Home > Prealgebra > Decomposing Fractions

George read 3/8 of his book on Thursday and 1/6 of his book on Friday. What fraction of his book did he read altogether on these days?

Answer 1

#(13/24)#

To add fractions you need to have the same number in the denominator of each one. This is called the “Least common denominator”. We find it by factoring each denominator into prime numbers, and then recombining the “common factors”.

For 8, the factors are #2*2*2# and for 6 they are #2*3#. Recombining only the ‘unique factors’ we obtain the least common denominator: #2*2*2*3 = 24#.

Now we can convert our given fractions into ones that can be added together by multiplying each one by the factors not originally in their factors.

#(3/8) * (3/3) = (9/24)# and #(1/6)*(4/4) = (4/24)#

#(9/24) + (4/24) = (13/24)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.