Simplify 7 3/4+8 4/5

$7 \frac{3}{4} + 8 \frac{4}{5}$

Step 1

Convert

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

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

$7 + \frac{3}{4} + 8 \frac{4}{5}$

Add

$7$ and

$\frac{3}{4}$ .

To write

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

$\frac{4}{4}$ .

$7 \cdot \frac{4}{4} + \frac{3}{4} + 8 \frac{4}{5}$

Combine

$7$ and

$\frac{4}{4}$ .

$\frac{7 \cdot 4}{4} + \frac{3}{4} + 8 \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 + 3}{4} + 8 \frac{4}{5}$

Simplify the numerator.

Multiply

$7$ by

$4$ .

$\frac{28 + 3}{4} + 8 \frac{4}{5}$

Add

$28$ and

$3$ .

$\frac{31}{4} + 8 \frac{4}{5}$

Step 2

Convert

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

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

$\frac{31}{4} + 8 + \frac{4}{5}$

Add

$8$ and

$\frac{4}{5}$ .

To write

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

$\frac{5}{5}$ .

$\frac{31}{4} + 8 \cdot \frac{5}{5} + \frac{4}{5}$

Combine

$8$ and

$\frac{5}{5}$ .

$\frac{31}{4} + \frac{8 \cdot 5}{5} + \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{31}{4} + \frac{8 \cdot 5 + 4}{5}$

Simplify the numerator.

Multiply

$8$ by

$5$ .

$\frac{31}{4} + \frac{40 + 4}{5}$

Add

$40$ and

$4$ .

$\frac{31}{4} + \frac{44}{5}$

Step 3

To write

$\frac{31}{4}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{31}{4} \cdot \frac{5}{5} + \frac{44}{5}$

Step 4

To write

$\frac{44}{5}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{31}{4} \cdot \frac{5}{5} + \frac{44}{5} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{31}{4}$ by

$\frac{5}{5}$ .

$\frac{31 \cdot 5}{4 \cdot 5} + \frac{44}{5} \cdot \frac{4}{4}$

Multiply

$4$ by

$5$ .

$\frac{31 \cdot 5}{20} + \frac{44}{5} \cdot \frac{4}{4}$

Multiply

$\frac{44}{5}$ by

$\frac{4}{4}$ .

$\frac{31 \cdot 5}{20} + \frac{44 \cdot 4}{5 \cdot 4}$

Multiply

$5$ by

$4$ .

$\frac{31 \cdot 5}{20} + \frac{44 \cdot 4}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{31 \cdot 5 + 44 \cdot 4}{20}$

Step 7

Simplify the numerator.

Multiply

$31$ by

$5$ .

$\frac{155 + 44 \cdot 4}{20}$

Multiply

$44$ by

$4$ .

$\frac{155 + 176}{20}$

Add

$155$ and

$176$ .

$\frac{331}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{331}{20}$

Decimal Form:

$16.55$

Mixed Number Form:

$16 \frac{11}{20}$

Simplify 7 3/4+8 4/5

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