Basic Math Examples

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

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

Step 1

Convert

2 \frac{2}{3}

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

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 2}{3} + 3 \frac{1}{2}

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

Step 1.2.4.2

Add

6

$6$ and

2

$2$ .

\frac{8}{3} + 3 \frac{1}{2}

$\frac{8}{3} + 3 \frac{1}{2}$

\frac{8}{3} + 3 \frac{1}{2}

$\frac{8}{3} + 3 \frac{1}{2}$

\frac{8}{3} + 3 \frac{1}{2}

$\frac{8}{3} + 3 \frac{1}{2}$

\frac{8}{3} + 3 \frac{1}{2}

$\frac{8}{3} + 3 \frac{1}{2}$

Step 2

Convert

3 \frac{1}{2}

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

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Step 2.1

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

\frac{8}{3} + 3 + \frac{1}{2}

$\frac{8}{3} + 3 + \frac{1}{2}$

Step 2.2

Add

3

$3$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8}{3} + 3 \cdot \frac{2}{2} + \frac{1}{2}

$\frac{8}{3} + 3 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine

3

$3$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8}{3} + \frac{3 \cdot 2}{2} + \frac{1}{2}

$\frac{8}{3} + \frac{3 \cdot 2}{2} + \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{8}{3} + \frac{3 \cdot 2 + 1}{2}

$\frac{8}{3} + \frac{3 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

2

$2$ .

\frac{8}{3} + \frac{6 + 1}{2}

$\frac{8}{3} + \frac{6 + 1}{2}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{8}{3} + \frac{7}{2}

$\frac{8}{3} + \frac{7}{2}$

\frac{8}{3} + \frac{7}{2}

$\frac{8}{3} + \frac{7}{2}$

\frac{8}{3} + \frac{7}{2}

$\frac{8}{3} + \frac{7}{2}$

\frac{8}{3} + \frac{7}{2}

$\frac{8}{3} + \frac{7}{2}$

Step 3

To write

\frac{8}{3}

$\frac{8}{3}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8}{3} \cdot \frac{2}{2} + \frac{7}{2}

$\frac{8}{3} \cdot \frac{2}{2} + \frac{7}{2}$

Step 4

To write

\frac{7}{2}

$\frac{7}{2}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{8}{3} \cdot \frac{2}{2} + \frac{7}{2} \cdot \frac{3}{3}

$\frac{8}{3} \cdot \frac{2}{2} + \frac{7}{2} \cdot \frac{3}{3}$

Step 5

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 5.1

Multiply

\frac{8}{3}

$\frac{8}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{8 \cdot 2}{3 \cdot 2} + \frac{7}{2} \cdot \frac{3}{3}

$\frac{8 \cdot 2}{3 \cdot 2} + \frac{7}{2} \cdot \frac{3}{3}$

Step 5.2

Multiply

3

$3$ by

2

$2$ .

\frac{8 \cdot 2}{6} + \frac{7}{2} \cdot \frac{3}{3}

$\frac{8 \cdot 2}{6} + \frac{7}{2} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{7}{2}

$\frac{7}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{2 \cdot 3}

$\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{2 \cdot 3}$

Step 5.4

Multiply

2

$2$ by

3

$3$ .

\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{6}

$\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{6}$

\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{6}

$\frac{8 \cdot 2}{6} + \frac{7 \cdot 3}{6}$

Step 6

Combine the numerators over the common denominator.

\frac{8 \cdot 2 + 7 \cdot 3}{6}

$\frac{8 \cdot 2 + 7 \cdot 3}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

8

$8$ by

2

$2$ .

\frac{16 + 7 \cdot 3}{6}

$\frac{16 + 7 \cdot 3}{6}$

Step 7.2

Multiply

7

$7$ by

3

$3$ .

\frac{16 + 21}{6}

$\frac{16 + 21}{6}$

Step 7.3

Add

16

$16$ and

21

$21$ .

\frac{37}{6}

$\frac{37}{6}$

\frac{37}{6}

$\frac{37}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{37}{6}

$\frac{37}{6}$

Decimal Form:

6.1 ¯ 6

$6.1\overline{6}$

Mixed Number Form:

6 \frac{1}{6}

$6 \frac{1}{6}$