Understanding Ratios: Language, Notation, and Relationships
For each ratio problem, identify which quantity comes first and which comes second. Label part-to-part (P:P) or part-to-whole (P:W) where indicated.
Recall / Warm-Up
A baker puts 3 chocolate chips into each cookie. If she makes 5 cookies, which number sentence shows how many chocolate chips she uses in all?
A pizza is cut into 8 equal slices and 3 slices have been eaten. Which fraction represents the portion of the pizza that has been eaten?
Which pair of numbers are factors of 12?
Fluency Practice
A bowl has 8 yellow and 12 purple candies. Which correctly describes the ratio of yellow to purple?
A parking lot has 7 trucks and 13 cars. Which statement uses correct ratio language for the ratio of trucks to cars?
A smoothie recipe uses 3 cups of fruit for every 1 cup of yogurt. Write the ratio of fruit to yogurt in fraction form (as a/b).
A class has 16 students who prefer soccer and 12 who prefer basketball. A student writes the ratio as 16:12. Is this correct, or must it be simplified?
A bag holds 5 baseballs and 3 tennis balls. Which of the following is a part-to-whole ratio?
Varied Practice
In a garden with 10 roses and 15 tulips, which statement describes the ratio of roses to tulips?
The ratio of cats to dogs is 5 to 2. Write this ratio in all three notations:
Words: 5 ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ 2
Colon: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ : ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Fraction: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ / ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
A classroom has 4 red counters and 6 blue counters. Which of the following is the fraction of counters that are red?
A fruit bowl has 4 apples and 6 oranges.
The part-to-part ratio of apples to oranges is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ : ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
The part-to-whole ratio of apples to total fruit is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ : ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
In a class of 28 students, 16 prefer soccer and 12 prefer basketball. Which statement is correct?
Word Problems
A birdhouse at the zoo has 18 birds. For every 2 wings, there is 1 beak.
Which ratio correctly describes the relationship between wings and beaks?
Write the ratio of wings to total parts (wings + beaks) as a fraction and classify it.
Fraction: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Classification: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
A recipe calls for 3 cups of oats, 2 cups of raisins, and 1 cup of honey.
Write the ratio of oats to the total ingredients in all three notations.
Words: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Colon: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Fraction: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
A student looks at a bag of 4 red and 6 green marbles and says: '4/6 of the marbles are red because the ratio of red to green is 4:6.'
Complete the correction.
Is the student correct? ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
The fraction of marbles that are red is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Error Analysis
Malik was shown 3 red tiles and 5 blue tiles. He was asked: "Describe the ratio of red to blue tiles." Malik answered: "There are 2 more blue tiles than red tiles, so the relationship is 2 more."
What error did Malik make, and what is the correct ratio of red to blue tiles?
Priya has a bag with 4 red and 6 green marbles. She was asked: "What fraction of the marbles are red?" She answered: "The ratio of red to green is 4:6, so the fraction of red marbles is 4/6."
What error did Priya make, and what is the correct fraction of marbles that are red?
Challenge / Extension
A school vote has 120 students voting for Candidate A and 360 voting for Candidate C. A school newspaper reports: "For every vote Candidate A received, Candidate C received nearly three votes." Verify this claim using ratio language, and explain whether the ratio 120:360 is equivalent to 1:3.
A bag has 8 yellow and 12 purple candies. A student claims: "The ratio 8:12 and the fraction 8/20 both describe the same thing — the relationship of yellow to everything." Is the student right? Explain.