Basic Math Examples

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

Step 1

Convert

$2 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$2$ and

$\frac{3}{8}$ .

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Step 1.2.1

To write

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

$\frac{8}{8}$ .

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

Step 1.2.2

Combine

$2$ and

$\frac{8}{8}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$2$ by

$8$ .

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

Step 1.2.4.2

Add

$16$ and

$3$ .

$\frac{19}{8} + 8 \frac{5}{6}$

Step 2

Convert

$8 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{19}{8} + 8 + \frac{5}{6}$

Step 2.2

Add

$8$ and

$\frac{5}{6}$ .

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Step 2.2.1

To write

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

$\frac{6}{6}$ .

$\frac{19}{8} + 8 \cdot \frac{6}{6} + \frac{5}{6}$

Step 2.2.2

Combine

$8$ and

$\frac{6}{6}$ .

$\frac{19}{8} + \frac{8 \cdot 6}{6} + \frac{5}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{19}{8} + \frac{8 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$8$ by

$6$ .

$\frac{19}{8} + \frac{48 + 5}{6}$

Step 2.2.4.2

Add

$48$ and

$5$ .

$\frac{19}{8} + \frac{53}{6}$

Step 3

To write

$\frac{19}{8}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{19}{8} \cdot \frac{3}{3} + \frac{53}{6}$

Step 4

To write

$\frac{53}{6}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{19}{8} \cdot \frac{3}{3} + \frac{53}{6} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

$24$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{19}{8}$ by

$\frac{3}{3}$ .

$\frac{19 \cdot 3}{8 \cdot 3} + \frac{53}{6} \cdot \frac{4}{4}$

Step 5.2

Multiply

$8$ by

$3$ .

$\frac{19 \cdot 3}{24} + \frac{53}{6} \cdot \frac{4}{4}$

Step 5.3

Multiply

$\frac{53}{6}$ by

$\frac{4}{4}$ .

$\frac{19 \cdot 3}{24} + \frac{53 \cdot 4}{6 \cdot 4}$

Step 5.4

Multiply

$6$ by

$4$ .

$\frac{19 \cdot 3}{24} + \frac{53 \cdot 4}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{19 \cdot 3 + 53 \cdot 4}{24}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$19$ by

$3$ .

$\frac{57 + 53 \cdot 4}{24}$

Step 7.2

Multiply

$53$ by

$4$ .

$\frac{57 + 212}{24}$

Step 7.3

Add

$57$ and

$212$ .

$\frac{269}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{269}{24}$

Decimal Form:

$11.208\overline{3}$

Mixed Number Form:

$11 \frac{5}{24}$