Simplify 8 3/4+7 3/4

$8 \frac{3}{4} + 7 \frac{3}{4}$

Step 1

Convert

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

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

$8 + \frac{3}{4} + 7 \frac{3}{4}$

Add

$8$ and

$\frac{3}{4}$ .

To write

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

$\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 7 \frac{3}{4}$

Combine

$8$ and

$\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 7 \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 7 \frac{3}{4}$

Simplify the numerator.

Multiply

$8$ by

$4$ .

$\frac{32 + 3}{4} + 7 \frac{3}{4}$

Add

$32$ and

$3$ .

$\frac{35}{4} + 7 \frac{3}{4}$

Step 2

Convert

$7 \frac{3}{4}$ to an improper fraction.

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

$\frac{35}{4} + 7 + \frac{3}{4}$

Add

$7$ and

$\frac{3}{4}$ .

To write

$7$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{35}{4} + 7 \cdot \frac{4}{4} + \frac{3}{4}$

Combine

$7$ and

$\frac{4}{4}$ .

$\frac{35}{4} + \frac{7 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{7 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply

$7$ by

$4$ .

$\frac{35}{4} + \frac{28 + 3}{4}$

Add

$28$ and

$3$ .

$\frac{35}{4} + \frac{31}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{35 + 31}{4}$

Step 4

Add

$35$ and

$31$ .

$\frac{66}{4}$

Step 5

Cancel the common factor of

$66$ and

$4$ .

Factor

$2$ out of

$66$ .

$\frac{2 (33)}{4}$

Cancel the common factors.

Factor

$2$ out of

$4$ .

$\frac{2 \cdot 33}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 33}{2 \cdot 2}$

Rewrite the expression.

$\frac{33}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{2}$

Decimal Form:

$16.5$

Mixed Number Form:

$16 \frac{1}{2}$

Simplify 8 3/4+7 3/4

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