Summer 2012
Understanding Ratios
1. The ratio of the number of boys to the number of girls at Archimedes’ Junior High
School is 4:5.
a) What fraction of the students are boys?
b) If there are 140 boys, how many students are there altogether? Solve this
problem in at least 2 ways.
2. A grocery store sells rice in bulk. The sign says: $4 for 5 pounds. At this store, you
can buy any number of pounds of rice at a time, and all prices include tax.
Alberto said,
“The ratio of the number of dollars to the number of pounds is 4:5. That’s $.80
per pound.”
Beth said,
“The sign says the ratio of the number of pounds to the number of dollars is 5:4.
That’s 1.25 pounds per dollar.”
a) Are Alberto and Beth both correct? Discuss with your group members.
Understanding Ratios
Page 1 of 2
Adopted by Illustrative Mathematics – Content Standards: Kindergarten Through Grade 8 (Grade 6), www.illustrativemathematics.org
Summer 2012
b) Claude needs 2 pounds of rice. Show Claude how much money he will need.
Solve this problem in at least 2 ways.
c) Dora has $10 and wants to stock up on rice. Show Dora how many pounds of
rice she can buy. Solve this problem in at least 2 ways.
d) Do you prefer to answer parts (b) and (c) using Alberto’s rate of $.80 per pound,
using Beth’s rate of 1.25 pounds per dollar, or using another strategy? Discuss
with your group members.
3. Compare problems 1 and 2 above and note any similarities or differences.
Discuss with your group members.
Understanding Ratios
Page 2 of 2
Adopted by Illustrative Mathematics – Content Standards: Kindergarten Through Grade 8 (Grade 6), www.illustrativemathematics.org