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

Algebra I All-in-One For Dummies

href="#fb3_img_img_e34d0c82-02d7-5d60-a2e2-3c4c586e2408.png" alt="math"/> being farthest left and the smallest of the two. The number 4 is, of course, larger than 0.

5 math . The only positive number is math , so it is largest. The number math is closest to 0, so it’s the largest of the negative numbers. The number math is the farthest from 0, so it’s the smallest.

6 math . The point of the inequality goes toward the smaller number.

7 math . The point of the inequality goes toward the smaller number, the math .

8 math . The number math is smaller than 11, so the point of the inequality points in that direction.

9 math . The point of the inequality always goes toward the smaller of the two numbers.

10 math . The number math is equal to itself, so the “greater than” part is just the other choice.

11 −2. The following number line shows that the number –2 is to the right of –8. The number –8 is farther from 0, so it is the smaller of the two numbers.

Schematic illustration of a numberline ranges from -8 to 0.

12 –1. The number –1 is to the right of –13. The number –13 is farther from 0.

13 –0.003. The following number line shows that the number –0.003 is to the right of –0.03, which means –0.003 is bigger than –0.03. You can also rewrite –0.03 as –0.030 for easier comparison.

Schematic illustration of a numberline ranges from -.03 to 0.

14 math . The number math , and math is to the left of math on the following number line. So math is larger than math .

Schematic illustration of a numberline ranges from -4/6 to 0.

15 3! math and math . math .

16 Neither. math and math . They are equal.

17 5! math and math . Thus math .

18 math . math and math . Thus math .

19 +1. The number 4 has the greater absolute value, so the answer is positive.

20 –6. The number –11 has the greater absolute value, so the answer is negative.

21 –23. Both of the numbers have negative signs; when the signs are the same, find the sum of their absolute values.

22 14. Number 47 has the greater absolute value.

23 0.

24 –20.

25 –3.

Or you may prefer to add the two numbers with the same sign first, like this:

26 –6. You can do this because order and grouping (association) don’t matter in addition.

You see more on the associative property in Chapter 3.

27 7. Change the –2 to +2 and the subtraction to addition. The signs are the same now, so find the sum.

28 2. Change the –8 to +8 and the subtraction to addition. The signs are different now, so find the difference.

29 –83. Change the +87 to –87 and the subtraction to addition. Yes, it looks like the 87 is negative, but that is the operation of subtraction, not the sign of the number.

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