What is #5/7 + 3/4#?

Question

Aurora Arias · Accepted Answer

#5/7+3/4=41/28=1 13/28#

Simplify:

#5/7+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,color(red)28,35,42...#

#4:# #4,8,12,16,20,24,color(red)28...#

The LCD is #28#.

Multiply each fraction by a fractional form of #1#, such as #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.

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

Simplify.

#20/28+21/28=#

#(20+21)/28=#

#41/28#

Since #41# is a prime number, the fraction cannot be reduced. However, we can convert it to a mixed number: #a 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 #(28)# is the denominator.

#41-:28="1 remainder 13"#

#41/28=1 13/28#

Emery Allen · Answer

undefined To add the fractions $ \frac{5}{7} $ and $ \frac{3}{4} $, you first need to find a common denominator. In this case, the least common multiple of 7 and 4 is 28. Then, rewrite each fraction with the common denominator and add the numerators.

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

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

Now, add the numerators:

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

$ = \frac{41}{28} $

So, $ \frac{5}{7} + \frac{3}{4} = \frac{41}{28} $.