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: 6. eSolutions Manual - Powered by Cognero
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3-4 Dividing Rational Numbers
6. SOLUTION: 7. SOLUTION: 8. SOLUTION: 9. SOLUTION: eSolutions Manual - Powered by Cognero
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.
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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
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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: eSolutions Manual - Powered by Cognero
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3-4 Dividing Rational Numbers
22. SOLUTION: 23. SOLUTION: 24. SOLUTION: 25. SOLUTION: eSolutions
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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.
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ALGEBRA Find each quotient. Write in simplest form.
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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: eSolutions Manual - Powered by Cognero
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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
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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
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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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