here are 32 sixth graders and 44 seventh graders in the video gaming club. Which ratio is the greatest?
A.the ratio of sixth graders to seventh graders
B.the ratio of sixth graders to club members
C.the ratio of club members to sixth graders
D.the ratio of club members to seventh graders
sixth:seventh = 32:44 = 8:11
sixth:club = 32:76 = 16:39
and so on. Finally, compare the fractions to find the greatest
or, since club is the greatest, and sixth is the smallest, club:sixth will be greatest ratio
To compare ratios, we need to determine the value of each ratio.
A. The ratio of sixth graders to seventh graders is 32:44. To find a simplified form of the ratio, we divide both numbers by their greatest common divisor, which is 4.
32 ÷ 4 = 8
44 ÷ 4 = 11
So, the ratio of sixth graders to seventh graders in simplified form is 8:11.
B. The ratio of sixth graders to club members is determined by adding the number of sixth graders to the number of seventh graders.
32 + 44 = 76
So, the ratio of sixth graders to club members is 32:76, which can be further simplified by dividing both numbers by 4.
32 ÷ 4 = 8
76 ÷ 4 = 19
Therefore, the ratio of sixth graders to club members in simplified form is 8:19.
C. The ratio of club members to sixth graders is determined by dividing the total number of club members by the number of sixth graders.
76 ÷ 32 = 2.375
Therefore, the ratio of club members to sixth graders is 2.375:1.
D. The ratio of club members to seventh graders is determined by dividing the total number of club members by the number of seventh graders.
76 ÷ 44 = 1.7272
Therefore, the ratio of club members to seventh graders is 1.7272:1.
To determine which ratio is the greatest, we compare the simplified forms of each ratio:
- 8:11
- 8:19
- 2.375:1
- 1.7272:1
The greatest ratio is B. the ratio of sixth graders to club members, which is 8:19.