Mary Jane Sterling - Algebra I All-in-One For Dummies

4 0.Any number dividing into 0 (except 0 itself) results in 0.

5 .When the signs are the same, you find the sum: .

6 .There is one negative sign.

7 .When the signs are different, you find the difference: . And the sign of that difference is the sign of the number with the greater absolute value.

8 4.Change the subtraction to addition, and change the second number to the opposite sign: .

9 .The two negative numbers come first, with being the smaller of the two. Then comes 0, which separates the negative numbers from the positive numbers. The fraction is smaller than 1, so it’s definitely smaller than 4.

10 11.3.This is the absolute value function. When applied, it produces positive numbers or 0.

11 .There are three negative signs.

12 .There are three negative signs, counting the sign in front of the fraction.

13 .The number is closer to 0 than , so is the smaller value.

14 2. and . The product of the two results is 2.

15 24. .

16 .Change the subtraction to addition, and change the second number to the opposite sign: .

Chapter 3

IN THIS CHAPTER

Embracing the different types of grouping symbols

Distributing over addition and subtraction

Incorporating inverses and identities

Utilizing the associative and commutative rules

Algebra has rules for everything, including a sort of shorthand notation to save time and space. The notation that comes with any particular property cuts down on misinterpretation because it’s very specific and universally known. (I give the guidelines for doing operations like addition, subtraction, multiplication, and division in Chapter 2.) In this chapter, you see the specific rules that apply when you use grouping symbols and rearrange terms. You also find how opposites attract — or not — in the form of inverses and identities.

The most commonly used grouping symbols in algebra are (in order from most to least common):

Parentheses ( )

Brackets [ ]

Braces { }

Fraction lines / or

Radicals

Absolute value symbols | |

Here’s what you need to know about grouping symbols: You must compute whatever is inside them (or under or over, in the case of the fraction line) first, before you can use that result to solve the rest of the problem. If what’s inside isn’t or can’t be simplified into one term, then anything outside the grouping symbol that multiplies one of the terms has to multiply them all — that’s the distributive property, which I cover in the next section.

Q.

A.Add the 4 and 2; then subtract the result from the 16: .

Q.Simplify .

A.Work from the inside out. First subtract the 7 from the 3; then subtract the –4 from the 6 by changing it to an addition problem. You can then multiply the 2 by the 10:

Q.

A.Combine what’s in the absolute value and parentheses first, before combining the results: