ACT Math · Pre-Algebra
Fractions, decimals, and integers
Operations on fractions, decimals, and integer arithmetic.
What's tested in this subtopic
Items test addition, subtraction, multiplication, and division of fractions and decimals; conversion between fractions, decimals, and percentages; and order of operations on mixed expressions.
Tactics that actually move your score
For fraction arithmetic, find a common denominator before adding or subtracting. For decimals, count the total decimal places when multiplying. The PEMDAS order applies inside-out for nested parentheses. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy If 8x − 5 = -21, what is the value of x?
- Easy If 5x + 10 = 15, what is the value of x?
- Medium If 3x + 4 = -23, what is the value of x?
- Medium If 9x + 1 = -89, what is the value of x?
- Medium If 7x + 2 = 72, what is the value of x?
- Hard If 8x − 9 = 7, what is the value of x?
- Easy If 6x + 11 = 47, what is the value of x?
- Easy If 4x + 8 = 8, what is the value of x?
- Medium If 7x − 1 = 69, what is the value of x?
- Medium If 7x − 1 = -64, what is the value of x?
- Medium If 9x − 9 = -18, what is the value of x?
- Hard If 8x + 4 = -20, what is the value of x?
- Easy If 9x − 2 = -29, what is the value of x?
- Easy If 9x + 1 = 82, what is the value of x?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in ACT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.