Praxis Core Math: Ratios, Proportions, and Percent Problems – Practice Questions
Preparing for the Praxis Core Math test requires more than memorizing formulas. Many questions test whether you can understand a situation, identify the correct mathematical relationship, and solve the problem efficiently.
One important skill area is working with ratios, proportions, fractions, decimals, and percentages. These concepts appear in many real-world situations and are useful for solving a wide range of quantitative problems.
In this practice lesson, you will review the basic concepts and work through several Praxis Core-style questions with step-by-step explanations.
What Is a Ratio?
A ratio compares two quantities.
For example, if a classroom has 12 boys and 18 girls, the ratio of boys to girls is:
12 : 18
This ratio can be simplified by dividing both numbers by 6:
2 : 3
Therefore, the ratio of boys to girls is 2 : 3.
Ratios can be written in several ways:
- 2 : 3
- 2/3
- 2 to 3
All three represent the same relationship.
What Is a Proportion?
A proportion is an equation stating that two ratios are equal.
For example:
3/5 = 6/10
Both ratios represent the same value, so they form a proportion.
To solve a proportion, you can use cross multiplication.
For example:
4/7 = x/21
Cross multiply:
4 × 21 = 7 × x
84 = 7x
Divide by 7:
x = 12
Therefore, the answer is 12.
Praxis Core Math Practice Questions
Question 1
A school has 15 teachers and 20 classrooms. What is the ratio of teachers to classrooms in simplest form?
A. 3 : 4
B. 4 : 3
C. 15 : 20
D. 5 : 4
Answer: A. 3 : 4
Explanation
The original ratio is:
15 : 20
The greatest common factor of 15 and 20 is 5.
Divide both numbers by 5:
15 ÷ 5 = 3
20 ÷ 5 = 4
Therefore:
15 : 20 = 3 : 4
Question 2
If 5 notebooks cost $15, how much would 8 notebooks cost at the same price per notebook?
A. $20
B. $24
C. $25
D. $30
Answer: B. $24
Explanation
First determine the cost of one notebook:
$15 ÷ 5 = $3
Therefore, 8 notebooks cost:
8 × $3 = $24
Question 3
A recipe requires 3 cups of flour to make 12 muffins. How many cups of flour are needed to make 20 muffins using the same ratio?
A. 4 cups
B. 5 cups
C. 6 cups
D. 8 cups
Answer: B. 5 cups
Explanation
The ratio of flour to muffins is:
3 cups / 12 muffins
For 20 muffins:
3/12 = x/20
Cross multiply:
12x = 60
x = 5
Therefore, 5 cups of flour are needed.
Percent Problems on the Praxis Core
Percent questions are another important area of quantitative reasoning.
Remember:
Percent means “per hundred.”
For example:
25% = 25/100 = 0.25
To find 25% of 80:
0.25 × 80 = 20
Therefore, 25% of 80 is 20.
Question 4
A student answers 36 out of 45 questions correctly. What percentage of the questions did the student answer correctly?
A. 70%
B. 75%
C. 80%
D. 85%
Answer: C. 80%
Explanation
Write the fraction:
36/45
Simplify:
36 ÷ 45 = 0.8
Convert the decimal to a percentage:
0.8 × 100 = 80%
The student answered 80% of the questions correctly.
Question 5
A jacket originally costs $80 and is discounted by 25%. What is the sale price?
A. $55
B. $60
C. $65
D. $70
Answer: B. $60
Explanation
First calculate the discount:
25% of $80:
0.25 × 80 = $20
Subtract the discount from the original price:
$80 − $20 = $60
The sale price is $60.
Fractions, Decimals, and Ratios
Praxis Core Math questions may require you to move between fractions, decimals, percentages, and ratios.
Some useful conversions are:
1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75%
1/5 = 0.2 = 20%
Understanding these relationships can make many questions faster to solve.
Question 6
Which value is greatest?
A. 0.45
B. 40%
C. 1/2
D. 0.48
Answer: C. 1/2
Explanation
Convert each value to a decimal:
0.45 = 0.45
40% = 0.40
1/2 = 0.50
0.48 = 0.48
The greatest value is:
0.50
Therefore, the answer is 1/2.
A Useful Strategy for Praxis Core Math
When solving a word problem, do not immediately start calculating.
Use this four-step approach:
Step 1: Identify what the question is asking
Read the final sentence carefully.
Step 2: Identify the important numbers
Ignore information that does not affect the solution.
Step 3: Choose the appropriate relationship
Ask yourself whether the problem involves:
- A ratio
- A proportion
- A percentage
- A fraction
- A decimal
- An equation
Step 4: Check your answer
Make sure the result makes sense in the context of the problem.
Question 7
A store increases the price of a $50 item by 20%. What is the new price?
A. $55
B. $60
C. $65
D. $70
Answer: B. $60
Explanation
Find 20% of $50:
0.20 × 50 = $10
Add the increase:
$50 + $10 = $60
The new price is $60.
Question 8
A classroom has 24 students. If 3/8 of the students participate in a science competition, how many students participate?
A. 6
B. 8
C. 9
D. 12
Answer: C. 9
Explanation
Calculate:
3/8 × 24
First divide:
24 ÷ 8 = 3
Then multiply:
3 × 3 = 9
Therefore, 9 students participate.
Question 9
If 4 pens cost $6, what is the cost of 10 pens at the same rate?
A. $12
B. $15
C. $16
D. $18
Answer: B. $15
Explanation
The cost of one pen is:
$6 ÷ 4 = $1.50
For 10 pens:
10 × $1.50 = $15
Question 10
A student scored 42 points out of a possible 60 points. What percentage of the points did the student earn?
A. 60%
B. 65%
C. 70%
D. 75%
Answer: C. 70%
Explanation
Write the fraction:
42/60
Convert to a decimal:
42 ÷ 60 = 0.70
Convert to a percentage:
0.70 × 100 = 70%
Therefore, the student earned 70%.
Quick Review
Before moving to another Praxis Core Math topic, make sure you understand these ideas:
Ratios
A ratio compares two quantities.
Proportions
A proportion shows that two ratios are equivalent.
Percentages
A percentage represents a value out of 100.
Cross Multiplication
Cross multiplication can be used to solve many proportion problems.
Unit Rate
A unit rate tells you the value for one unit.
For example:
$15 for 5 notebooks
$15 ÷ 5 = $3 per notebook
Common Mistakes to Avoid
1. Reversing the ratio
If the question asks for the ratio of teachers to students, write:
teachers : students
Do not automatically reverse the order.
2. Forgetting to simplify
A ratio such as 15 : 20 can be simplified to:
3 : 4
3. Confusing percentage increase with the final price
If an $80 item increases by 25%, the increase is $20, but the final price is $100.
4. Calculating before understanding
Take a moment to identify what the question is asking before choosing an operation.
Final Praxis Core Math Tip
The fastest test-takers are not necessarily the ones who calculate the fastest. They are often the ones who identify the mathematical relationship quickly.
When you see a word problem, ask:
“What relationship is this question testing?”
Once you identify the relationship, the calculation often becomes much easier.
Practice a few problems every day, review your mistakes, and focus on understanding why an answer is correct.
Conclusion
Ratios, proportions, percentages, fractions, and decimals are foundational skills for Praxis Core Math. Strong performance in these areas can also make many real-world quantitative problems easier to understand.
Use the practice questions in this lesson as a starting point. Try solving each problem yourself before reading the explanation. Then review any mistakes and repeat the questions later.
Keep practicing, focus on the reasoning, and build accuracy before speed.
Frequently Asked Questions
Is Praxis Core Math difficult?
The difficulty depends on your current mathematics skills and preparation. Regular practice with quantitative reasoning problems can help you become more comfortable with the test format.
Should I memorize formulas for Praxis Core Math?
You should understand the important mathematical relationships rather than relying only on memorization. Knowing when and why to use a formula is especially important.
How can I improve my Praxis Core Math score?
Practice consistently, review incorrect answers, identify the type of problem you missed, and work on solving similar questions until the underlying concept becomes clear.
Are ratios and percentages important for Praxis Core Math preparation?
They are useful foundational skills for quantitative reasoning. Practicing them can also strengthen your ability to interpret real-world mathematical situations.
Disclaimer
This article is provided for educational and test-preparation purposes. Praxis is a trademark of ETS. This website is independently operated and is not affiliated with or endorsed by ETS.
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