Basic Math Examples

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

Step 1

Convert

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

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Step 1.1

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

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

Step 1.2

Add

$2$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Step 1.2.2

Combine

$2$ and

$\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$2$ .

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

Step 1.2.4.2

Add

$4$ and

$1$ .

$\frac{5}{2} - 4 \frac{2}{3}$

Step 2

Convert

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

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Step 2.1

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

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

Step 2.2

Add

$4$ and

$\frac{2}{3}$ .

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Step 2.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

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

Step 2.2.2

Combine

$4$ and

$\frac{3}{3}$ .

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$4$ by

$3$ .

$\frac{5}{2} - \frac{12 + 2}{3}$

Step 2.2.4.2

Add

$12$ and

$2$ .

$\frac{5}{2} - \frac{14}{3}$

Step 3

To write

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

$\frac{3}{3}$ .

$\frac{5}{2} \cdot \frac{3}{3} - \frac{14}{3}$

Step 4

To write

$- \frac{14}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{5}{2} \cdot \frac{3}{3} - \frac{14}{3} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{5}{2}$ by

$\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 \cdot 3} - \frac{14}{3} \cdot \frac{2}{2}$

Step 5.2

Multiply

$2$ by

$3$ .

$\frac{5 \cdot 3}{6} - \frac{14}{3} \cdot \frac{2}{2}$

Step 5.3

Multiply

$\frac{14}{3}$ by

$\frac{2}{2}$ .

$\frac{5 \cdot 3}{6} - \frac{14 \cdot 2}{3 \cdot 2}$

Step 5.4

Multiply

$3$ by

$2$ .

$\frac{5 \cdot 3}{6} - \frac{14 \cdot 2}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 14 \cdot 2}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$5$ by

$3$ .

$\frac{15 - 14 \cdot 2}{6}$

Step 7.2

Multiply

$- 14$ by

$2$ .

$\frac{15 - 28}{6}$

Step 7.3

Subtract

$28$ from

$15$ .

$\frac{- 13}{6}$

Step 8

Move the negative in front of the fraction.

$- \frac{13}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{6}$

Decimal Form:

$- 2.1\overline{6}$

Mixed Number Form:

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