Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $5$ .

$(\frac{3}{2} - \frac{2}{5}) \div \frac{20 + 2}{5} \cdot \frac{3}{4}$

Step 2.2.4.2

Add $20$ and $2$ .

$(\frac{3}{2} - \frac{2}{5}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3

Simplify the numerator.

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Step 3.1

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

$(\frac{3}{2} \cdot \frac{5}{5} - \frac{2}{5}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.2

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

$(\frac{3}{2} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{2}{2}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.3

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

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Step 3.3.1

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

$(\frac{3 \cdot 5}{2 \cdot 5} - \frac{2}{5} \cdot \frac{2}{2}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.3.2

Multiply $2$ by $5$ .

$(\frac{3 \cdot 5}{10} - \frac{2}{5} \cdot \frac{2}{2}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.3.3

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

$(\frac{3 \cdot 5}{10} - \frac{2 \cdot 2}{5 \cdot 2}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.3.4

Multiply $5$ by $2$ .

$(\frac{3 \cdot 5}{10} - \frac{2 \cdot 2}{10}) \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 - 2 \cdot 2}{10} \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $5$ .

$\frac{15 - 2 \cdot 2}{10} \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.5.2

Multiply $- 2$ by $2$ .

$\frac{15 - 4}{10} \div \frac{22}{5} \cdot \frac{3}{4}$

Step 3.5.3

Subtract $4$ from $15$ .

$\frac{11}{10} \div \frac{22}{5} \cdot \frac{3}{4}$

Step 4

To divide by a fraction, multiply by its reciprocal.

$\frac{11}{10} \cdot \frac{5}{22} \cdot \frac{3}{4}$

Step 5

Cancel the common factor of $11$ .

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Step 5.1

Factor $11$ out of $22$ .

$\frac{11}{10} \cdot \frac{5}{11 (2)} \cdot \frac{3}{4}$

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $10$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{3}{4}$

Step 7

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$\frac{1}{2 \cdot 2} \cdot \frac{3}{4}$

Step 8

Multiply $2$ by $2$ .

$\frac{1}{4} \cdot \frac{3}{4}$

Step 9

Multiply $\frac{1}{4} \cdot \frac{3}{4}$ .

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Step 9.1

Multiply $\frac{1}{4}$ by $\frac{3}{4}$ .

$\frac{3}{4 \cdot 4}$

Step 9.2

Multiply $4$ by $4$ .

$\frac{3}{16}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{16}$

Decimal Form:

$0.1875$