How do you add #7\frac { 2} { 3} + 2\frac { 3} { 5}#?

1 Answer
seol
Apr 3, 2017

#154/15#

Explanation:

Converting a mixed number to improper fraction form:
Multiply the whole number by the fraction's denominator, then add the resulting product to the numerator.
#ab/c\rarr(a(c)+b)/c#

Now we are going to use that to convert the two mixed numbers in your equation.
#7 2/3\rarr(7(3)+2)/3=(21+2)/3=23/3#
#2 3/5\rarr(2(5)+3)/3=(10+3)/5=13/5#

So now you have #23/3+13/5#. Next step is to convert these improper fractions so that you have the same denominators.
To do that, find the least common multiple (LCM) of the denominators.

The LCM of 3 and 5 is 15, #3\cdot5=15#. Therefore, multiply where needed...
#(23/3xx5/5)+(13/5xx3/3)\rarr(23xx5)/15+(13xx3)/15#

...and simplify.
#115/15+39/15=(115+39)/15=154/15#

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