ANSWER: 1-2 Complex Fractions and Unit Rates
Simplify.
4. 1. SOLUTION: SOLUTION: ANSWER: ANSWER: 5. SOLUTION: 2. SOLUTION: ANSWER: 3. ANSWER: 6. SOLUTION: SOLUTION: ANSWER: ANSWER: 4. SOLUTION: 7. Mary is making pillows for her Life Skills class.She
bought
yards of fabric. Her total cost was $15.
What was the cost per yard?
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SOLUTION: To find the cost per yard, divide $15 by 2 yards.
So, Doug rowed at a speed of 7 miles per hour.
ANSWER: 1-2 Complex Fractions and Unit Rates
7. Mary is making pillows for her Life Skills class.She
bought
yards of fabric. Her total cost was $15.
What was the cost per yard?
ANSWER: 7 miles per hour
9. Monica reads
pages of a mystery book in 9
minutes. What is her average reading rate in pages
per minute?
SOLUTION: SOLUTION: To find the cost per yard, divide $15 by 2 yards.
To find Monica's reading rate, divide 7 by 9. Write
Write 2
7 as
as
.
So, the cost of the fabric was $6 per yard.
So, Monica can read
ANSWER: $6 per yard
page per minute.
ANSWER: 8. Doug entered a canoe race. He rowed miles in hour. What is his average speed in miles per hour?
SOLUTION: To find Doug's average speed, divide his miles rowed
by his time. Write
as .
.
Write the percent as a fraction in simplest form.
10. %
SOLUTION: So, Doug rowed at a speed of 7 miles per hour.
ANSWER: ANSWER: 7 miles per hour
9. Monica reads
pages of a mystery book in 9
minutes. What is her average reading rate in pages
per minute?
11. %
SOLUTION: SOLUTION: To find Monica's reading rate, divide 7 by 9. Write
7 as
.
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ANSWER: 1-2 Complex Fractions and Unit Rates
11. %
SOLUTION: ANSWER: 13. A bank is offering home loans at an interest rate of
%. Write the interest as a fraction in simplest
form.
SOLUTION: ANSWER: 12. %
So, the interest rate written as a fraction in simplest
form is
.
ANSWER: SOLUTION: 14. Be Precise Karl measured the wingspan of the
butterfly and the moth shown below. How many
times larger is the moth than the butterfly?
ANSWER: 13. A bank is offering home loans at an interest rate of
%. Write the interest as a fraction in simplest
form.
SOLUTION: eSolutions Manual - Powered by Cognero
So, the interest rate written as a fraction in simplest
SOLUTION: To determine how many times larger the moth is,
divide 3 by 3 . Write 3 as and 3 as .
Page 3
form is
.
ANSWER: 1-2 Complex Fractions and Unit Rates
14. Be Precise Karl measured the wingspan of the
butterfly and the moth shown below. How many
times larger is the moth than the butterfly?
ANSWER: times larger
15. Construct an Argument Explain how complex
fractions can be used to solve problems involving
ratios. SOLUTION: Students should recognize that complex fractions are
fractions with a numerator, denominator, or both that
are also fractions. So, if one of the numbers in the
ratio is a fraction, then the ratio can be a complex
fraction.
ANSWER: Sample answer: If one of the numbers in the ratio is
a fraction, then the ratio can be a complex fraction.
16. Reason Inductively Write three different complex
fractions that simplify to .
SOLUTION: Students should write three complex fractions that
simplify to .
Sample answer:
,
,
,
,
ANSWER: SOLUTION: To determine how many times larger the moth is,
divide 3 by 3 . Write 3 as and 3 as .
Sample answer:
17. Persevere with Problems Use mental math to find
the value of
.
SOLUTION: Students should mentally write the expression as
. Then they should notice the
following: 124 in the first denominator and 124 in the
third numerator divide to equal one, 230 in the second
numerator and 230 in third denominator divide to
equal one, and simplifies to .
So, the moth is
times larger than the butterfly.
ANSWER: times larger
15. Construct an Argument Explain how complex
fractions can be used to solve problems involving
ratios. SOLUTION: eSolutions Manual - Powered by Cognero
Students should recognize that complex fractions are
fractions with a numerator, denominator, or both that
are also fractions. So, if one of the numbers in the
ANSWER: 18. Justify Conclusions The value of a mutual fund
increased by
. Write
as a fraction in
simplest form. Justify your answer.
SOLUTION: Sample answer: Write
as
over 100. Then write
as an improper fraction. Divide the
numerator by the denominator. Page 4
ANSWER: equal one, and
simplifies to .
; Sample answer: Write
ANSWER: 1-2 Complex Fractions and Unit Rates
increased by
. Write
as a fraction in
simplest form. Justify your answer.
19. Persevere with Problems The distance around the
tire of a motorized scooter is 21.98 inches. The tires
make one revolution every
second. Find the
speed of the scooter in miles per hour. Round to the
nearest tenth. (Hint: The speed of an object
spinning in a circle is equal to the distance
around the circle divided by the time it takes to
complete one revolution.)
SOLUTION: as
over 100.
as an improper fraction. Divide the
Then write
numerator by the denominator. 18. Justify Conclusions The value of a mutual fund
Sample answer: Write
as
over 100. Then write
as an improper fraction. Divide the
numerator by the denominator. SOLUTION: mph. First change 21.98 into a fraction, then
divide by . Then change the units by multiplying by
appropriate conversion rates.
ANSWER: ; Sample answer: Write
as
over 100.
as an improper fraction. Divide the
Then write
numerator by the denominator. 19. Persevere with Problems The distance around the
tire of a motorized scooter is 21.98 inches. The tires
make one revolution every
second. Find the
speed of the scooter in miles per hour. Round to the
nearest tenth. (Hint: The speed of an object
spinning in a circle is equal to the distance
around the circle divided by the time it takes to
complete one revolution.)
ANSWER: SOLUTION: mph
mph. First change 21.98 into a fraction, then
divide by . Then change the units by multiplying by
appropriate conversion rates.
Simplify.
20. SOLUTION: ANSWER: 4
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ANSWER: 1-2 Complex Fractions and Unit Rates
mph
ANSWER: Simplify.
23. 20. SOLUTION: SOLUTION: ANSWER: 4
ANSWER: 2
21. SOLUTION: 24. SOLUTION: ANSWER: 20
ANSWER: 22. SOLUTION: 25. SOLUTION: ANSWER: 23. SOLUTION: eSolutions
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ANSWER: Page 6
26. Mrs. Frasier is making costumes for the school play.
So, Mrs. Frasier can make 8 costumes.
ANSWER: 1-2 Complex Fractions and Unit Rates
25. SOLUTION: ANSWER: 8 costumes
27. A lawn company advertises that they can spread
7,500 square feet of grass seed in
hours. Find the
number of square feet of grass seed that can be
spread per hour.
SOLUTION: To find the number of square feet of grass seed that
can be spread per hour, divide 7,500 square feet of
grass seed by 2 hours.
ANSWER: 26. Mrs. Frasier is making costumes for the school play.
Each costume requires 0.75 yard of fabric. She
bought 6 yards of fabric. How many costumes can
Mrs. Frasier make?
SOLUTION: To find the number of costumes Mrs. Frasier can
make, divide the yards she bought by the amount of
fabric required for each costume. Write 0.75 as .
ANSWER: 3,000 square feet per hour
Write the percent as a fraction in simplest form.
28. %
SOLUTION: So, Mrs. Frasier can make 8 costumes.
ANSWER: ANSWER: 8 costumes
27. A lawn company advertises that they can spread
7,500 square feet of grass seed in
hours. Find the
number of square feet of grass seed that can be
spread per hour.
SOLUTION: To find the number of square feet of grass seed that
can be spread per hour, divide 7,500 square feet of
grassManual
seed -by
2 hours.
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29. %
SOLUTION: Page 7
ANSWER: 1-2 Complex Fractions and Unit Rates
29. %
SOLUTION: ANSWER: 31. Justify Conclusions The value of a certain stock increased by %. Explain how to write % as
fraction in simplest form. SOLUTION: Students can refer to Example 5, Exercises 10-12,
and Exercises 27-29 to explain how to write 1 % as
a complex fraction.
Sample answer: Set 1 over 100. Write 1 as an
improper fraction. Then divide the numerator by the
denominator.
ANSWER: ANSWER: 30. over 100. Write
as
; Sample answer: Set an improper fraction. Then divide the numerator by
the denominator.
%
SOLUTION: ANSWER: yards of fabric at a remnant sale for
32. Debra bough
$13. Determine if each of the following remnant
deals have the same unit price as Debra's deal.
Select yes or no.
a.
yards for $16 b.
yards for $11 c.
yards for $26 SOLUTION: To find the unit price, divide the amount of money
spent on each remnant by the number of yards. Debra's deal:
31. Justify Conclusions The value of a certain stock increased by %. Explain how to write % as
fraction in simplest form. SOLUTION: Students can refer to Example 5, Exercises 10-12,
and Exercises 27-29 to explain how to write 1 % as
a complex fraction.
Sample answer: Set 1 over 100. Write 1 as an
improper fraction. Then divide the numerator by the
denominator.
Debra's deal was $4 per yard.
a.
ANSWER: over 100. Write
as
; Sample answer: Set an improper fraction. Then divide the numerator by
the denominator.
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c.
Debra's deal
was $4 per
1-2 Complex
Fractions
andyard.
Unit Rates
a.
So, this is not the same deal.
b.
yards for $26 33. The table shows the distances traveled by 4 cyclists.
Sort the speeds of the riders, in miles per hour, from
slowest to fastest.
Which rider had the fastest rate of speed?
SOLUTION: Lorena; Determine each speed by dividing the
distance by the time. Elena:
.
So, this is the same deal.
c. Julio:
So, this is the same deal.
ANSWER: a.
yards for $16 b.
yards for $11 c.
yards for $26 Kevin:
33. The table shows the distances traveled by 4 cyclists.
Sort the speeds of the riders, in miles per hour, from
slowest to fastest.
Lorena:
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There are 2,000 pounds in 1 ton. So, there are 5 × 2,000 or 10,000 pounds in 5 tons.
1-2 Complex Fractions and Unit Rates
Lorena:
ANSWER: 10,000
36. 8 gallons =
quarts
SOLUTION: There are 4 quarts in 1 gallon. So, there are 8 × 4 or 32 quarts in 8 gallons.
ANSWER: 32
Fill in the box with the equivalent metric
measurement.
37. 1 meter =
So, Lorena had the fastest rate of speed.
ANSWER: Lorena;
centimeters
SOLUTION: There are 100 centimeters in 1 meter.
ANSWER: 100
38. 1 liter =
milliliters
SOLUTION: There are 1,000 milliliters in 1 liter.
ANSWER: 1,000
Fill in the box with the equivalent customary
measurement. 34. 2 feet =
inches
SOLUTION: There are 12 inches in 1 foot. So, there are 2 × 12 or 24 inches in 2 feet.
ANSWER: 24
35. 5 tons =
pounds
SOLUTION: There are 2,000 pounds in 1 ton. So, there are 5 × 2,000 or 10,000 pounds in 5 tons.
ANSWER: 10,000
36. 8 gallons =
quarts
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SOLUTION: There are 4 quarts in 1 gallon. So, there are 8 × 4 or Page 10