How do you evaluate #\frac { 25} { 31} \cdot \frac { 62} { 105} + \frac { 3} { 7}#?

1 Answer
Y
May 14, 2017

Write out the prime factorization for each number and cancel if possible, then find the LCD to add the fractions.
Answer: #19/21#

Explanation:

Evaluate #25/31*62/105+3/7#

First, we can write out the prime factorization for each value:
#=5^2/31*(31*2)/(3*5*7)+3/7#

Now, we look to cancel values that appear in the numerator and the denominator, #5# and #31#:
#=5/1*2/(3*7)+3/7#

We can simplify the multiplication to:
#=10/(3*7)+3/7#

To add the fractions, we notice that lowest common denominator would be #3*7=21#, which would require us to multiply #3/7# by #3/3#:
#=10/(3*7)+3/7*3/3#
#=10/(3*7)+9/(3*7)#
#=(10+9)/(3*7)#
#=19/21#

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