Basic Math Examples

$4 \frac{2}{3} - 2 \frac{1}{6}$

Step 1

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

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Step 1.1

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

$4 + \frac{2}{3} - 2 \frac{1}{6}$

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $3$ .

$\frac{12 + 2}{3} - 2 \frac{1}{6}$

Step 1.2.4.2

Add $12$ and $2$ .

$\frac{14}{3} - 2 \frac{1}{6}$

Step 2

Convert $2 \frac{1}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{14}{3} - (2 + \frac{1}{6})$

Step 2.2

Add $2$ and $\frac{1}{6}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{14}{3} - (2 \cdot \frac{6}{6} + \frac{1}{6})$

Step 2.2.2

Combine $2$ and $\frac{6}{6}$ .

$\frac{14}{3} - (\frac{2 \cdot 6}{6} + \frac{1}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{14}{3} - \frac{2 \cdot 6 + 1}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $6$ .

$\frac{14}{3} - \frac{12 + 1}{6}$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{14}{3} - \frac{13}{6}$

Step 3

To write $\frac{14}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{14}{3} \cdot \frac{2}{2} - \frac{13}{6}$

Step 4

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

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Step 4.1

Multiply $\frac{14}{3}$ by $\frac{2}{2}$ .

$\frac{14 \cdot 2}{3 \cdot 2} - \frac{13}{6}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{14 \cdot 2}{6} - \frac{13}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{14 \cdot 2 - 13}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $14$ by $2$ .

$\frac{28 - 13}{6}$

Step 6.2

Subtract $13$ from $28$ .

$\frac{15}{6}$

Step 7

Cancel the common factor of $15$ and $6$ .

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Step 7.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $6$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{5}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$