Simplify 4 1/2+3 5/8

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

Step 1

Convert

$4 \frac{1}{2}$ to an improper fraction.

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

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

Add

$4$ and

$\frac{1}{2}$ .

To write

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

$\frac{2}{2}$ .

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

Combine

$4$ and

$\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$2$ .

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

Add

$8$ and

$1$ .

$\frac{9}{2} + 3 \frac{5}{8}$

Step 2

Convert

$3 \frac{5}{8}$ to an improper fraction.

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

$\frac{9}{2} + 3 + \frac{5}{8}$

Add

$3$ and

$\frac{5}{8}$ .

To write

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

$\frac{8}{8}$ .

$\frac{9}{2} + 3 \cdot \frac{8}{8} + \frac{5}{8}$

Combine

$3$ and

$\frac{8}{8}$ .

$\frac{9}{2} + \frac{3 \cdot 8}{8} + \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{3 \cdot 8 + 5}{8}$

Simplify the numerator.

Multiply

$3$ by

$8$ .

$\frac{9}{2} + \frac{24 + 5}{8}$

Add

$24$ and

$5$ .

$\frac{9}{2} + \frac{29}{8}$

Step 3

To write

$\frac{9}{2}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{9}{2} \cdot \frac{4}{4} + \frac{29}{8}$

Step 4

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{9}{2}$ by

$\frac{4}{4}$ .

$\frac{9 \cdot 4}{2 \cdot 4} + \frac{29}{8}$

Multiply

$2$ by

$4$ .

$\frac{9 \cdot 4}{8} + \frac{29}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 4 + 29}{8}$

Step 6

Simplify the numerator.

Multiply

$9$ by

$4$ .

$\frac{36 + 29}{8}$

Add

$36$ and

$29$ .

$\frac{65}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{8}$

Decimal Form:

$8.125$

Mixed Number Form:

$8 \frac{1}{8}$

Simplify 4 1/2+3 5/8

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