Basic Math Examples

$\frac{3}{4} \div 2 (1 \frac{5}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 1

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$\frac{3}{4} \div 2 (1 + \frac{5}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 1.2

Add $1$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$\frac{3}{4} \div 2 (\frac{6}{6} + \frac{5}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3}{4} \div 2 (\frac{6 + 5}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 1.2.3

Add $6$ and $5$ .

$\frac{3}{4} \div 2 (\frac{11}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$\frac{\frac{3}{4}}{2} (\frac{11}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{4} \cdot \frac{1}{2} (\frac{11}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.3

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

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Step 2.3.1

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

$\frac{3}{4 \cdot 2} (\frac{11}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.3.2

Multiply $4$ by $2$ .

$\frac{3}{8} (\frac{11}{6} - \frac{1}{2}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.4

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{8} (\frac{11}{6} - \frac{1}{2} \cdot \frac{3}{3}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{3}{8} (\frac{11}{6} - \frac{3}{2 \cdot 3}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.5.2

Multiply $2$ by $3$ .

$\frac{3}{8} (\frac{11}{6} - \frac{3}{6}) + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{3}{8} \cdot \frac{11 - 3}{6} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.7

Subtract $3$ from $11$ .

$\frac{3}{8} \cdot \frac{8}{6} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.8

Cancel the common factor of $3$ .

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Step 2.8.1

Factor $3$ out of $6$ .

$\frac{3}{8} \cdot \frac{8}{3 (2)} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.8.2

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8}{3 \cdot 2} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.8.3

Rewrite the expression.

$\frac{1}{8} \cdot \frac{8}{2} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.9

Cancel the common factor of $8$ .

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Step 2.9.1

Cancel the common factor.

$\frac{1}{8} \cdot \frac{8}{2} + \frac{3}{2} \cdot \frac{5}{2}$

Step 2.9.2

Rewrite the expression.

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

Step 2.10

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

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Step 2.10.1

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

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

Step 2.10.2

Multiply $3$ by $5$ .

$\frac{1}{2} + \frac{15}{2 \cdot 2}$

Step 2.10.3

Multiply $2$ by $2$ .

$\frac{1}{2} + \frac{15}{4}$

Step 3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} \cdot \frac{2}{2} + \frac{15}{4}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{2}{2 \cdot 2} + \frac{15}{4}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{2}{4} + \frac{15}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 + 15}{4}$

Step 6

Add $2$ and $15$ .

$\frac{17}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{4}$

Decimal Form:

$4.25$

Mixed Number Form:

$4 \frac{1}{4}$