Carolyn spent 3/4 of an hour on her math homework, 5/6 of an hour on history, and 5/12 of an hour on science.

Which of the following is a true statement;
a.)5/6<5/12, b.)5/12<3/4, c.)5/6<3/4, d.)5/12>3/4

change them to common denominators. I will do a, c for you.

a) 10/12<5/12 ?
b)
c) 10/12<9/12 ?
d)

so you see, a, c are not true. Duh.

b.)5/12<3/4,

To compare the fractions and determine which is greater, we need to find a common denominator. In this case, we can use the least common multiple (LCM) of the denominators.

The denominators in the given fractions are 6, 12, and 4. The LCM of these numbers is 12. So, we can convert the fractions to have a denominator of 12.

- For 5/6, we multiply the numerator and denominator by 2, resulting in 10/12.
- For 5/12, no conversion is necessary since the denominator is already 12.
- For 3/4, we multiply the numerator and denominator by 3, resulting in 9/12.

Now we have the following fractions in terms of a denominator of 12:
- 10/12
- 5/12
- 9/12

Looking at these fractions, we can see that 10/12 is the largest, followed by 9/12, and then 5/12. Therefore, the correct statement is:

b.) 5/12 < 3/4