Basic Math Examples

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

$8 \frac{3}{4} + 2 \frac{1}{2}$

Step 1

Convert

8 \frac{3}{4}

$8 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

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

$8 + \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2

Add

8

$8$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

$8 \cdot \frac{4}{4} + \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.2

Combine

8

$8$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{8 \cdot 4}{4} + \frac{3}{4} + 2 \frac{1}{2}

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{8 \cdot 4 + 3}{4} + 2 \frac{1}{2}

$\frac{8 \cdot 4 + 3}{4} + 2 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

8

$8$ by

4

$4$ .

\frac{32 + 3}{4} + 2 \frac{1}{2}

$\frac{32 + 3}{4} + 2 \frac{1}{2}$

Step 1.2.4.2

Add

32

$32$ and

3

$3$ .

\frac{35}{4} + 2 \frac{1}{2}

$\frac{35}{4} + 2 \frac{1}{2}$

\frac{35}{4} + 2 \frac{1}{2}

$\frac{35}{4} + 2 \frac{1}{2}$

\frac{35}{4} + 2 \frac{1}{2}

$\frac{35}{4} + 2 \frac{1}{2}$

\frac{35}{4} + 2 \frac{1}{2}

$\frac{35}{4} + 2 \frac{1}{2}$

Step 2

Convert

2 \frac{1}{2}

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

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Step 2.1

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

\frac{35}{4} + 2 + \frac{1}{2}

$\frac{35}{4} + 2 + \frac{1}{2}$

Step 2.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{35}{4} + 2 \cdot \frac{2}{2} + \frac{1}{2}

$\frac{35}{4} + 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{35}{4} + \frac{2 \cdot 2}{2} + \frac{1}{2}

$\frac{35}{4} + \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{35}{4} + \frac{2 \cdot 2 + 1}{2}

$\frac{35}{4} + \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{35}{4} + \frac{4 + 1}{2}

$\frac{35}{4} + \frac{4 + 1}{2}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{35}{4} + \frac{5}{2}

$\frac{35}{4} + \frac{5}{2}$

\frac{35}{4} + \frac{5}{2}

$\frac{35}{4} + \frac{5}{2}$

\frac{35}{4} + \frac{5}{2}

$\frac{35}{4} + \frac{5}{2}$

\frac{35}{4} + \frac{5}{2}

$\frac{35}{4} + \frac{5}{2}$

Step 3

To write

\frac{5}{2}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{35}{4} + \frac{5}{2} \cdot \frac{2}{2}

$\frac{35}{4} + \frac{5}{2} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

4

$4$ , 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{2}{2}

$\frac{2}{2}$ .

\frac{35}{4} + \frac{5 \cdot 2}{2 \cdot 2}

$\frac{35}{4} + \frac{5 \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply

2

$2$ by

2

$2$ .

\frac{35}{4} + \frac{5 \cdot 2}{4}

$\frac{35}{4} + \frac{5 \cdot 2}{4}$

\frac{35}{4} + \frac{5 \cdot 2}{4}

$\frac{35}{4} + \frac{5 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

\frac{35 + 5 \cdot 2}{4}

$\frac{35 + 5 \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

5

$5$ by

2

$2$ .

\frac{35 + 10}{4}

$\frac{35 + 10}{4}$

Step 6.2

Add

35

$35$ and

10

$10$ .

\frac{45}{4}

$\frac{45}{4}$

\frac{45}{4}

$\frac{45}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{45}{4}

$\frac{45}{4}$

Decimal Form:

11.25

$11.25$

Mixed Number Form:

11 \frac{1}{4}

$11 \frac{1}{4}$