Simplify 4 3/8+2 3/4

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

Step 1

Convert

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

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

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

Add

$4$ and

$\frac{3}{8}$ .

To write

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

$\frac{8}{8}$ .

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

Combine

$4$ and

$\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$8$ .

$\frac{32 + 3}{8} + 2 \frac{3}{4}$

Add

$32$ and

$3$ .

$\frac{35}{8} + 2 \frac{3}{4}$

Step 2

Convert

$2 \frac{3}{4}$ to an improper fraction.

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

$\frac{35}{8} + 2 + \frac{3}{4}$

Add

$2$ and

$\frac{3}{4}$ .

To write

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

$\frac{4}{4}$ .

$\frac{35}{8} + 2 \cdot \frac{4}{4} + \frac{3}{4}$

Combine

$2$ and

$\frac{4}{4}$ .

$\frac{35}{8} + \frac{2 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{35}{8} + \frac{2 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply

$2$ by

$4$ .

$\frac{35}{8} + \frac{8 + 3}{4}$

Add

$8$ and

$3$ .

$\frac{35}{8} + \frac{11}{4}$

Step 3

To write

$\frac{11}{4}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{35}{8} + \frac{11}{4} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{11}{4}$ by

$\frac{2}{2}$ .

$\frac{35}{8} + \frac{11 \cdot 2}{4 \cdot 2}$

Multiply

$4$ by

$2$ .

$\frac{35}{8} + \frac{11 \cdot 2}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{35 + 11 \cdot 2}{8}$

Step 6

Simplify the numerator.

Multiply

$11$ by

$2$ .

$\frac{35 + 22}{8}$

Add

$35$ and

$22$ .

$\frac{57}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{57}{8}$

Decimal Form:

$7.125$

Mixed Number Form:

$7 \frac{1}{8}$

Simplify 4 3/8+2 3/4

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