On the ACT Reading test, a strong vocabulary will help you earn a higher score. The same is also true for the ACT Math test! Being able to quickly distinguish between integers and numbers will get you closer to achieving your desired score on the ACT's Math section. There are eight common words that will give you a hint as to where you should begin solving, and in some cases, how to eliminate answers. Commit these terms to memory before your next practice test and see how much your score improves!
Numbers are a very large set of, well, just about any type of number, whether that's positive, negative, zero, a square root, or any other value. Integers are a subset of all numbers (just as all squares are rectangles). Specifically, this refers to any number that can be written without a fraction or decimal. For example, √16, -234, and 0 are integers, while 3/4 and 4.97 are not.
Integers show up in lots of different question types on the ACT Math test. Here's an example of one of the most basic forms in which they'll appear.
For integers x and y such that xy = 14, which of the following is NOT a possible value of x ?
To determine which values of x are possible and which one is not, try out each answer choice in the equation. If the resulting value of y is not an integer, you've found the value of x that is NOT possible. For example, plugging in 2 from choice (A) into the equation yields 2y = 14. When solved, y = 7. That's an integer, so 2 is a possible value of x. For (B), y = 14, and for (C), y = –2. These are both integers, so those values also work for x. For (D), the equation becomes –8y = 14, and y = 14/8. That's not an integer, so –8 is NOT a possible value for x and (D) is the correct answer.
Quick Trick: As you go through your answer choices, cross out eliminated choices so you can keep track of them.
Even and odd are likely terms you're familiar with. Even numbers are divisible by 2 and odd numbers are not. This applies whether the numbers are positive or negative. The number 0 is considered even, despite the fact that it isn't technically divisible by 2. Knowing some rules about these two terms can help you eliminate answer choices if you're stuck.
Quick Trick: An even number multiplied by an odd number will yield an even number. If you multiply an odd number by an odd number, you'll end up with another odd number.
When thinking about positive and negative numbers, just picture a number line. Any number that is greater than zero on the number line is positive; anything less than zero is negative.
Quick Trick: If you multiply an odd number of negatives together, you'll end up with a negative number.
On the ACT Math Test, consecutive means "in increasing order." The word consecutive is often used in problems where you're looking to identify a number in a sequence or equation. Take a look at the following sample question to see for yourself.
The sum of four consecutive even integers is t. What is the sum, in terms of t, of the two larger of these integers?
A. t/2 - 4
C. t/2 + 4
D. t + 2
E. t + 4
Instead of solving for the variable, t, plug in your own four consecutive even integers and add them together to find t. For example, 2 + 4 + 6 + 8 = 20. In this case, use 20 for t. The largest two integers are 6 and 8, which make 14 when added together. Now, look at your answer choices.
Quick Trick: The correct answer is whichever choice equals 14 when you plug in 20 for t. In this case, that's (C).
A number's reciprocal is its inverse. To find the reciprocal, flip the number's numerator and denominator. For example, the reciprocal of 4 is 1/4. One important rule to remember: 0 does not have a reciprocal! 1/0 is undefined.
Quick Trick: A number multiplied by its reciprocal is 1.
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