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Special algebra terms are used to describe how numbers function and how they relate to each other Knowing what these terms mean is important to your ASVAB success: Composite number: A whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers, which means that it has more than two factors Examples of composite numbers are 6, 8, and 9 Exponents: You can think of exponents as a shorthand method of indicating multiplication For example, 15 15 can also be expressed as 152, which is also known as 15 squared or 15 to the second power The small number (2) written slightly above and to the right of a number is called the exponent An exponent indicates the number of times you multiply the number it accompanies by itself 152 (15 15) isn t the same as 15 2 To express 15 15 15 using this shorthand method, simply write it as 153, which is also called 15 cubed or 15 to the third power Again, 153 isn t the same as 15 3 Factors: Numbers that can divide into a composite number To factor a composite number, you simply determine the numbers that you can divide into it For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8), so 2 and 4 are factors of 8 Prime number: A whole number that can be divided evenly by itself and by 1 but not by any other number, which means that it has exactly two factors (Check out the definition of factor a bit earlier in this list) Examples of prime numbers are 2, 5, and 11
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When all things are equal: The algebra equation
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Algebra problems are equations, which means that the quantities on both sides of the equal sign are equal they re the same 2 = 2 1 + 1 = 2 And 3 1 = 2 In all these cases, the quantities are the same on both sides of the equal sign So, if x = 2, then x is 2 because the equal sign says so
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Part III: All s Fair in Math and War: Arithmetic Skills Solving one-step equations involving addition and subtraction
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If x + 1 = 2, then x must be 1, because only 1 added to 1 is 2 So far, so simple, so good But what if the equation is a little more complicated: x + 47,432 = 50,000 To find out what x equals, which solves the problem, you need to isolate x on one side of the equal sign To get that job done, you have to move any other numbers on the x side of the equal sign to the other side of the equal sign By looking at the x side of the equation, you can see that it s an addition problem To move the number on the x side to the opposite side, you have to perform the inverse operation The inverse operation of addition is subtraction (For a full rundown on inverse operations, check out 7) So, to move 47,432 from the x side to the non-x side of the equation, simply subtract it from both sides: x + 47,432 47,432 = 50,000 47,432 Performing these operations removes the 47,432 from the x side of the equation (47,432 47,432 = 0, so that side of the equation is x + 0 or simply x) and gives you 2,568 on the non-x side of the equation (50,000 47,432 = 2,568) You re left with the final answer: x = 2,568 To double-check that this answer is correct, plug your answer into the original problem: x + 47,432 = 50,000 2,568 + 47,432 = 50,000 If you plug the answer in and it doesn t work, you ve made an error in your calculations Start again; remember that you re trying to isolate x on one side of the equation You can perform any calculation on either side of an equation as long as you do it to both sides of the equation That keeps the equation equal
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