What this area covers
- Converting between fractions, decimals and percentages
- Ratios and proportions, including dosage calculations
- Solving one- and two-step equations
- Order of operations
- Estimating and comparing rational numbers
- Translating word problems into equations
Concepts that come up most in our question bank:
Where students lose marks
Most lost marks here are setup errors, not arithmetic. Proportion problems go wrong when the units on the two sides do not match — milligrams against millilitres, for instance.
How to study it
Write the units next to every number as you set a proportion up, and check they cancel before you calculate. For percentage change, be careful whether the question asks for the change or the final amount; those are different answers and both will be offered.
Practice questions
Answer these, then check them to see the full explanation for every option — including why each wrong answer is wrong.
- Question 1
Evaluate: 8 + 3 × (6 - 2)²
Correct answer: A. Follow order of operations (PEMDAS): Parentheses first: (6 - 2) = 4. Exponents: 4² = 16. Multiplication: 3 × 16 = 48. Addition: 8 + 48 = 56.
- B. 176 results from computing (8 + 3) × (6 - 2)² = 11 × 16 = 176, which incorrectly adds before multiplying.
- C. 44 results from computing 8 + 3 × (6 - 2) × 2 instead of squaring (6-2).
- D. 200 results from other calculation errors in the order of operations.
- Question 2
A patient's weight decreased from 200 pounds to 180 pounds. What is the percent decrease?
Correct answer: B. Percent decrease = (change ÷ original) × 100. Change = 200 - 180 = 20 pounds. Percent decrease = (20 ÷ 200) × 100 = 10%.
- A. 20% would be a 40-pound decrease from 200 pounds (200 × 0.20 = 40). The actual decrease is only 20 pounds.
- C. 15% would be a 30-pound decrease (200 × 0.15 = 30), not a 20-pound decrease.
- D. 11.1% would result from dividing the change by the new weight (20 ÷ 180) instead of the original weight (20 ÷ 200).
- Question 3
Simplify: 5/6 - 1/4
Correct answer: B. Find the LCD of 6 and 4, which is 12. Convert: 5/6 = 10/12 and 1/4 = 3/12. Subtract: 10/12 - 3/12 = 7/12.
- A. 4/2 = 2. You cannot subtract numerators and denominators separately (5-1)/(6-4).
- C. 1/3 = 4/12, which is not the result of 10/12 - 3/12 = 7/12.
- D. 2/3 = 8/12, not 7/12.
- Question 4
If a recipe requires a ratio of 2 cups of flour to 3 cups of sugar, how many cups of sugar are needed if 8 cups of flour are used?
Correct answer: B. Set up a proportion: 2/3 = 8/x. Cross-multiply: 2x = 3 × 8 = 24. Divide: x = 24/2 = 12 cups of sugar. Alternatively, 8 is 4 times 2, so multiply 3 by 4 to get 12.
- A. 10 would result from adding 2 + 8 or another incorrect calculation.
- C. 6 cups would be the amount if the ratio were 2:3 and only 4 cups of flour were used (half of 8, not the full proportion).
- D. 16 cups would result from multiplying 8 × 2, which doesn't apply the ratio correctly.
- Question 5
Solve for x: 2(x - 3) = 14
Correct answer: A. Distribute: 2x - 6 = 14. Add 6 to both sides: 2x = 20. Divide by 2: x = 10. Check: 2(10 - 3) = 2(7) = 14 ✓
- B. 8.5 results from dividing 14 by 2 first (getting 7) then adding 3/2, which is incorrect.
- C. 5.5 results from adding 14 + 3 = 17 then dividing by 2, skipping the distribution step incorrectly.
- D. If x = 7: 2(7 - 3) = 2(4) = 8, not 14.
- Question 6
Which of the following is the prime factorization of 60?
Correct answer: B. 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2² × 3 × 5. All factors (2, 3, 5) are prime numbers.
- A. 10 is not prime (10 = 2 × 5). Prime factorization requires all factors to be prime.
- C. 4 and 15 are not prime (4 = 2² and 15 = 3 × 5). This is a factorization but not a prime factorization.
- D. 30 is not prime (30 = 2 × 3 × 5). Both factors must be broken down to primes.
- Question 7
Multiply: 2/3 × 4/5
Correct answer: B. Multiply numerators: 2 × 4 = 8. Multiply denominators: 3 × 5 = 15. Result: 8/15. This fraction is already in simplest form since 8 and 15 share no common factors.
- A. 6/8 results from adding numerators and denominators (2+4)/(3+5), which is incorrect for multiplication.
- C. 8/8 = 1, which is not the product of 2/3 and 4/5.
- D. 6/15 = 2/5, which is not the product of 2/3 × 4/5.
- Question 8
A store marks up the price of an item by 40%. If the wholesale cost is $50, what is the retail price?
Correct answer: A. Markup amount = 40% of $50 = 0.40 × $50 = $20. Retail price = wholesale cost + markup = $50 + $20 = $70. Alternatively: $50 × 1.40 = $70.
- B. $90 would be an 80% markup ($50 × 1.80), not 40%.
- C. $60 would be a 20% markup ($50 × 1.20), not 40%.
- D. $45 would be a 10% discount, not a 40% markup.
- Question 9
Solve the inequality: 4x - 8 > 12
Correct answer: A. Add 8 to both sides: 4x > 20. Divide both sides by 4: x > 5. The inequality sign does not flip because we divided by a positive number.
- B. x > 1 results from dividing 12 by 4 = 3, then subtracting 2, which is not the correct process.
- C. x < 5 has the wrong inequality direction. When solving, we didn't multiply or divide by a negative number, so the sign stays >.
- D. x > 3 results from adding 8 to get 20, but then dividing only the 12 by 4 instead of 20 by 4.
- Question 10
What is the least common multiple (LCM) of 6 and 8?
Correct answer: B. List multiples: 6: 6, 12, 18, 24, 30... and 8: 8, 16, 24, 32... The smallest number that appears in both lists is 24. Alternatively: 6 = 2 × 3 and 8 = 2³. LCM = 2³ × 3 = 24.
- A. 48 is a common multiple of 6 and 8, but not the least common multiple. LCM is the smallest shared multiple.
- C. 14 is not a multiple of either 6 or 8.
- D. 12 is a multiple of 6 but not of 8 (8 does not divide evenly into 12).
Keep going
TEAS Dojo has 120 questions on numbers and algebra alone, plus timed full-length exams across all four sections.
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