Middle School Math Quiz: Writing And Simplifying Ratios

6 questions · exam conditions

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Writing And Simplifying RatiosQuestion 1 of 6

At a school dance, the ratio of seventh graders to eighth graders is 5:3. If there are 45 seventh graders at the dance, what is the ratio of eighth graders to the total number of students at the dance?

27:72

3:8

27:45

9:24

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Middle School Math Quiz

Middle School Math Quiz: Writing And Simplifying Ratios

Practice Writing And Simplifying Ratios in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Writing And Simplifying Ratios, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

27:72
3:8
27:45
9:24 (correct answer)

Explanation: Since the ratio of 7th to 8th graders is 5:3 and there are 45 seventh graders, we can find 8th graders: 45÷5 = 9 students per ratio unit, so 8th graders = 3×9 = 27. Total students = 45 + 27 = 72. The ratio of 8th graders to total is 27:72. Simplifying by dividing by 3: 9:24. Choice A is unsimplified. Choice B uses the original ratio parts incorrectly. Choice C compares 8th graders to 7th graders only.

Question 2

A class of 28 students took a survey about favorite pets. The results showed that 12 students chose dogs, 8 chose cats, 5 chose birds, and 3 chose fish. What is the simplified ratio that compares students who chose mammals to students who chose non-mammals?

5:2 (correct answer)
20:8
12:8
3:2

Explanation: When you encounter ratio problems involving categories, you need to carefully classify the items before comparing. This question asks you to compare mammals to non-mammals among the pet choices. First, identify which pets are mammals and which aren't. Dogs and cats are both mammals, while birds and fish are not mammals. So you have:

Mammals: 12 students (dogs) + 8 students (cats) = 20 students
Non-mammals: 5 students (birds) + 3 students (fish) = 8 students

The ratio of students who chose mammals to non-mammals is 20:8. However, ratios should always be simplified by dividing both numbers by their greatest common factor. Since both 20 and 8 are divisible by 4, you get

20 ÷ 4 = 5

and

8 ÷ 4 = 2

, giving you the simplified ratio 5:2. Looking at the wrong answers: B) 20:8 is the correct ratio before simplification, but ratios must be in simplest form. C) 12:8 incorrectly compares only dogs to cats, missing the broader mammal vs. non-mammal classification. D) 3:2 appears to reverse part of the comparison or use incorrect groupings. When working with ratios, always remember to simplify by finding the greatest common factor. Also, read the question carefully to understand what categories you're actually comparing—don't just focus on the individual items listed.

Question 3

A fruit stand sells apples, oranges, and bananas. The number of apples is 3 times the number of oranges, and the number of bananas is twice the number of apples. If there are 8 oranges, what is the simplified ratio of oranges to the total number of fruits?

1:10 (correct answer)
8:80
8:72
2:15

Explanation: When you encounter ratio problems involving multiple relationships, work step-by-step to find all quantities before forming your ratio. Start by using the given information systematically. You know there are 8 oranges. Since apples are 3 times the number of oranges:

3 \times 8 = 24

apples. Since bananas are twice the number of apples:

2 \times 24 = 48

bananas. The total number of fruits is

8 + 24 + 48 = 80

fruits. The ratio of oranges to total fruits is

8:80

. To simplify this ratio, divide both terms by their greatest common factor, which is 8:

8 ÷ 8 = 1

and

80 ÷ 8 = 10

. So the simplified ratio is

1:10

. Looking at the answer choices: A)

1:10

is correct—this is our simplified ratio. B)

8:72

uses the wrong total; perhaps someone miscalculated by forgetting to include all fruits in the total. C)

8:80

is the unsimplified version of the correct ratio—always check if the question asks for simplified form. D)

2:15

appears to come from incorrect calculations of the individual fruit quantities. Remember that ratio problems often have multiple steps, so organize your work clearly. First find all individual quantities, then calculate totals, then form the ratio, and finally check whether simplification is required. The key trap here is forgetting to simplify—many ratio questions specifically ask for the simplified form.

Question 4

A recipe calls for ingredients in the ratio of flour:sugar:butter as 12:8:3. Maria wants to make a smaller batch using only 2 cups of sugar. What is the simplified ratio of flour to butter in her smaller batch?

12:3
3:1
4:1 (correct answer)
8:2

Explanation: When you encounter ratio problems, remember that ratios show proportional relationships that must be maintained even when quantities change. The key is finding the scale factor and applying it consistently. The original ratio is flour:sugar:butter = 12:8:3. Maria wants to use 2 cups of sugar instead of the original 8 parts sugar. To find the scale factor, divide the new amount by the original:

\frac{2}{8} = \frac{1}{4}

. This means she's making ¼ of the original recipe. Apply this scale factor to all ingredients: flour becomes

12 \times \frac{1}{4} = 3

cups, and butter becomes

3 \times \frac{1}{4} = \frac{3}{4}

cups. The ratio of flour to butter is

3:\frac{3}{4}

, which simplifies to

\frac{3}{\frac{3}{4}} = 3 \times \frac{4}{3} = 4

. So the ratio is 4:1. Looking at the wrong answers: Choice A) 12:3 uses the original flour and butter amounts without scaling down – this ignores that Maria is making a smaller batch. Choice B) 3:1 might result from incorrectly thinking the butter amount stays at 1 instead of ¾. Choice D) 8:2 appears to use incorrect scaling or confusion about which ingredients we're comparing. The correct answer is C) 4:1. Study tip: In ratio problems involving recipe scaling, always find the scale factor first by comparing the new amount to the original amount of any given ingredient, then apply that same factor to all other ingredients before simplifying your final ratio.

Question 5

A basketball team's roster has 8 guards, 6 forwards, and 4 centers. If the coach wants to compare the number of guards to non-guards on the team, what is the simplified ratio of guards to non-guards?

8:10
4:5 (correct answer)
8:18
2:3

Explanation: First, find the total number of non-guards: forwards + centers = 6 + 4 = 10. The ratio of guards to non-guards is 8:10. To simplify, divide both terms by their GCD of 2: 8÷2 = 4 and 10÷2 = 5, giving 4:5. Choice A is the unsimplified ratio. Choice C incorrectly uses total players (18) instead of non-guards. Choice D results from incorrectly using only centers (4) as non-guards.

Question 6

In a parking lot, the ratio of red cars to blue cars is 7:4, and the ratio of blue cars to white cars is 3:5. What is the simplified ratio of red cars to white cars?

7:5
84:60
21:20 (correct answer)
28:15

Explanation: When you encounter ratio problems with multiple relationships, you need to find a common term to connect the ratios. Here, blue cars appear in both ratios, so they're your bridge between red and white cars. Start with your given ratios: red to blue is 7:4, and blue to white is 3:5. Notice that blue cars are represented by different numbers (4 and 3) in each ratio. To connect them, you need to make these numbers equal by finding their least common multiple. The LCM of 4 and 3 is 12. Scale up each ratio so the blue car count becomes 12:

Red to blue 7:4 becomes 21:12 (multiply by 3)
Blue to white 3:5 becomes 12:20 (multiply by 4)

Now you can see that for every 21 red cars, there are 12 blue cars, and for every 12 blue cars, there are 20 white cars. This gives you red to white as 21:20. Looking at the answer choices: Choice A (7:5) incorrectly takes the first and last numbers from the original ratios without accounting for the different scales. Choice B (84:60) represents the correct ratio multiplied by 4, but it's not simplified. Choice D (28:15) appears to come from an error in finding the common multiple or scaling incorrectly. Choice C (21:20) is correct and already in simplest form since 21 and 20 share no common factors other than 1. Study tip: Always identify the connecting term in multi-step ratio problems, then scale ratios to make that term equal before combining them.