Introducing Ratios
What is a ratio? Give an example.
A ratio is a comparison of two quantities.
True or False: 2:3 and 4:6 are equivalent ratios.
True (both simplify to 2:3, or 4:6 = 2×2 : 3×2)
What is a ratio table used for?
A ratio table is used to organize and find equivalent ratios or to solve ratio problems.
The ratio of cats to dogs at a shelter is 3:4. If there are 12 cats, how many dogs are there?
16 dogs
The ratio of red marbles to blue marbles is 3:7. If there are 30 marbles total, how many are red?
9 red marbles
Write the ratio "3 apples to 5 oranges" in three different ways.
3:5, 3 to 5, 3/5
Find two ratios equivalent to 5:7.
Examples: 10:14, 15:21, 20:28 (any two are acceptable)
Complete this ratio table: If 2 pencils cost $1, then 6 pencils cost ____.
$3 (multiply both quantities by 3)
A smoothie recipe uses strawberries and bananas in a ratio of 5:2. If you use 10 strawberries, how many bananas should you use?
4 bananas
A fruit punch recipe uses cranberry juice and sparkling water in a ratio of 2:5. If you make 35 cups of punch, how many cups of cranberry juice did you use?
10 cups of cranberry juice
In a class, the ratio of boys to girls is 4:5. If there are 12 boys, how many girls are there?
15 girls
A recipe calls for 3 cups of flour to 2 cups of sugar. If you want to make a larger batch using 9 cups of flour, how much sugar do you need?
6 cups of sugar
A car travels 120 miles in 2 hours. Create a ratio table showing the distance traveled in 1, 2, 3, and 4 hours.
In a school, the ratio of 6th graders to 7th graders is 7:5. If there are 240 students total, how many are 6th graders?
140 sixth graders
Two numbers are in the ratio 4:9. Their sum is 52. What are the two numbers?
16 and 36
A paint mixture uses blue and yellow paint in a ratio of 2:3. If you use 8 cups of blue paint, how many cups of yellow paint do you need?
12 cups of yellow paint
Are the ratios 6:8 and 9:12 equivalent? Explain your reasoning using at least two different methods.
Yes, they are equivalent.
A ratio table shows that 4 pounds of apples cost $6. Use the table to find the cost of 10 pounds of apples.
$15 (unit rate is $1.50 per pound, so 10 × $1.50 = $15, or build the table: 2 lb = $3, 4 lb = $6, 8 lb = $12, 10 lb = $15)
Two quantities are in the ratio 3:8. If the smaller quantity is 15, what is the larger quantity?
40
A recipe for 4 people uses 6 eggs. You want to make enough for 14 people, but eggs only come in dozens. How many dozens of eggs should you buy, and how many eggs will you have left over?
Buy 2 dozen eggs; 3 eggs left over.
Three quantities are in the ratio 2:5:3. If the smallest quantity is 12, what are the other two quantities?
30 and 18
Which of these ratios is NOT equivalent to the others: 15:20, 9:12, 12:15, or 6:8? Explain your reasoning.
12:15 is NOT equivalent (it simplifies to 4:5, while the others all simplify to 3:4)
Create a ratio table to solve: A machine produces 450 widgets in 6 hours. At this rate, how long will it take to produce 1,125 widgets?
15 hours (450 ÷ 6 = 75 widgets per hour; 1,125 ÷ 75 = 15 hours)
A photograph measuring 4 inches by 6 inches is enlarged so that the longer side is 15 inches. What is the length of the shorter side? Is the ratio of the sides preserved?
10 inches; yes, the ratio is preserved
A store sells trail mix. The ratio of peanuts to raisins to chocolate chips is 5:3:2. If a bag contains 120 pieces of peanuts, how many total pieces are in the bag?
240 pieces total