Simplify 4 5/8+8 5/6

$4 \frac{5}{8} + 8 \frac{5}{6}$

Step 1

Convert

$4 \frac{5}{8}$ to an improper fraction.

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

$4 + \frac{5}{8} + 8 \frac{5}{6}$

Add

$4$ and

$\frac{5}{8}$ .

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$4 \cdot \frac{8}{8} + \frac{5}{8} + 8 \frac{5}{6}$

Combine

$4$ and

$\frac{8}{8}$ .

$\frac{4 \cdot 8}{8} + \frac{5}{8} + 8 \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 5}{8} + 8 \frac{5}{6}$

Simplify the numerator.

Multiply

$4$ by

$8$ .

$\frac{32 + 5}{8} + 8 \frac{5}{6}$

Add

$32$ and

$5$ .

$\frac{37}{8} + 8 \frac{5}{6}$

Step 2

Convert

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

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

$\frac{37}{8} + 8 + \frac{5}{6}$

Add

$8$ and

$\frac{5}{6}$ .

To write

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

$\frac{6}{6}$ .

$\frac{37}{8} + 8 \cdot \frac{6}{6} + \frac{5}{6}$

Combine

$8$ and

$\frac{6}{6}$ .

$\frac{37}{8} + \frac{8 \cdot 6}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{37}{8} + \frac{8 \cdot 6 + 5}{6}$

Simplify the numerator.

Multiply

$8$ by

$6$ .

$\frac{37}{8} + \frac{48 + 5}{6}$

Add

$48$ and

$5$ .

$\frac{37}{8} + \frac{53}{6}$

Step 3

To write

$\frac{37}{8}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{37}{8} \cdot \frac{3}{3} + \frac{53}{6}$

Step 4

To write

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

$\frac{4}{4}$ .

$\frac{37}{8} \cdot \frac{3}{3} + \frac{53}{6} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{37}{8}$ by

$\frac{3}{3}$ .

$\frac{37 \cdot 3}{8 \cdot 3} + \frac{53}{6} \cdot \frac{4}{4}$

Multiply

$8$ by

$3$ .

$\frac{37 \cdot 3}{24} + \frac{53}{6} \cdot \frac{4}{4}$

Multiply

$\frac{53}{6}$ by

$\frac{4}{4}$ .

$\frac{37 \cdot 3}{24} + \frac{53 \cdot 4}{6 \cdot 4}$

Multiply

$6$ by

$4$ .

$\frac{37 \cdot 3}{24} + \frac{53 \cdot 4}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{37 \cdot 3 + 53 \cdot 4}{24}$

Step 7

Simplify the numerator.

Multiply

$37$ by

$3$ .

$\frac{111 + 53 \cdot 4}{24}$

Multiply

$53$ by

$4$ .

$\frac{111 + 212}{24}$

Add

$111$ and

$212$ .

$\frac{323}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{323}{24}$

Decimal Form:

$13.458\overline{3}$

Mixed Number Form:

$13 \frac{11}{24}$

Simplify 4 5/8+8 5/6

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