Transcript Answer

Write
as a decimal.
Method 1 Use paper and pencil.
Answer: 0.0625
Write
as a decimal.
Method 2 Use a calculator.
1
16
Answer: 0.0625
ENTER
0.0625
Write
as a decimal.
Answer: 0.375
Write
as a decimal.
Write as the sum of an
integer and a fraction.
Add.
Answer: 1.25
Write
as a decimal.
Answer: 2.6
Write
as a decimal.
The digits 12 repeat.
Answer:
Write
as a decimal.
The digits 18 repeat.
Answer:
a. Write
as a decimal.
Answer:
b. Write
as a decimal.
Answer:
Replace  with <, >, or = to make
sentence.
a true
Write the sentence.
Write
as a decimal.
In the tenths place,
Answer: On a number line, 0.7 is to the right of 0.65, so
.
.
Replace  with <, >, or = to make
sentence.
Answer: <
a true
Grades Jeremy got a score of
and
on his first quiz
on his second quiz. Which grade was the
higher score?
Write the fractions as decimals and then compare the
decimals.
Quiz #1:
Quiz #2:
Answer: The scores were the same, 0.80.
Baking One recipe for cookies requires
of a cup
of butter and a second recipe for cookies requires
of a cup of butter. Which recipe uses less butter?
Answer: the second recipe
Write
Answer:
as a fraction.
Write
as an
improper fraction.
Write 10 as a fraction.
Answer:
a. Write
as a fraction.
Answer:
b. Write –6 as a fraction.
Answer:
Write 0.26 as a fraction or mixed number in
simplest form.
0.26 is 26 hundredths.
Answer:
Simplify. The GCF of
26 and100 is 2.
Write 2.875 as a fraction or mixed number in
simplest form.
2.875 is 2 and 875 thousandths.
Answer:
Simplify. The GCF of
875 and 1000 is 125.
Write each decimal as a fraction or mixed number in
simplest form.
a. 0.84
Answer:
b. 3.625
Answer:
Write
as a fraction in simplest form.
Let N represent the number.
Multiply each side by 100
because two digits repeat.
Subtract N from 100N to eliminate the repeating
part, 0.3939...
Divide each side by 99.
Simplify.
Answer:
Check 13
33
ENTER
0.3939393939
Write
Answer:
as a fraction in simplest form.
Identify all sets to which the number 15 belongs.
Answer: 15 is a whole number, an integer, a natural
number, and a rational number.
Identify all sets to which the number
Answer:
is a rational number.
belongs.
Identify all sets to which the number 0.30303030...
belongs.
Answer: 0.30303030... is a nonterminating, repeating
decimal. So, it is a rational number.
Identify all sets to which each number belongs.
a. –7
Answer: integer, rational
b.
Answer: rational
c. 0.24242424...
Answer: rational
Find
. Write the product in simplest form.
Multiply the numerators.
Multiply the denominators.
Answer:
Simplify. The GCF of 10 and
40 is 10.
Find
Answer:
.
Find
. Write the product in simplest form.
Divide 8 and 6 by their GCF, 2.
Multiply the numerators and
multiply the denominators.
Answer:
Simplify.
Find
Answer:
. Write the product in simplest form.
Find
. Write the product in simplest form.
Divide 2 and 4 by their GCF, 2.
Multiply the numerators and
multiply the denominators.
Answer:
Simplify.
Find
Answer:
.
Find
. Write the product in simplest form.
Rename
and rename
.
Divide by the GCF, 3.
Multiply.
Answer:
Simplify.
Find
Answer:
. Write the product in simplest form.
Find
. Write the product in simplest form.
The GCF of
Answer:
Simplify.
and q is q.
Find
Answer:
. Write the product in simplest form.
Track The track at Cole’s school is
mile around.
If Cole runs one lap in two minutes, how far (in miles)
does he run in 30 minutes?
Words
Distance equals the rate multiplied by the time.
Variables Let d = distance, r = rate, and t = time.
Formula d = rt
mile per 2 minutes • 30 minutes
Write the formula.
15
1
Divide by the common
factors and units.
Multiply.
Simplify.
Answer: Cole runs
miles in 30 minutes.
Check
The problem asks for the distance. When
you divide the common units, the answer
is expressed in miles. So, the answer is
reasonable.
Walking Bob walks
mile in 12 minutes.
How far does he walk in 30 minutes?
Answer:
Find the multiplicative inverse of
.
The product is 1.
Answer: The multiplicative inverse or reciprocal of
.
Find the multiplicative inverse of
.
Write as an improper fraction.
The product is 1.
Answer: The reciprocal of
.
Find the multiplicative inverse of each number.
a.
Answer:
b.
Answer:
Find
. Write the quotient in simplest form.
Multiply by the multiplicative
inverse of
,
.
Divide 5 and 10 by their GCF, 5.
Answer:
Simplify.
Find
Answer:
. Write the quotient in simplest form.
Find
. Write the quotient in simplest form.
Write 3 as
.
Multiply by the multiplicative
inverse of
Answer:
, .
Multiply the numerators and
multiply the denominators.
Find
Answer:
. Write the quotient in simplest form.
Find
. Write the quotient in simplest form.
Rename the mixed numbers
as improper fractions.
Multiply by the multiplicative
inverse of
,
.
Divide out common factors.
Answer:
Simplify.
Find
Answer:
. Write the quotient in simplest form.
Find
. Write the quotient in simplest form.
Multiply by the multiplicative
inverse of
,
.
Divide out common factors.
Answer:
Simplify.
Find
Answer:
. Write the quotient in simplest form.
Travel How many gallons of gas are needed to travel
miles if a car gets
miles per gallon?
To find how many gallons, divide
.
Write as improper fractions.
Multiply by the reciprocal of
.
105
1
Divide out common
factors.
2
17
Simplify.
Answer:
gallons of gas are needed.
Check Use dimensional analysis to examine the units.
Divide out
the units.
Simplify.
The result is expressed as gallons. This agrees with your
answer of
gallons of gas.
Sewing Emily has
yards of fabric. She wants to
make pillows which each require
yards of fabric
to complete. How many pillows can Emily make?
Answer:
or 8 pillows
Example 1 Add Fractions
Example 2 Add Mixed Numbers
Example 3 Subtract Fractions
Example 4 Subtract Mixed Numbers
Example 5 Add Algebraic Fractions
Find
. Write the sum in simplest form.
Estimate
The denominators are the
same. Add the numerators.
Answer:
Simplify and rename as a
mixed number.
Find
Answer:
. Write the sum in simplest form.
Find
. Write the sum in simplest form.
Add the whole numbers
and fractions separately.
Add the numerators.
Answer:
Simplify.
Find
Answer:
. Write the sum in simplest form.
Find
. Write the difference in simplest form.
Estimate
The denominators are the same.
Subtract the numerators.
Answer:
Simplify.
Find
Answer:
. Write the difference in simplest form.
. Estimate
Evaluate
Replace r with
and q with
Write the mixed numbers as
improper fractions.
Subtract the numerators.
Answer:
Simplify.
.
Evaluate
Answer:
.
Find
. Write the sum in simplest form.
The denominators are the same.
Add the numerators.
Add the numerators.
Answer:
Simplify.
Find
Answer:
. Write the sum in simplest form.
Find the LCM of 168 and 180.
Number
Prime Factorization
Exponential Form
168
180
The prime factors of both numbers are 2, 3, 5, and 7.
Multiply the greatest powers of 2, 3, 5, and 7 appearing
in either factorization.
Answer: The LCM of 168 and 180 is 2520.
Find the LCM of 144 and 96.
Answer: 288
Find the LCM of
.
Multiply the greatest power of
each prime factor.
Answer: The LCM of
.
Find the LCM of
Answer:
.
Find the LCD of
.
Write the prime factorization of 8 and 20.
Highlight the greatest power of each prime factor.
Multiply.
Answer: The LCD of
.
Find the LCD of
Answer: 36
.
Find the LCD of
Answer: The LCD of
.
.
Find the LCD of
Answer:
Replace with <, >, or = to make
statement.
a true
The LCD of the fractions is
. Rewrite the
fractions using the LCD and then compare the numerators.
Multiply the fraction by
to make
the denominator 105.
Multiply the fraction by
the denominator 105.
to make
Answer: Since
is to the left of
, then
.
on the number line.
Replace with <, >, or = to make
statement.
Answer: <
a true
Find
.
Use
as the
common denominator.
Rename each fraction with
the common denominator.
Answer:
Add the numerators.
Find
Answer:
.
Find
.
Estimate
The LCD is 30.
Rename each fraction
with the LCD.
Add the numerators.
Answer:
Simplify.
Find
Answer:
.
Find
. Write in simplest form.
Write the mixed numbers
as improper fractions.
Rename fractions using
the LCD, 24.
Simplify.
Add the numerators.
Answer:
Simplify.
Find
Answer:
.
Find
.
The LCD is 16.
Rename
Answer:
using the LCD.
Subtract the numerators.
Find
Answer:
.
Find
.
Write the mixed numbers
as improper fractions.
Rename the fractions
using the LCD.
Simplify.
Answer:
Subtract.
Find
Answer:
.
Jogging Juyong jogged three days this week. She
jogged
miles,
miles, and
miles. How far
did she jog altogether?
Explore You know the distances Juyong jogged each day.
Plan
Add the daily distances together to find the total
distance. Estimate your answer.
Solve
Rename the fractions with LCD, 20.
Add the like
fractions.
Answer:
Juyong jogged
Examine
Since
reasonable.
miles.
is close to
, the answer is
Gardening Howard’s tomato plants grew
during the first week after sprouting,
the second week, and
inches
inches during
inches the third week. Find
the total growth during the first three weeks after
sprouting.
Answer:
inches
Movies The revenue of the 10 highest grossing movies
as of June 2000 are given in the table. Find the mean,
median, and mode of the revenues.
Top 10 Movie
Revenues
(millions of $)
601
461
431
400
357
330
313
309
306
290
Answer: The mean revenue is $379.8 million.
To find the median, order the numbers from least
to greatest.
290, 306, 309, 313, 330, 357, 400, 431, 461, 601
There is an even
number of items.
Find the mean of
the two middle
numbers.
Answer: The median revenue is $343.5 million.
Answer: There is no mode because each number in the
set occurs once.
Test Scores The test scores for a class of nine
students are 85, 93, 78, 99, 62, 83, 90, 75, 85.
Find the mean, median, and mode of the test scores.
Answer: mean, 83.3; median, 85; mode, 85
Olympics The line plot below shows the number of
gold medals earned by each country that
participated in the 1998 Winter Olympic games in
Nagano, Japan. Find the mean, median, and mode
for the gold medals won.
Answer: The mean is 2.875.
There are 24 numbers. The median number is the
average of the 12th and 13th numbers.
Answer: The median is 2.
The number 0 occurs most frequently in the set of data.
Answer: The mode is 0.
Families A survey of school-age children shows the
family sizes displayed in the line plot below. Find the
mean, median, and mode.
Answer: mean, 4.3; median, 5; mode, 5
Quiz scores The quiz scores for a math class are
8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an
extreme value and describe how it affects the mean.
The data value 0 appears to be an extreme value.
Calculate the mean with and without the extreme value
to find how it affects the mean.
mean with extreme value
mean without extreme value
Answer: The extreme value 0 decreases the mean
by 8.2 – 7.5 or about 0.7.
Birth Weight The birth weights of ten newborn babies
are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5, 7.9, 4.1,
8.0, 7.5. Identify an extreme value and describe how it
affects the mean.
Answer: 4.1; it decreases the mean by about 0.4.
The table shows the monthly salaries of the employees
at two bookstores. Find the mean, median, and mode
for each set of data. Based on the averages, which
bookstore pays its employees better?
Bob’s Books
Bob’s
The
Books
Reading
Place
1290
1400
1400
1600
3650
1400
1450
1550
1600
2000
mean:
median: 1290, 1400, 1400, 1600, 3650
median
mode: $1400
Bob’s
Books
The
Reading
Place
1290
1400
1400
1600
3650
1400
1450
1550
1600
2000
The Reading Place
mean:
median: 1400, 1450, 1550, 1600, 2000
median
mode: none
Answer: The $3650 salary at Bob’s Books is an extreme
value that increases the mean salary. The employees at
The Reading Place are generally better paid as shown
by the median.
The number of hours spent exercising each week by
men and women are given in the table. Find the mean,
median, and mode for each set of data. Based on the
averages, which gender exercises more?
Men
5
2
3
8
12
4
Women Answer: Men: mean,
1
6
4
2
1
8
5.7; median, 4.5;
mode, none
Women: mean, 3.7; median, 3;
mode, 1
Men seem to exercise more.
Grid–In Test Item Jenny’s bowling average is 146.
Today she bowled 138, 140, and 145. What does she
need to score on her fourth game to maintain her
average?
Read the Test Item
Find the sum of the first three games. Then write an
equation to find the score needed on the fourth game.
Solve the Test Item
Step 1
Find the sum of the first three games x.
mean of the first three scores
sum of first three scores
Multiply each side
by 3.
Simplify.
Step 2
Find the fourth score, x.
mean
Write an equation.
Substitution.
Multiply each side by 4 and simplify.
Subtract 423 from each side
and simplify.
Answer: Jenny needs to score at least 161 to maintain
her average of 146.
Emily scored 73, 82, and 85 on her first three math
tests. What score does Emily need on the fourth
test to give her an average of 82 for the four tests?
Answer: 88
Solve
. Check your solution.
Write the equation.
Add
to each side.
Simplify.
Rename the fractions using
the LCD and add.
Answer:
Simplify.
Check
Write the original equation.
Replace y with
Simplify.
.
Solve
Answer:
. Check your solution.
Solve
. Check your solution.
Write the equation.
Subtract 8.6 from each side.
Answer:
Simplify.
Check:
Write the original equation.
Replace m with 2.6.
Simplify.
Solve
Answer: 6.1
. Check your solution.
Solve
. Check your solution.
Write the equation.
Divide each side by 9.
Answer:
Check:
Simplify.
Write the original equation.
Replace a with 0.4.
Simplify.
Solve
Answer: 0.8
. Check your solution.
Solve
. Check your solution.
Write the equation.
Multiply each side by 6.
Answer:
Simplify.
Check:
Write the original equation.
Replace x with 48.
Simplify.
Solve
. Check your solution.
Write the equation.
Multiply each side by
Answer:
.
Simplify. Check the solution.
Check:
Write the original equation.
Replace t with –10.
Simplify.
a. Solve
. Check your solution.
Answer: 45
b. Solve
Answer: 16
. Check your solution.
State whether the sequence –5, –1, 3, 7, 11, ... is
arithmetic. If it is, state the common difference and
write the next three terms.
–5,
–1,
Notice that
3,
7,
11
, and so on.
Answer: The terms have a common difference of
, so
the sequence is arithmetic. Continue the pattern
to find the next three terms.
11,
15,
19,
23
Answer: The next three terms of the sequence
are 15, 19, and 23.
State whether the sequence 12, 7, 2, –3, –8, ... is
arithmetic. If it is, state the common difference and
write the next three terms.
Answer: arithmetic; –5; –13, –18, –23
State whether the sequence 0, 2, 6, 12, 20, ... is
arithmetic. If it is, state the common difference and
write the next three terms.
0,
2,
6,
12,
20
The terms do not have a common difference.
Answer: The sequence is not arithmetic. However, if the
pattern continues, the next three differences will
be 10, 12, and 14.
20,
30,
42,
56
The next three terms are 30, 42, and 56.
State whether the sequence 20, 17, 11, 2, –10, ... is
arithmetic. If it is, state the common difference and
write the next three terms.
Answer: not arithmetic
State whether the sequence 2, 4, 4, 8, 8, 16, 16 ... is
geometric. If it is, state the common ratio and write
the next three terms.
2,
4,
4,
8,
8,
16,
16
Answer: There is no common ratio. The sequence is
not geometric.
State whether the sequence 27, –9, 3, –1,
, ... is
geometric. If it is, state the common ratio and write
the next three terms.
27,
–9,
3,
–1,
Answer: The common ratio is
, so the sequence is
geometric. Continue the pattern to find the next three terms.
,
,
,
The next three terms are
,
, and
.
a. State whether the sequence 2, 8, 32, 128, 512, ... is
geometric. If it is, state the common ratio and write
the next three terms.
Answer: geometric; 4; 2048, 8192, 32,768
b. State whether the sequence 100, 20, 4,
,
... is
geometric. If it is, state the common ratio and write
the next three terms.
Answer: geometric; ;
,
,
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