Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 56

1 4.6. The number 4.6 is to the right of 0 on the number line, and is to the left of 0. And, of course, a positive number will be larger than a negative number.

2 0. Even though 0 isn’t positive (or negative), it’s to the right of , so 0 is larger.

3 . To make the comparison easier, rewrite as , so it has the same number of decimal places as . The number is closer to 0 (on the left of 0), so it is larger.

4 . The two negative numbers are the smallest, with the being farthest left and the smallest of the two. The number 4 is, of course, larger than 0.

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

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

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

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

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

10 . The number 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.

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.

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

15 3! and . .

16 Neither. and . They are equal.

17 5! and . Thus .

18 . and . Thus .

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.

30 15. Change the –15 to +15 and the subtraction to addition.

31 9.2. Change the –6.8 to +6.8 and the subtraction to addition.

32 –4. Change the –11 to +11 and the subtraction to addition.

33 –18. The multiplication problem has one negative, and 1 is an odd number.

34 –14. The multiplication problem has one negative, and 1 is an odd number.

35 18. The multiplication problem has two negatives, and 2 is an even number.

36 144. The multiplication problem has two negatives.

37 –2. The multiplication problem has five negatives.

38 60. The multiplication problem has two negatives.

39 2. The division problem has two negatives.

40 –8. The division problem has one negative.

41 –6. Three negatives result in a negative.

42 30. The division problem has two negatives.

43 –4. The division problem has five negatives.

44 –1. The division problem has one negative.

45 4. Adding 0 to a number doesn’t change the number.

46 –4. Change the problem to and add.

47 0. Multiplying by 0 always gives you 0 as a result.

48 0. Dividing 0 by a nonzero number always gives you 0.

If you’re ready to test your skills a bit more, take the following chapter quiz that incorporates all the chapter topics.