Representing and Reasoning About Ratios
A class has 12 boys and 18 girls.
a. What is the ratio of boys to girls?
b. What does the ratio mean in this situation?
a. 12:18 or 2:3
b. For every 2 boys, there are 3 girls.
Which ratio is equivalent to 4:7?
A. 8:14
B. 8:12
C. 12:18
D. 16:21
Answer: A. 8:14
A car travels 240 miles in 4 hours.
What is the unit rate?
Answer: 60 miles per hour
What is 25% of 80?
Answer: 20
A store sells a box of 12 granola bars for $7.20.
Another store sells 20 granola bars for $11.00.
Which store has the better unit price, and what is the percent difference between the two unit prices?
Store A:
$7.20 ÷ 12 = $0.60/bar
Store B:
$11 ÷ 20 = $0.55/bar
Store B is cheaper by $0.05.
Percent difference compared with Store A:
$0.05 ÷ $0.60 = 0.0833...
About 8.3% cheaper
A recipe uses 3 cups of flour for every 2 cups of sugar.
If you use 9 cups of flour, how much sugar will you need?
Answer: 6 cups of sugar
Complete the table.
Red Blue
3 5
6 ?
? 20
15 ?
Red Blue
3 5
6 10
12 20
15 25
A 6-pack of juice costs $4.50.
What is the cost per juice?
Answer:
$4.50 ÷ 6 = $0.75 per juice
A shirt costs $60 and is on sale for 20% off.
How much is the discount?
Answer:
20% of $60 = $12
The ratio of fiction books to nonfiction books in a classroom library is 5:3.
There are 64 books total.
Then the teacher adds 16 nonfiction books.
What is the new ratio of fiction to nonfiction books?
5 + 3 = 8 parts
64 ÷ 8 = 8
Fiction: 5 × 8 = 40
Nonfiction: 3 × 8 = 24
After adding 16 nonfiction:
24 + 16 = 40
New ratio = 40:40 = 1:1
Answer: 1:1
The ratio of red marbles to blue marbles in a bag is 5:3. There are 40 red marbles.
How many marbles are in the bag altogether?
5 → 40, so the scale factor is 8.
Blue: 3 × 8 = 24
Total: 40 + 24 = 64 marbles
The ratio of cats to dogs at an animal shelter is 4:7.
Which three ratios are equivalent to 4:7?
8:14, 12:21, 20:35, 24:42
Store A sells 8 notebooks for $12.
Store B sells 5 notebooks for $8.
Which store has the better price per notebook?
Answer:
Store A: $12 ÷ 8 = $1.50 each
Store B: $8 ÷ 5 = $1.60 each
Store A is the better buy.
A student answered 42 out of 50 questions correctly.
What percent did the student answer correctly?
Answer:
42 ÷ 50 = 0.84
0.84 = 84%
Two students describe the ratio of apples to oranges as follows:
Are they describing the same ratio? Explain how you know.
Answer: Yes.
28 ÷ 4 = 7 and 49 ÷ 7 = 7, so both quantities were multiplied by the same factor.
Both ratios represent 4:7.
A student says:
“The ratios 18:24 and 27:36 are not equivalent because the numbers are different.”
Do you agree? Explain.
Answer: No.
18:24 simplifies to 3:4.
27:36 also simplifies to 3:4.
Therefore, the ratios are equivalent.
A runner completes 3 miles in 22.5 minutes.
At this rate, how long would it take the runner to complete 8 miles?
22.5 ÷ 3 = 7.5 minutes per mile
7.5 × 8 = 60 minutes
A bicycle originally costs $240.
It is marked 30% off.
What is the sale price?
30% of $240 = $72
$240 − $72 = $168
A school has boys and girls in a ratio of 3:5.
After 12 boys and 4 girls leave for an assembly, the ratio becomes 1:2.
How many boys and girls were there originally?
Answer: 36 boys and 60 girls
Check:
36 − 12 = 24
60 − 4 = 56
24:56 = 3:7, not 1:2.
So this situation is actually impossible.
Answer: No possible original numbers satisfy both conditions.
Three teams are mixing blue and yellow paint.
Which teams have the same blue-to-yellow ratio? Which team is different?
Team A: 6:10 = 3:5
Team B: 9:15 = 3:5
Team C: 14:21 = 2:3
Teams A and B are equivalent. Team C is different.
Two students are comparing how quickly they can read.
Who reads at the faster rate?
Bonus (+)$100 How many words would each student read in 20 minutes?”
Ava:
1,200 ÷ 8 = 150 words/minute
Noah:
1,650 ÷ 11 = 150 words/minute
They read at the same rate.
Bonus: 3000 words each
A jacket is marked 40% off. After the discount, the price is $72.
What was the original price of the jacket?
Answer:
If it is 40% off, the sale price is 60% of the original price.
60% of original = $72
$72 ÷ 0.60 = $120
Original price: $120