It’s important to know correct mathematics vocabulary. For instance, if a question asks for an integer and you come up with 7.23, you know you’re wrong since that’s not an integer. Here, we’ll work through the math basics.
The following terms are important in mathematics and in answering math questions on tests. It’s absolutely critical to know what’s being asked if you want to answer correctly. For instance, if you’re asked to “name the next consecutive prime integer on the number line after 7,” you’d need to know what’s meant by both “consecutive,” “number line,” “prime,” and “integer.” Otherwise, you’re up the creek without a paddle, as they say. (Just so you know, “consecutive” means in regular succession without gaps, the “number line” refers to all real numbers graphed on a line a “prime” number is a number that cannot be evenly divided into (except by 1), and an “integer” is a number on the number line (but not a decimal or fraction). Therefore, the answer is 11.)
The number line is a graphic to show numbers. Theoretically, all “real numbers” are on the number line. The number line typically looks like this:
The number line measures the distance from zero. For instance, “3” is three units from 0; and “-4” is four units from 0, or 6 units from “2”. If desired, decimals or fractions could be shown on the number line as well.
Counting numbers start with “1” and go up to infinity. They are the numbers that you count with, so zero and negative numbers are not counting numbers. Counting numbers do not have fractions or decimals. They are 1,2,3,4,5… etc.
Whole numbers are the same as counting numbers, with zero included. They are 0,1,2,3,4…etc.
An integer is a number on the number line. Integers are both positive and negative, extend to infinity, and include zero. Integers do not have fractions or decimals. They are … –3,-2,-1,0,1,2,3… etc.
The absolute value of a number is its distance from zero on a number line. Absolute value is usually shown with these marks: |n| with n being any number. Absolute is always positive and can include decimals or fractions. For example, -5.124 has an absolute value of 5.124, since it is 5.124 units from zero.
Sum refers to addition. When asked for the sum of numbers, simply add them together.
Difference refers to subtraction. When asked for the difference between numbers, subtract them.
The product of two (or more) numbers refers to multiplication.
“Quotient” refers to division. When asked for a quotient, divide the numbers.
When a number is prime, it cannot be evenly divided into by another number (other than 1). For example, 8 can be evenly divided by either 4 or 2, therefore it’s not prime. However, 7 cannot be even divided into and is therefore a prime number.
A factor is a number that can evenly divide another number. In the example above for the number 8, both 4 and 2 are factors of 8 because they can evenly divide 8. Or in other words, 4 and 2 divide into 8 without any “remainders” or numbers left over.
A variable in algebra is a symbol, usually a letter, which can represent a number. That number is said to vary or change, therefore it’s a “variable.” Probably the most common variables used are x, y, and n, but in reality any letter or symbol could be used.