# What is 5/7 + 3/4?

Mar 11, 2018

$\frac{5}{7} + \frac{3}{4} = \frac{41}{28} = 1 \frac{13}{28}$

#### Explanation:

Simplify:

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

In order to add or subtract fractions, they must have the same denominator. We can determine the least common denominator (LCD) by listing the multiples of each denominator, and finding the lowest multiple they have in common.

$7 :$ $7 , 14 , 21 , \textcolor{red}{28} , 35 , 42. . .$

$4 :$ $4 , 8 , 12 , 16 , 20 , 24 , \textcolor{red}{28.} . .$

The LCD is $28$.

Multiply each fraction by a fractional form of $1$, such as $\frac{3}{3}$, that will give each fraction the denominator $28$. This will change the numbers, but not the value of each fraction.

5/7xxcolor(teal)(4/4)+3/4xxcolor(magenta)(7/7

Simplify.

$\frac{5 \times \textcolor{t e a l}{4}}{7 \times \textcolor{t e a l}{4}} + \frac{3 \times \textcolor{m a \ge n t a}{7}}{4 \times \textcolor{m a \ge n t a}{7}}$

Simplify.

$\frac{20}{28} + \frac{21}{28} =$

$\frac{20 + 21}{28} =$

$\frac{41}{28}$

Since $41$ is a prime number, the fraction cannot be reduced. However, we can convert it to a mixed number: $a \frac{b}{c}$.

Divide $41$ by $28$ using long division to get a whole number quotient and a remainder. The whole number quotient is the whole number in the mixed number, the remainder is the numerator, and the divisor $\left(28\right)$ is the denominator.

$41 \div 28 = \text{1 remainder 13}$

$\frac{41}{28} = 1 \frac{13}{28}$