Basic Math Examples

$2 \frac{1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

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.

$2 + \frac{1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

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

$\frac{2}{2}$ .

$2 \cdot \frac{2}{2} + \frac{1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

Step 1.2.2

Combine

$2$ and

$\frac{2}{2}$ .

$\frac{2 \cdot 2}{2} + \frac{1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$2$ .

$\frac{4 + 1}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

Step 1.2.4.2

Add

$4$ and

$1$ .

$\frac{5}{2} + 3 \frac{3}{4} + 5 \frac{1}{8}$

Step 2

Convert

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

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Step 2.1

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

$\frac{5}{2} + 3 + \frac{3}{4} + 5 \frac{1}{8}$

Step 2.2

Add

$3$ and

$\frac{3}{4}$ .

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Step 2.2.1

To write

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

$\frac{4}{4}$ .

$\frac{5}{2} + 3 \cdot \frac{4}{4} + \frac{3}{4} + 5 \frac{1}{8}$

Step 2.2.2

Combine

$3$ and

$\frac{4}{4}$ .

$\frac{5}{2} + \frac{3 \cdot 4}{4} + \frac{3}{4} + 5 \frac{1}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{3 \cdot 4 + 3}{4} + 5 \frac{1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$4$ .

$\frac{5}{2} + \frac{12 + 3}{4} + 5 \frac{1}{8}$

Step 2.2.4.2

Add

$12$ and

$3$ .

$\frac{5}{2} + \frac{15}{4} + 5 \frac{1}{8}$

Step 3

Convert

$5 \frac{1}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{5}{2} + \frac{15}{4} + 5 + \frac{1}{8}$

Step 3.2

Add

$5$ and

$\frac{1}{8}$ .

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Step 3.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{5}{2} + \frac{15}{4} + 5 \cdot \frac{8}{8} + \frac{1}{8}$

Step 3.2.2

Combine

$5$ and

$\frac{8}{8}$ .

$\frac{5}{2} + \frac{15}{4} + \frac{5 \cdot 8}{8} + \frac{1}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{15}{4} + \frac{5 \cdot 8 + 1}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

$5$ by

$8$ .

$\frac{5}{2} + \frac{15}{4} + \frac{40 + 1}{8}$

Step 3.2.4.2

Add

$40$ and

$1$ .

$\frac{5}{2} + \frac{15}{4} + \frac{41}{8}$

Step 4

Find the common denominator.

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Step 4.1

Multiply

$\frac{5}{2}$ by

$\frac{4}{4}$ .

$\frac{5}{2} \cdot \frac{4}{4} + \frac{15}{4} + \frac{41}{8}$

Step 4.2

Multiply

$\frac{5}{2}$ by

$\frac{4}{4}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{15}{4} + \frac{41}{8}$

Step 4.3

Multiply

$\frac{15}{4}$ by

$\frac{2}{2}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{15}{4} \cdot \frac{2}{2} + \frac{41}{8}$

Step 4.4

Multiply

$\frac{15}{4}$ by

$\frac{2}{2}$ .

$\frac{5 \cdot 4}{2 \cdot 4} + \frac{15 \cdot 2}{4 \cdot 2} + \frac{41}{8}$

Step 4.5

Multiply

$2$ by

$4$ .

$\frac{5 \cdot 4}{8} + \frac{15 \cdot 2}{4 \cdot 2} + \frac{41}{8}$

Step 4.6

Reorder the factors of

$4 \cdot 2$ .

$\frac{5 \cdot 4}{8} + \frac{15 \cdot 2}{2 \cdot 4} + \frac{41}{8}$

Step 4.7

Multiply

$2$ by

$4$ .

$\frac{5 \cdot 4}{8} + \frac{15 \cdot 2}{8} + \frac{41}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 15 \cdot 2 + 41}{8}$

Step 6

Simplify each term.

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Step 6.1

Multiply

$5$ by

$4$ .

$\frac{20 + 15 \cdot 2 + 41}{8}$

Step 6.2

Multiply

$15$ by

$2$ .

$\frac{20 + 30 + 41}{8}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add

$20$ and

$30$ .

$\frac{50 + 41}{8}$

Step 7.2

Add

$50$ and

$41$ .

$\frac{91}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{8}$

Decimal Form:

$11.375$

Mixed Number Form:

$11 \frac{3}{8}$