Basic Math Examples

$2 \frac{5}{8} + 5 \frac{3}{6}$

Step 1

Convert

$2 \frac{5}{8}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{5}{8} + 5 \frac{3}{6}$

Step 1.2

Add

$2$ and

$\frac{5}{8}$ .

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Step 1.2.1

To write

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

$\frac{8}{8}$ .

$2 \cdot \frac{8}{8} + \frac{5}{8} + 5 \frac{3}{6}$

Step 1.2.2

Combine

$2$ and

$\frac{8}{8}$ .

$\frac{2 \cdot 8}{8} + \frac{5}{8} + 5 \frac{3}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 + 5}{8} + 5 \frac{3}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$8$ .

$\frac{16 + 5}{8} + 5 \frac{3}{6}$

Step 1.2.4.2

Add

$16$ and

$5$ .

$\frac{21}{8} + 5 \frac{3}{6}$

Step 2

Convert

$5 \frac{3}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{21}{8} + 5 + \frac{3}{6}$

Step 2.2

Add

$5$ and

$\frac{3}{6}$ .

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Step 2.2.1

To write

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

$\frac{6}{6}$ .

$\frac{21}{8} + 5 \cdot \frac{6}{6} + \frac{3}{6}$

Step 2.2.2

Combine

$5$ and

$\frac{6}{6}$ .

$\frac{21}{8} + \frac{5 \cdot 6}{6} + \frac{3}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{21}{8} + \frac{5 \cdot 6 + 3}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$5$ by

$6$ .

$\frac{21}{8} + \frac{30 + 3}{6}$

Step 2.2.4.2

Add

$30$ and

$3$ .

$\frac{21}{8} + \frac{33}{6}$

Step 3

Cancel the common factor of

$33$ and

$6$ .

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Step 3.1

Factor

$3$ out of

$33$ .

$\frac{21}{8} + \frac{3 (11)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$3$ out of

$6$ .

$\frac{21}{8} + \frac{3 \cdot 11}{3 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{21}{8} + \frac{3 \cdot 11}{3 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{21}{8} + \frac{11}{2}$

Step 4

To write

$\frac{11}{2}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{21}{8} + \frac{11}{2} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

$8$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{11}{2}$ by

$\frac{4}{4}$ .

$\frac{21}{8} + \frac{11 \cdot 4}{2 \cdot 4}$

Step 5.2

Multiply

$2$ by

$4$ .

$\frac{21}{8} + \frac{11 \cdot 4}{8}$

Step 6

Combine the numerators over the common denominator.

$\frac{21 + 11 \cdot 4}{8}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$11$ by

$4$ .

$\frac{21 + 44}{8}$

Step 7.2

Add

$21$ and

$44$ .

$\frac{65}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{8}$

Decimal Form:

$8.125$

Mixed Number Form:

$8 \frac{1}{8}$