Algebra Examples

$2 \frac{3}{4} \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{3}{4}) \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

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

$(2 \cdot \frac{4}{4} + \frac{3}{4}) \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$(\frac{2 \cdot 4}{4} + \frac{3}{4}) \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 3}{4} \div (1 \frac{1}{2} - \frac{2}{5})$

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} \div (1 \frac{1}{2} - \frac{2}{5})$

Step 2

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} \div (1 + \frac{1}{2} - \frac{2}{5})$

Step 2.2

Add $1$ and $\frac{1}{2}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{11}{4} \div (\frac{2}{2} + \frac{1}{2} - \frac{2}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{11}{4} \div (\frac{2 + 1}{2} - \frac{2}{5})$

Step 2.2.3

Add $2$ and $1$ .

$\frac{11}{4} \div (\frac{3}{2} - \frac{2}{5})$

Step 3

Rewrite the division as a fraction.

$\frac{\frac{11}{4}}{\frac{3}{2} - \frac{2}{5}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{4} \cdot \frac{1}{\frac{3}{2} - \frac{2}{5}}$

Step 5

Simplify the denominator.

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Step 5.1

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11}{4} \cdot \frac{1}{\frac{3}{2} \cdot \frac{5}{5} - \frac{2}{5}}$

Step 5.2

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

$\frac{11}{4} \cdot \frac{1}{\frac{3}{2} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{2}{2}}$

Step 5.3

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

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Step 5.3.1

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

$\frac{11}{4} \cdot \frac{1}{\frac{3 \cdot 5}{2 \cdot 5} - \frac{2}{5} \cdot \frac{2}{2}}$

Step 5.3.2

Multiply $2$ by $5$ .

$\frac{11}{4} \cdot \frac{1}{\frac{3 \cdot 5}{10} - \frac{2}{5} \cdot \frac{2}{2}}$

Step 5.3.3

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

$\frac{11}{4} \cdot \frac{1}{\frac{3 \cdot 5}{10} - \frac{2 \cdot 2}{5 \cdot 2}}$

Step 5.3.4

Multiply $5$ by $2$ .

$\frac{11}{4} \cdot \frac{1}{\frac{3 \cdot 5}{10} - \frac{2 \cdot 2}{10}}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{11}{4} \cdot \frac{1}{\frac{3 \cdot 5 - 2 \cdot 2}{10}}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $3$ by $5$ .

$\frac{11}{4} \cdot \frac{1}{\frac{15 - 2 \cdot 2}{10}}$

Step 5.5.2

Multiply $- 2$ by $2$ .

$\frac{11}{4} \cdot \frac{1}{\frac{15 - 4}{10}}$

Step 5.5.3

Subtract $4$ from $15$ .

$\frac{11}{4} \cdot \frac{1}{\frac{11}{10}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{4} (1 (\frac{10}{11}))$

Step 7

Multiply $\frac{10}{11}$ by $1$ .

$\frac{11}{4} \cdot \frac{10}{11}$

Step 8

Cancel the common factor of $11$ .

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Step 8.1

Cancel the common factor.

$\frac{11}{4} \cdot \frac{10}{11}$

Step 8.2

Rewrite the expression.

$\frac{1}{4} \cdot 10$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $4$ .

$\frac{1}{2 (2)} \cdot 10$

Step 9.2

Factor $2$ out of $10$ .

$\frac{1}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 9.3

Cancel the common factor.

$\frac{1}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 9.4

Rewrite the expression.

$\frac{1}{2} \cdot 5$

Step 10

Combine $\frac{1}{2}$ and $5$ .

$\frac{5}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$