Algebra Examples

$4 \frac{2}{5} \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1

Convert $4 \frac{2}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(4 + \frac{2}{5}) \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1.2

Add $4$ and $\frac{2}{5}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(4 \cdot \frac{5}{5} + \frac{2}{5}) \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1.2.2

Combine $4$ and $\frac{5}{5}$ .

$(\frac{4 \cdot 5}{5} + \frac{2}{5}) \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 2}{5} \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $5$ .

$\frac{20 + 2}{5} \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 1.2.4.2

Add $20$ and $2$ .

$\frac{22}{5} \div (\frac{7}{10} + 2 \frac{3}{5})$

Step 2

Convert $2 \frac{3}{5}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{22}{5} \div (\frac{7}{10} + 2 + \frac{3}{5})$

Step 2.2

Add $2$ and $\frac{3}{5}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{22}{5} \div (\frac{7}{10} + 2 \cdot \frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{22}{5} \div (\frac{7}{10} + \frac{2 \cdot 5}{5} + \frac{3}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{22}{5} \div (\frac{7}{10} + \frac{2 \cdot 5 + 3}{5})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $5$ .

$\frac{22}{5} \div (\frac{7}{10} + \frac{10 + 3}{5})$

Step 2.2.4.2

Add $10$ and $3$ .

$\frac{22}{5} \div (\frac{7}{10} + \frac{13}{5})$

Step 3

Rewrite the division as a fraction.

$\frac{\frac{22}{5}}{\frac{7}{10} + \frac{13}{5}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{22}{5} \cdot \frac{1}{\frac{7}{10} + \frac{13}{5}}$

Step 5

Simplify the denominator.

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Step 5.1

To write $\frac{13}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{22}{5} \cdot \frac{1}{\frac{7}{10} + \frac{13}{5} \cdot \frac{2}{2}}$

Step 5.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.1

Multiply $\frac{13}{5}$ by $\frac{2}{2}$ .

$\frac{22}{5} \cdot \frac{1}{\frac{7}{10} + \frac{13 \cdot 2}{5 \cdot 2}}$

Step 5.2.2

Multiply $5$ by $2$ .

$\frac{22}{5} \cdot \frac{1}{\frac{7}{10} + \frac{13 \cdot 2}{10}}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{22}{5} \cdot \frac{1}{\frac{7 + 13 \cdot 2}{10}}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $13$ by $2$ .

$\frac{22}{5} \cdot \frac{1}{\frac{7 + 26}{10}}$

Step 5.4.2

Add $7$ and $26$ .

$\frac{22}{5} \cdot \frac{1}{\frac{33}{10}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{22}{5} (1 (\frac{10}{33}))$

Step 7

Multiply $\frac{10}{33}$ by $1$ .

$\frac{22}{5} \cdot \frac{10}{33}$

Step 8

Cancel the common factor of $11$ .

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Step 8.1

Factor $11$ out of $22$ .

$\frac{11 (2)}{5} \cdot \frac{10}{33}$

Step 8.2

Factor $11$ out of $33$ .

$\frac{11 \cdot 2}{5} \cdot \frac{10}{11 \cdot 3}$

Step 8.3

Cancel the common factor.

$\frac{11 \cdot 2}{5} \cdot \frac{10}{11 \cdot 3}$

Step 8.4

Rewrite the expression.

$\frac{2}{5} \cdot \frac{10}{3}$

Step 9

Cancel the common factor of $5$ .

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Step 9.1

Factor $5$ out of $10$ .

$\frac{2}{5} \cdot \frac{5 (2)}{3}$

Step 9.2

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 \cdot 2}{3}$

Step 9.3

Rewrite the expression.

$2 (\frac{2}{3})$

Step 10

Combine $2$ and $\frac{2}{3}$ .

$\frac{2 \cdot 2}{3}$

Step 11

Multiply $2$ by $2$ .

$\frac{4}{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$