Simplify 7 8/13+3 13/15

$7 \frac{8}{13} + 3 \frac{13}{15}$

Step 1

Convert

$7 \frac{8}{13}$ to an improper fraction.

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

$7 + \frac{8}{13} + 3 \frac{13}{15}$

Add

$7$ and

$\frac{8}{13}$ .

To write

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

$\frac{13}{13}$ .

$7 \cdot \frac{13}{13} + \frac{8}{13} + 3 \frac{13}{15}$

Combine

$7$ and

$\frac{13}{13}$ .

$\frac{7 \cdot 13}{13} + \frac{8}{13} + 3 \frac{13}{15}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 13 + 8}{13} + 3 \frac{13}{15}$

Simplify the numerator.

Multiply

$7$ by

$13$ .

$\frac{91 + 8}{13} + 3 \frac{13}{15}$

Add

$91$ and

$8$ .

$\frac{99}{13} + 3 \frac{13}{15}$

Step 2

Convert

$3 \frac{13}{15}$ to an improper fraction.

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

$\frac{99}{13} + 3 + \frac{13}{15}$

Add

$3$ and

$\frac{13}{15}$ .

To write

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

$\frac{15}{15}$ .

$\frac{99}{13} + 3 \cdot \frac{15}{15} + \frac{13}{15}$

Combine

$3$ and

$\frac{15}{15}$ .

$\frac{99}{13} + \frac{3 \cdot 15}{15} + \frac{13}{15}$

Combine the numerators over the common denominator.

$\frac{99}{13} + \frac{3 \cdot 15 + 13}{15}$

Simplify the numerator.

Multiply

$3$ by

$15$ .

$\frac{99}{13} + \frac{45 + 13}{15}$

Add

$45$ and

$13$ .

$\frac{99}{13} + \frac{58}{15}$

Step 3

To write

$\frac{99}{13}$ as a fraction with a common denominator, multiply by

$\frac{15}{15}$ .

$\frac{99}{13} \cdot \frac{15}{15} + \frac{58}{15}$

Step 4

To write

$\frac{58}{15}$ as a fraction with a common denominator, multiply by

$\frac{13}{13}$ .

$\frac{99}{13} \cdot \frac{15}{15} + \frac{58}{15} \cdot \frac{13}{13}$

Step 5

Write each expression with a common denominator of

$195$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{99}{13}$ by

$\frac{15}{15}$ .

$\frac{99 \cdot 15}{13 \cdot 15} + \frac{58}{15} \cdot \frac{13}{13}$

Multiply

$13$ by

$15$ .

$\frac{99 \cdot 15}{195} + \frac{58}{15} \cdot \frac{13}{13}$

Multiply

$\frac{58}{15}$ by

$\frac{13}{13}$ .

$\frac{99 \cdot 15}{195} + \frac{58 \cdot 13}{15 \cdot 13}$

Multiply

$15$ by

$13$ .

$\frac{99 \cdot 15}{195} + \frac{58 \cdot 13}{195}$

Step 6

Combine the numerators over the common denominator.

$\frac{99 \cdot 15 + 58 \cdot 13}{195}$

Step 7

Simplify the numerator.

Multiply

$99$ by

$15$ .

$\frac{1485 + 58 \cdot 13}{195}$

Multiply

$58$ by

$13$ .

$\frac{1485 + 754}{195}$

Add

$1485$ and

$754$ .

$\frac{2239}{195}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2239}{195}$

Decimal Form:

$11.48205128 \dots$

Mixed Number Form:

$11 \frac{94}{195}$

Simplify 7 8/13+3 13/15

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