Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

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

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{3}{4} \cdot \frac{7}{3} - (1 \frac{2}{3} \div \frac{4}{3})$

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.

$\frac{3}{4} \cdot \frac{7}{3} - (1 + \frac{2}{3}) \div \frac{4}{3}$

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.

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

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{3}{4} \cdot \frac{7}{3} - \frac{3 + 2}{3} \div \frac{4}{3}$

Step 2.2.3

Add $3$ and $2$ .

$\frac{3}{4} \cdot \frac{7}{3} - \frac{5}{3} \div \frac{4}{3}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{7}{3} - \frac{5}{3} \div \frac{4}{3}$

Step 3.1.2

Rewrite the expression.

$\frac{1}{4} \cdot 7 - \frac{5}{3} \div \frac{4}{3}$

Step 3.2

Combine $\frac{1}{4}$ and $7$ .

$\frac{7}{4} - \frac{5}{3} \div \frac{4}{3}$

Step 3.3

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{4} - (\frac{5}{3} \cdot \frac{3}{4})$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$\frac{7}{4} - (\frac{5}{3} \cdot \frac{3}{4})$

Step 3.4.2

Rewrite the expression.

$\frac{7}{4} - (5 (\frac{1}{4}))$

Step 3.5

Combine $5$ and $\frac{1}{4}$ .

$\frac{7}{4} - \frac{5}{4}$

Step 4

Simplify terms.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{7 - 5}{4}$

Step 4.2

Subtract $5$ from $7$ .

$\frac{2}{4}$

Step 4.3

Cancel the common factor of $2$ and $4$ .

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Step 4.3.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $4$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$