Simplify 8 3/4+5 9/10

$8 \frac{3}{4} + 5 \frac{9}{10}$

Step 1

Convert

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

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

$8 + \frac{3}{4} + 5 \frac{9}{10}$

Add

$8$ and

$\frac{3}{4}$ .

To write

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

$\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 5 \frac{9}{10}$

Combine

$8$ and

$\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 5 \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 5 \frac{9}{10}$

Simplify the numerator.

Multiply

$8$ by

$4$ .

$\frac{32 + 3}{4} + 5 \frac{9}{10}$

Add

$32$ and

$3$ .

$\frac{35}{4} + 5 \frac{9}{10}$

Step 2

Convert

$5 \frac{9}{10}$ to an improper fraction.

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

$\frac{35}{4} + 5 + \frac{9}{10}$

Add

$5$ and

$\frac{9}{10}$ .

To write

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

$\frac{10}{10}$ .

$\frac{35}{4} + 5 \cdot \frac{10}{10} + \frac{9}{10}$

Combine

$5$ and

$\frac{10}{10}$ .

$\frac{35}{4} + \frac{5 \cdot 10}{10} + \frac{9}{10}$

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{5 \cdot 10 + 9}{10}$

Simplify the numerator.

Multiply

$5$ by

$10$ .

$\frac{35}{4} + \frac{50 + 9}{10}$

Add

$50$ and

$9$ .

$\frac{35}{4} + \frac{59}{10}$

Step 3

To write

$\frac{35}{4}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{35}{4} \cdot \frac{5}{5} + \frac{59}{10}$

Step 4

To write

$\frac{59}{10}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{35}{4} \cdot \frac{5}{5} + \frac{59}{10} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of

$20$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{35}{4}$ by

$\frac{5}{5}$ .

$\frac{35 \cdot 5}{4 \cdot 5} + \frac{59}{10} \cdot \frac{2}{2}$

Multiply

$4$ by

$5$ .

$\frac{35 \cdot 5}{20} + \frac{59}{10} \cdot \frac{2}{2}$

Multiply

$\frac{59}{10}$ by

$\frac{2}{2}$ .

$\frac{35 \cdot 5}{20} + \frac{59 \cdot 2}{10 \cdot 2}$

Multiply

$10$ by

$2$ .

$\frac{35 \cdot 5}{20} + \frac{59 \cdot 2}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{35 \cdot 5 + 59 \cdot 2}{20}$

Step 7

Simplify the numerator.

Multiply

$35$ by

$5$ .

$\frac{175 + 59 \cdot 2}{20}$

Multiply

$59$ by

$2$ .

$\frac{175 + 118}{20}$

Add

$175$ and

$118$ .

$\frac{293}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{293}{20}$

Decimal Form:

$14.65$

Mixed Number Form:

$14 \frac{13}{20}$

Simplify 8 3/4+5 9/10

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