3-4 Dividing Rational Numbers Find the multiplicative inverse of each number.

1.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of

 is  .

2.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction.  =  So, the multiplicative inverse of

 is 

.

3. –63 SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of –63 is

.

Find each quotient. Write in simplest form.

4.  SOLUTION:  

5.  SOLUTION:  

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SOLUTION:  

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3-4 Dividing Rational Numbers 6.  SOLUTION:  

7.  SOLUTION:  

8.  SOLUTION:  

9.  SOLUTION:  

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10. MULTIPLE CHOICE Sonia is making a quilted wall hanging that is 38 inches wide. If each quilt square is

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3-4 Dividing Rational Numbers 9.  SOLUTION:  

10. MULTIPLE CHOICE Sonia is making a quilted wall hanging that is 38 inches wide. If each quilt square is  inches wide, how many squares will she need to complete one row of the wall hanging? A B8 C D 190

SOLUTION:   To find the number of squares Sonia will need, divide the width of the wall hanging, 38 inches, by the width of each quilt square,

 inches.

Sonia will need 8 squares. So, Choice B is the correct answer. ALGEBRA Find each quotient. Write in simplest form.

11.  SOLUTION:  

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SOLUTION:  

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3-4 Dividing Rational Numbers 12.  SOLUTION:  

13.  SOLUTION:  

Find the multiplicative inverse of each number.

14.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of

 is 

.

 is 

 or 

15.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of .

16.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction.  =  So, the multiplicative inverse of eSolutions Manual - Powered by Cognero

17. 

 is 

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number, first write the mixed number as an improper fraction.  = 

3-4 So, Dividing Rational Numbers the multiplicative inverse of  is 

.

17.  SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. To find the multiplicative inverse of a mixed number, first write the mixed number as an improper fraction.  =  So, the multiplicative inverse of

 is 

.

18. 19 SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of 19 is

.

19. –54 SOLUTION:   Two numbers whose product is 1 are called multiplicative inverses. So, the multiplicative inverse of –54 is

.

Find each quotient. Write in simplest form.

20.  SOLUTION:  

21.  SOLUTION:  

22.  SOLUTION:  

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3-4 Dividing Rational Numbers 22.  SOLUTION:  

23.  SOLUTION:  

24.  SOLUTION:  

25.  SOLUTION:  

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SOLUTION:  

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3-4 Dividing Rational Numbers 26.  SOLUTION:  

27.  SOLUTION:  

28. COOKING Hannah is making chocolate chip cookies. How many batches of cookies can she make if she has  cups of brown sugar? Use the recipe card.

SOLUTION:   To find the number of batches Hannah can make, divide the amount of brown sugar she has, amount of brown sugar needed for one batch,

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 cups, by the 

 cups.

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3-4 Dividing Rational Numbers 28. COOKING Hannah is making chocolate chip cookies. How many batches of cookies can she make if she has  cups of brown sugar? Use the recipe card.

SOLUTION:   To find the number of batches Hannah can make, divide the amount of brown sugar she has, amount of brown sugar needed for one batch,

 cups, by the 

 cups.

Hannah can make 5 batches of cookies.

29. DRAMA CLUB How many play costumes can be made with

 yards of fabric if each costume requires 

 yards?

SOLUTION:   To find the number of costumes that can be made, divide the total amount of fabric, fabric needed for each costume,

 yards, by the amount of 

 yards.

So, 12 costumes can be made. eSolutions Manual - Powered by Cognero

ALGEBRA Find each quotient. Write in simplest form.

30. 

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3-4 Dividing Rational Numbers

Hannah can make 5 batches of cookies.

29. DRAMA CLUB How many play costumes can be made with

 yards of fabric if each costume requires 

 yards?

SOLUTION:   To find the number of costumes that can be made, divide the total amount of fabric, fabric needed for each costume,

 yards, by the amount of 

 yards.

So, 12 costumes can be made. ALGEBRA Find each quotient. Write in simplest form.

30.  SOLUTION:  

31.  SOLUTION:  

32.  SOLUTION:  

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3-4 Dividing Rational Numbers 32.  SOLUTION:  

33.  SOLUTION:  

34. BABYSITTING Barbara babysat for

 hours and earned $19.50. What was her hourly rate?

SOLUTION:   To find Barbara’s hourly rate, divide the amount she earned, $19.50, by the number of hours she babysat,

 hours.

First write 19.50 as a mixed number. 19.50 = Then, divide.

So, Barbara earned $6 per hour.

35. TRAINS A train traveled 405 miles in

 hours. How fast was the train traveling on average? (Hint: distance

equals the rate multiplied by the time.)

SOLUTION:   To find how fast the train was traveling on average, divide the total distance, 405 miles, by the time,

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 hours.

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3-4 Dividing Rational Numbers So, Barbara earned $6 per hour.

35. TRAINS A train traveled 405 miles in

 hours. How fast was the train traveling on average? (Hint: distance

equals the rate multiplied by the time.)

SOLUTION:   To find how fast the train was traveling on average, divide the total distance, 405 miles, by the time,

 hours.

So, the train was traveling 90 miles per hour on average.

36. PHOTOS Sydney reduced her favorite photograph to put in a scrapbook. How many times as wide is the actual photo than the reduced photo?

SOLUTION:   To find how many times as wide the actual photo is than the reduced photo, divide the width of the actual photo by the width of the reduced photo. 4 ÷ 3 =  So, the actual photo is

 as wide as the reduced photo.

ALGEBRA Evaluate each expression if m =

,n=

, and p = 6.

37. mn ÷ p SOLUTION:  

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the width of the reduced photo. 4 ÷ 3 = 

3-4 So, Dividing the actualRational photo is Numbers  as wide as the reduced photo. ALGEBRA Evaluate each expression if m =

,n=

, and p = 6.

37. mn ÷ p SOLUTION:  

38.  SOLUTION:  

39. np ÷ m SOLUTION:  

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40. TIE DYE Ms. Augello is making tie dye shirts with her students. Each gallon of hot water needs

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 cup of tie dye. 

3-4 Dividing Rational Numbers 39. np ÷ m SOLUTION:  

40. TIE DYE Ms. Augello is making tie dye shirts with her students. Each gallon of hot water needs

 cup of tie dye. 

 cups of tie dye, how many batches of solution will she be able to make?

If Ms. Augello has

SOLUTION:   To find the number of batches Ms. Augello will be able to make, divide the total amount of dye, amount of dye needed for one batch,

 cups, by the 

 cup.

So, Ms. Augello will be able to make 7 batches.

41. The model below shows

.

  How many

There

 

s are in

s in

?

.

  The model below shows How many

s are in

. ?

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3-4 Dividing Rational Numbers

So, Ms. Augello will be able to make 7 batches.

41. The model below shows

.

  How many

 

There

s are in

s in

?

.

  The model below shows How many

s are in

There are 3

s in

. ?

.

Make a conjecture about what happens to the quotient as the value of the divisor increases. Test your conjecture.

SOLUTION:   Sample answer: As the value of the divisor increases, the quotient decreases.  = 6  = 3  = 

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