Question

The table shows the fraction of students from differentgrade levels who are in favor of adding new items tothe lunch menu at their school. Which list shows the grade levels in order from the greatest fraction of students to the least fraction of students ?

Answer 1

First, write all the fractions using the same denominator. To do so, find the least common multiple of all denominatos. The denominators are:

`50,20,25,75,5`

The least common multiple of all those numbers is 300.

Use 300 as a common denominator for all fractions to be able to compare their values.

5th grade

`(33)/(50)=(33*6)/(50*6)=(198)/(300)`

6th grade

`(13)/(20)=(13*15)/(20*15)=(195)/(300)`

7th grade

`(18)/(25)=(18*12)/(25*12)=(216)/(300)`

8th grade

`(51)/(75)=(51*4)/(75*4)=(204)/(300)`

9th grade

`(3)/(5)=(3*60)/(5*60)=(180)/(300)`

Now, we can compare the numerators to list the fraction from greatest to lowest:

`\begin{gathered} (216)/(300)>(204)/(300)>(198)/(300)>(195)/(300)>(180)/(300) \\ \Leftrightarrow(18)/(25)>(51)/(75)>(33)/(50)>(13)/(20)>(3)/(5) \\ \Leftrightarrow7th\text{ grade}>8th\text{ grade}>5th\text{ grade}>6th\text{ grade}>9th\text{ grade} \end{gathered}`

Therefore, the list of grade levels in order from the greatest fraction of students to the least fraction of students, is:

7th grade (18/25)

8th grade (51/75)

5th grade (33/50)

6th grade (13/20)

9th grade (3/5)