Sharpen your math skills with this targeted quiz on ACT Math concepts such as fractions, ratios, and proportions. Tackle medium-level questions designed to build confidence with real-world scenarios and problem-solving strategies.
Which is the simplest form of the fraction 24/36?
Explanation: Dividing both the numerator and denominator of 24/36 by their greatest common factor, which is 12, gives 2/3. The option 3/2 is the reciprocal, which is incorrect. The choices 4/9 and 6/9 are not fully reduced; they represent partial simplifications but are not in their simplest form.
If 5 pencils cost 80 cents, how much would 8 pencils cost at the same rate?
Explanation: Set up the proportion 5/80 = 8/x and solve for x, obtaining x = 128 cents. While 96 cents comes from multiplying incorrectly, 160 cents assumes doubling instead of proportional scaling, and 13 cents results from a careless calculation. The correct rate is maintained only with 128 cents.
What is the sum of 1/4 and 2/3?
Explanation: To add 1/4 and 2/3, find a common denominator (12) and add: 3/12 + 8/12 = 11/12. The option 7/12 is the result of incorrectly subtracting instead of adding. The choices 2/7 and 3/4 are not related to the proper calculation and show errors in either process or simplification.
A recipe needs flour and sugar in the ratio 5:2. If you use 20 cups of flour, how many cups of sugar should you use?
Explanation: Since the ratio is 5:2, setting 5 parts to 20 cups means each part represents 4 cups. For sugar (2 parts), 2 × 4 = 8 cups. Option 10 mistakes matching both quantities, 12 uses an incorrect factor, and 5 ignores the actual ratio requirement for sugar.
What is 7/20 expressed as a percentage?
Explanation: To convert 7/20 into a percentage, multiply by 100 to get 35%. While 28% comes from mistakenly multiplying by 4 instead of 5, 14% assumes division by a different denominator, and 70% doubles the correct answer by error. Only 35% reflects the accurate calculation.