} + \frac{11}{20}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $4$ by $2$ .

$\frac{\frac{\frac{8 - 1}{70}}{3}}{10} + \frac{11}{20}$

Step 4.2

Subtract $1$ from $8$ .

$\frac{\frac{\frac{7}{70}}{3}}{10} + \frac{11}{20}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $7$ and $70$ .

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Step 5.1.1

Factor $7$ out of $7$ .

$\frac{\frac{\frac{7 (1)}{70}}{3}}{10} + \frac{11}{20}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $7$ out of $70$ .

$\frac{\frac{\frac{7 \cdot 1}{7 \cdot 10}}{3}}{10} + \frac{11}{20}$

Step 5.1.2.2

Cancel the common factor.

$\frac{\frac{\frac{7 \cdot 1}{7 \cdot 10}}{3}}{10} + \frac{11}{20}$

Step 5.1.2.3

Rewrite the expression.

$\frac{\frac{\frac{1}{10}}{3}}{10} + \frac{11}{20}$

Step 5.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{1}{10}}{3} \cdot \frac{1}{10} + \frac{11}{20}$

Step 5.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{10} \cdot \frac{1}{3} \frac{1}{10} + \frac{11}{20}$

Step 5.4

Multiply $\frac{1}{10} \cdot \frac{1}{3}$ .

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Step 5.4.1

Multiply $\frac{1}{10}$ by $\frac{1}{3}$ .

$\frac{1}{10 \cdot 3} \cdot \frac{1}{10} + \frac{11}{20}$

Step 5.4.2

Multiply $10$ by $3$ .

$\frac{1}{30} \cdot \frac{1}{10} + \frac{11}{20}$

Step 5.5

Multiply $\frac{1}{30} \cdot \frac{1}{10}$ .

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Step 5.5.1

Multiply $\frac{1}{30}$ by $\frac{1}{10}$ .

$\frac{1}{30 \cdot 10} + \frac{11}{20}$

Step 5.5.2

Multiply $30$ by $10$ .

$\frac{1}{300} + \frac{11}{20}$

Step 6

To write $\frac{11}{20}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{1}{300} + \frac{11}{20} \cdot \frac{15}{15}$

Step 7

Write each expression with a common denominator of $300$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{11}{20}$ by $\frac{15}{15}$ .

$\frac{1}{300} + \frac{11 \cdot 15}{20 \cdot 15}$

Step 7.2

Multiply $20$ by $15$ .

$\frac{1}{300} + \frac{11 \cdot 15}{300}$

Step 8

Combine the numerators over the common denominator.

$\frac{1 + 11 \cdot 15}{300}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $11$ by $15$ .

$\frac{1 + 165}{300}$

Step 9.2

Add $1$ and $165$ .

$\frac{166}{300}$

Step 10

Cancel the common factor of $166$ and $300$ .

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Step 10.1

Factor $2$ out of $166$ .

$\frac{2 (83)}{300}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $300$ .

$\frac{2 \cdot 83}{2 \cdot 150}$

Step 10.2.2

Cancel the common factor.

$\frac{2 \cdot 83}{2 \cdot 150}$

Step 10.2.3

Rewrite the expression.

$\frac{83}{150}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{150}$

Decimal Form:

$0.55\overline{3}$