Читать книгу Algebra I All-in-One For Dummies - Mary Jane Sterling, Mary Sterling Jane - Страница 95

1 . First, divide the 29 by 8. The number 8 divides 29 three times with a remainder of 5.

2 . Multiply the 4 and 9 and then add the 5, which equals 41. Then write the fraction with this result in the numerator and the 9 in the denominator.

3 . Multiply the 4 times 100 and add the 7. Put the sum over 100.

4 . Ignore the negative sign at first; you don’t want it involved in the computation. First multiply the 2 times 13 to get 26. Add the 1 to get 27. You have 27 in the numerator, 13 in the denominator, and now you put the negative sign in front.

5 . The number 11 divides 402 a total of 36 times with 6 left over. The 36 goes in front, with the 6 in the numerator and 11 in the denominator. This example makes it especially apparent that the mixed number is more understandable.

6 . Divide 7 into 19, for a quotient of 2. The remainder 5 goes in the numerator. Put the negative sign in front of the 2.

7 . To get 28 in the denominator, multiply 7 by 4:

8 . Multiply both the numerator and denominator by 5:

9 . The number 4 is the greatest common divisor of 16 and 60 because and . So multiply by to get

Or, if you prefer, divide both the numerator and denominator by 4:

10 . The largest common divisor of 63 and 84 is 21, because and . So

But let’s say you do this in two steps — both dividing by a common factor.

You see that both 63 and 84 are divisible by 7. So divide both the numerator and denominator by 7.

Now you see that the new version has a numerator and denominator divisible by 3.

It took two steps instead of one, but you have the same answer.

11 . Yes, this is completely reduced. You can write 14 as and 15 as , but they don’t share any common factors.

12 . No. Both 39 and 26 are divisible by 13. You may not be completely familiar with the multiples of 13, but if you just note that 39 is divisible by 3 and 26 is divisible by 2, you come up with and and you can reduce the fraction:

13 . No. Here’s another situation where you look for common factors. Both of these numbers are divisible by 3. (Chapter 8 contains all the rules of divisibility you’ll be needing.)

You can stop right there, because 47 is a prime number.

14 . Yes. This is completely reduced.

Just to check the factors: . The numerator shows a prime factorization. You see more of this in Chapter 8.

15 . The left fraction can be reduced by dividing by 7. Then the two denominators can be reduced by dividing by 3. Then find the cross-product.

16 . The right fraction can be reduced by dividing by 20. Then the two numerators can be reduced by dividing by 3. Then find the cross-product.

17 . The right fraction can be reduced by dividing by 12. Then the two denominators can be reduced by dividing by 9. Then find the cross-product.

18 . The left fraction can be reduced by dividing by 2. Then the two numerators can be reduced by dividing by 13. Then find the cross-product.

19 . Fill in the proportion: . Then let x represent the new cinnamon:

20 . Set up the proportion:

21 and . The largest common factor of 7 and 8 is 1. So the least common denominator is 56, the product of the denominators: . Here are the details:

22 and . The largest common factor of 12 and 18 is 6. The least common denominator is 36. . Here are the details:

23 and . The largest common factor of x and 6 is 1. The least common denominator is their product: 6x. Break it down: and .

24 and . The largest common factor of x and is 1. Their least common denominator is their product: . Here’s the long of it: and .

25 , , and . The least common denominator of fractions with denominators of 2, 3, and 5 is 30. Write it out:

26 , , and . The last two denominators, and , have a common factor of x. And the product of all three denominators is 6x². Divide the product by x and you get 6x. In long hand:

27 . The least common denominator is 24.

28 . The least common denominator is 15.

Or, leaving the whole number parts separate:

29 .

30 .

31 . Here’s a chance to use the box method.

The least common denominator is .

32 . Go ahead and put the negative sign in front of the work in the first step. With one of the three fractions being negative, you know that the answer will be negative.

33 . Change the first fraction to a mixed number.

34 . This time the answer is positive, because there are two negative fractions in the problem.

35 . The answer will be positive, because there are two negative fractions.

36 .

37 .

38 .

39 .

40 4.

41 .

42 36,000. Simplify inside the parentheses first.

43 –2.999948. By the order of operations, you multiply first and then subtract 3 from the result.

44 0.6. Dividing, you have .

45 . because

46 .

47 . .

48 .

because two digits repeat .

49 .

because three digits repeat: .

50 4.173. The number 7 follows the 2 in the thousandths place. Because 7 is greater than 5, you round up.

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