Basic Math Examples

2 \frac{1}{2} + \frac{2}{3}

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

Step 1

Convert

2 \frac{1}{2}

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

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

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

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{5}{2} + \frac{2}{3}

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

\frac{5}{2} + \frac{2}{3}

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

\frac{5}{2} + \frac{2}{3}

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

\frac{5}{2} + \frac{2}{3}

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

Step 2

To write

\frac{5}{2}

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3

To write

\frac{2}{3}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4

Write each expression with a common denominator of

6

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

1

$1$ .

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Step 4.1

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4.2

Multiply

2

$2$ by

3

$3$ .

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

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

Step 4.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.4

Multiply

3

$3$ by

2

$2$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

5

$5$ by

3

$3$ .

\frac{15 + 2 \cdot 2}{6}

$\frac{15 + 2 \cdot 2}{6}$

Step 6.2

Multiply

2

$2$ by

2

$2$ .

\frac{15 + 4}{6}

$\frac{15 + 4}{6}$

Step 6.3

Add

15

$15$ and

4

$4$ .

\frac{19}{6}

$\frac{19}{6}$

\frac{19}{6}

$\frac{19}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{19}{6}

$\frac{19}{6}$

Decimal Form:

3.1\overline{6}

$3.1\overline{6}$

Mixed Number Form:

3 \frac{1}{6}

$3 \frac{1}{6}$