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

1 Answer
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