Study Guide and Review - Rational Numbers
Choose the correct term or number to complete the sentence.
1. 1.875 is an example of a (terminating, repeating) decimal.
SOLUTION: Because the digits end, 1.875 is a terminating decimal.
ANSWER: terminating
2. A common denominator for the fractions
and is (7, 12).
SOLUTION: Because it is a multiple of both 3 and 4, 12 is a common denominator for the fractions
and .
ANSWER: 12
3. To add like fractions, add the (numerators, denominators).
SOLUTION: When adding like fractions, add the numerators and write the result over the denominator.
ANSWER: numerators
4. When dividing by a fraction, multiply by its (value, reciprocal).
SOLUTION: When dividing by a fraction, multiply by its multiplicative inverse, or reciprocal.
ANSWER: reciprocal
5. Fractions with different denominators are called (like, unlike) fractions.
SOLUTION: Fractions with different denominators are called unlike fractions.
ANSWER: unlike
6. The mixed number
can be renamed as .
SOLUTION: can be renamed as
because represents the same value as .
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7. When multiplying fractions, multiply the numerators and (multiply, keep) the denominators.
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SOLUTION: Fractions with different denominators are called unlike fractions.
ANSWER: Study
Guide and Review - Rational Numbers
unlike
6. The mixed number
can be renamed as .
SOLUTION: can be renamed as
because represents the same value as .
ANSWER: 7. When multiplying fractions, multiply the numerators and (multiply, keep) the denominators.
SOLUTION: To multiply fractions, multiply the numerators and multiply the denominators.
ANSWER: multiply
8. Fractions, terminating decimals, and repeating decimals are (integers, rational numbers).
SOLUTION: Rational numbers can be fractions, terminating decimals, and repeating decimals.
ANSWER: rational numbers
9. 3.16 × 103 is expressed in (scientific notation, standard form).
SOLUTION: 3
The number 3.16 is between 1 and 10. So, 3.16 × 10 is expressed in scientific notation.
ANSWER: scientific notation
10. The least common denominator for
and
is (4, 24)
SOLUTION: The least common denominator for 8 and 12 is 24 because 24 is the least number that is a multiple of both 8 and 24.
ANSWER: 24
Write the decimal as a fraction in simplest form.
11. 0.7
SOLUTION: The final digit, 7, is in the tenths place. So, 0.7 =
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.
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SOLUTION: The least common denominator for 8 and 12 is 24 because 24 is the least number that is a multiple of both 8 and 24.
ANSWER: Study
Guide and Review - Rational Numbers
24
Write the decimal as a fraction in simplest form.
11. 0.7
SOLUTION: The final digit, 7, is in the tenths place. So, 0.7 =
.
ANSWER: 12. 0.44
SOLUTION: The final digit, 4, is in the hundredths place.
So, 0.44 =
.
ANSWER: 13. 0.05
SOLUTION: The final digit, 5, is in the hundredths place.
So, 0.05 =
.
ANSWER: 14. RUNNING Jeremy ran a mile in 5 minutes and 8 seconds. Write this time in minutes as a decimal.
SOLUTION: Because there are 60 seconds in one minute, 5 minutes and 8 seconds can be represented by the mixed number
.
Think of the mixed number as a sum.
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Write
as a decimal.
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ANSWER: Study Guide and Review - Rational Numbers
14. RUNNING Jeremy ran a mile in 5 minutes and 8 seconds. Write this time in minutes as a decimal.
SOLUTION: Because there are 60 seconds in one minute, 5 minutes and 8 seconds can be represented by the mixed number
.
Think of the mixed number as a sum.
Write
as a decimal.
So,
.
So, the time is
.
ANSWER: Replace the
15. 37.5%
with <, >, or = to make a true sentence.
SOLUTION: Write 37.5% as a fraction by first writing it as a decimal.
The last digit is in the thousandths place.
So, 37.5% is equal to
.
FindManual
equivalent
fractions.
The
eSolutions
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by Cognero
LCD is 24.
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So, the time is
.
ANSWER: Study Guide and Review - Rational Numbers
Replace the
15. 37.5%
with <, >, or = to make a true sentence.
SOLUTION: Write 37.5% as a fraction by first writing it as a decimal.
The last digit is in the thousandths place.
So, 37.5% is equal to
.
Find equivalent fractions. The LCD is 24.
Since
, then
.
ANSWER: < 16. –0.45
SOLUTION: Write
So,
as a decimal.
= –0.45.
Since –0.45 = –0.45, then –0.45 =
.
ANSWER: =
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17. SCHOOL Michael received a
the higher score?
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on his English quiz and an 81% on his biology test. In which class did he receive
Since –0.45 = –0.45, then –0.45 =
.
ANSWER: Study
Guide and Review - Rational Numbers
=
17. SCHOOL Michael received a
on his English quiz and an 81% on his biology test. In which class did he receive
the higher score?
SOLUTION: and 81%.
Compare
Write
as a decimal.
=
Write 81% as a decimal.
81% = 0.81
Since
> 0.81, then > 81%.
So, Michael received a higher score in English than in biology.
ANSWER: English
Add or subtract. Write in simplest form.
18. SOLUTION: ANSWER: 19. SOLUTION: eSolutions Manual - Powered by Cognero
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ANSWER: Study Guide and Review - Rational Numbers
19. SOLUTION: ANSWER: 20. SOLUTION: ANSWER: 21. SOLUTION: ANSWER: Add or subtract. Write in simplest form.
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22. SOLUTION: Page 7
ANSWER: Study Guide and Review - Rational Numbers
Add or subtract. Write in simplest form.
22. SOLUTION: Rename using the LCD, 18.
ANSWER: 23. SOLUTION: Rename using the LCD, 10.
ANSWER: 1
24. RUNNING Teresa ran
mile while Yolanda ran mile. By what fraction did Teresa run more than Yolanda?
SOLUTION: Subtract Yolanda’s distance from Teresa’s distance.
Rename using the LCD, 12.
So, Teresa ran
ANSWER: mile more than Yolanda.
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ANSWER: Study
Guide and Review - Rational Numbers
1
24. RUNNING Teresa ran
mile while Yolanda ran mile. By what fraction did Teresa run more than Yolanda?
SOLUTION: Subtract Yolanda’s distance from Teresa’s distance.
Rename using the LCD, 12.
So, Teresa ran
mile more than Yolanda.
ANSWER: Add or subtract. Write in simplest form.
25. SOLUTION: ANSWER: 26. SOLUTION: Since
is less than , rename
before subtracting.
ANSWER: 27. eSolutions
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SOLUTION: Rename using the LCD, 15.
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ANSWER: Study Guide and Review - Rational Numbers
27. SOLUTION: Rename using the LCD, 15.
ANSWER: 28. SOLUTION: Rename using the LCD, 12.
ANSWER: 29. BABYSITTING Lucas watched his little sister for
hours on Friday, hours on Saturday, and hours on Sunday. For how many hours did Lucas watch his little sister?
SOLUTION: Find the sum of the hours Lucas spent watching his sister on Friday, Saturday, and Sunday.
Rename using the LCD, 12.
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So, Lucas watched his sister for
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hours.
ANSWER: Study Guide and Review - Rational Numbers
29. BABYSITTING Lucas watched his little sister for
hours on Friday, hours on Saturday, and hours on Sunday. For how many hours did Lucas watch his little sister?
SOLUTION: Find the sum of the hours Lucas spent watching his sister on Friday, Saturday, and Sunday.
Rename using the LCD, 12.
So, Lucas watched his sister for
hours.
ANSWER: Multiply. Write in simplest form.
30. SOLUTION: ANSWER: 31. SOLUTION: eSolutions Manual - Powered by Cognero
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ANSWER: Study Guide and Review - Rational Numbers
31. SOLUTION: ANSWER: 32. SOLUTION: ANSWER: 33. SOLUTION: eSolutions Manual - Powered by Cognero
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ANSWER: Study Guide and Review - Rational Numbers
33. SOLUTION: ANSWER: 34. FOOD An average slice of American cheese is about
-inch thick. What is the height in simplest form of a
package containing 20 slices?
SOLUTION: Multiply the thickness of one slice by the number of slices to find the height of the package.
So, the height of a package containing 20 slices of cheese is
inches.
ANSWER: 35. COOKIES A cookie jar contains three types of cookies: oatmeal, chocolate chip, and sugar. Sixty percent are
chocolate chip. Half of the remaining cookies are oatmeal. If there are 9 oatmeal cookies, how many cookies are in
the jar? Use the draw a diagram strategy.
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ANSWER: Study Guide and Review - Rational Numbers
35. COOKIES A cookie jar contains three types of cookies: oatmeal, chocolate chip, and sugar. Sixty percent are
chocolate chip. Half of the remaining cookies are oatmeal. If there are 9 oatmeal cookies, how many cookies are in
the jar? Use the draw a diagram strategy.
SOLUTION: If sixty percent of the cookies are chocolate chip, then forty percent of the cookies are either oatmeal or sugar. If
half of the remaining cookies are oatmeal, then twenty percent of all the cookies must be oatmeal and twenty
percent must be sugar. If 9 oatmeal cookies make up twenty percent of the jar, then there are 45 cookies in the jar.
5 × 20% = 100%
5 × 9 cookies = 45 cookies
ANSWER: 45 cookies
Divide. Write in simplest form.
36. SOLUTION: Multiply by the reciprocal of
.
ANSWER: 37. eSolutions Manual - Powered by Cognero
SOLUTION: Page 14
ANSWER: Study Guide and Review - Rational Numbers
37. SOLUTION: Multiply by the reciprocal of
.
ANSWER: –6
38. SOLUTION: Rename
as . Multiply by the reciprocal of
.
ANSWER: 39. SOLUTION: Multiply by the reciprocal of
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.
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ANSWER: Study Guide and Review - Rational Numbers
39. SOLUTION: Multiply by the reciprocal of
.
ANSWER: 40. MEASUREMENT How many
-inch lengths are in
inches?
SOLUTION: Divide
by . Rename
So, there are 54
as -inch lengths in
. Multiply by the reciprocal of
.
inches.
ANSWER: 54
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