what is the sum of 2/5+1/6+1/3+1/4?

Question

Marti grouped all her CD's into separate categories. She said "2/5 of my CD's are rock music,1/6 are jazz,1/3 are hip hop and 1/4 are country music.Explain why Marti's statement cannot be correct

Answer 1

If the fractions don't add up to 1 then Marti has left something out, over accounted or is no good at sums! To find out the sum of the fractions find the lowest common denominator by breaking down the denominators into factors: 5 and 3 have no factors but 2 is a common factor of 4 and 6. 6=2*3, 4=2*2 and we have 3 and 5. What's the maximum number of 2's together? Two. What's the maximum number of 3's. One. And there's one 5. The denominator we need is 2*2*3*5=60. Divide each denominator into 60 and multiply by the numerator: (24+10+20+15)/60=69/60, which is bigger than 1. So Marti is wrong! And we know why!