Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 3}{4} \div 1 \frac{2}{3} \cdot 3$

Step 1.2.4.2

Add $12$ and $3$ .

$\frac{15}{4} \div 1 \frac{2}{3} \cdot 3$

Step 2

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{15}{4} \div (1 + \frac{2}{3}) \cdot 3$

Step 2.2

Add $1$ and $\frac{2}{3}$ .

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Step 2.2.1

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

$\frac{15}{4} \div (\frac{3}{3} + \frac{2}{3}) \cdot 3$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{15}{4} \div \frac{3 + 2}{3} \cdot 3$

Step 2.2.3

Add $3$ and $2$ .

$\frac{15}{4} \div \frac{5}{3} \cdot 3$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{4} \cdot \frac{3}{5} \cdot 3$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Factor $5$ out of $15$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Combine $\frac{3}{4}$ and $3$ .

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

Step 6

Multiply $3$ by $3$ .

$\frac{9}{4} \cdot 3$

Step 7

Multiply $\frac{9}{4} \cdot 3$ .

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Step 7.1

Combine $\frac{9}{4}$ and $3$ .

$\frac{9 \cdot 3}{4}$

Step 7.2

Multiply $9$ by $3$ .

$\frac{27}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{4}$

Decimal Form:

$6.75$

Mixed Number Form:

$6 \frac{3}{4}$