FeatureLesson
Course 3Course 3
LessonMain
Find three different odd numbers whose sum is 21. List all possibilities.
1, 3, 17; 1, 5, 15; 1, 7, 13; 1, 9, 11; 3, 5, 13; 3, 7, 11; 5, 7, 9
LESSON 2-1LESSON 2-1
FactorsFactors
Problem of the Day
2-1
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-1LESSON 2-1
(For help, go to Lesson 1-4.)
Simplify each expression.
2. –10(10) 3. –8(– 7)
4. 5(– 4)(– 2) 5. –1 • 1 • 0
FactorsFactors
1. Vocabulary Review When you multiply two numbers, the result is called the ? .
Check Skills You’ll Need
Check Skills You’ll Need
2-1
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. product 2. –100 3. 56 4. 40 5. 0
LESSON 2-1LESSON 2-1
FactorsFactors
Check Skills You’ll Need
2-1
FeatureLesson
Course 3Course 3
LessonMain
Identify each number as prime or composite. Explain.
FactorsFactorsLESSON 2-1LESSON 2-1
a. 57 Composite; the sum of the digits is 12, which is divisible by 3.
b. 1,354 Composite; the number is divisible by 2.
c. 43 Prime; the number is divisible only by 43 and 1.
d. 975 Composite; the number is divisible by 5.
Quick Check
Additional Examples
2-1
FeatureLesson
Course 3Course 3
LessonMain
Use a factor tree to find the prime factorization of 588.
FactorsFactorsLESSON 2-1LESSON 2-1
The prime factorization of 588 is 2 • 2 • 3 • 7 • 7, or 22 • 3 • 72.
The number 588 is divisible by 2 because the units digit is 8.
588
1472prime
493prime
Stop when all factors are prime.
7 7prime
2942prime
Begin the factor tree with 2 • 294.
Quick Check
Additional Examples
2-1
FeatureLesson
Course 3Course 3
LessonMain
Find the GCF of 55 and 231.
FactorsFactorsLESSON 2-1LESSON 2-1
Step 1 Find the prime factorization of each number.
Step 2 Find the product of the common prime factors of each number.
55 = 5 • 11
231 = 3 • 7 • 11
The only common prime factor is 11. The GCF of 55 and 231 is 11.
55
115
231
773
117
Quick Check
Additional Examples
2-1
FeatureLesson
Course 3Course 3
LessonMain
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
32: 1, 2, 4, 8, 16, 32
The factors 1, 2, and 4 are common to both numbers.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
32: 1, 2, 4, 8, 16, 32
The GCF is 4.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
32: 1, 2, 4, 8, 16, 32
Begin by finding the factors of 36 and 32.
A band with 36 members is marching with a 32-member
band. If the two bands are to have the same number of columns,
what is the greatest number of columns in which you could
arrange the two bands?
FactorsFactorsLESSON 2-1LESSON 2-1
So, 4 is the greatest number of columns in which you can arrange the bands.
Quick Check
Additional Examples
2-1
FeatureLesson
Course 3Course 3
LessonMain
FactorsFactors
Write the prime factorization of each number.
1. 24 2. 27 3. 31
Find the GCF of each pair of numbers.
4. 4 and 14 5. 18 and 27
23 • 3
LESSON 2-1LESSON 2-1
33 31
2 9
Lesson Quiz
2-1
FeatureLesson
Course 3Course 3
LessonMain
At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis, 23 went hiking, and the rest of the campers stayed in their cabins. If 83 kids were in the camp, how many stayed indoors?
31
LESSON 2-2LESSON 2-2
Equivalent Forms of Rational NumbersEquivalent Forms of Rational Numbers
Problem of the Day
2-2
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-2LESSON 2-2
Equivalent Forms of Rational NumbersEquivalent Forms of Rational Numbers
(For help, go to Lesson 2-1.)
Find the GCF of each pair of numbers.
2. 6, 12 3. 8, 12 4. 25, 50 5. 36, 40
1. Vocabulary Review Name the prime factorization of 100.
Check Skills You’ll Need
Check Skills You’ll Need
2-2
FeatureLesson
Course 3Course 3
LessonMain
Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersLESSON 2-2LESSON 2-2
Solutions
1. 2 • 2 • 5 • 5
2. 6 = 2 • 3, 12 = 2 • 2 • 3; GCF = 6
3. 8 = 2 • 2 • 2, 12 = 2 • 2 • 3; GCF = 2 • 2 = 4
4. 25 = 5 • 5, 50 = 2 • 5 • 5; GCF = 5 • 5 = 25
5. 36 = 2 • 2 • 3 • 3, 40 = 2 • 2 • 5; GCF = 2 • 2 = 4
Check Skills You’ll Need
2-2
FeatureLesson
Course 3Course 3
LessonMain
Write in simplest form using the GCF.
Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersLESSON 2-2LESSON 2-2
138150
Divide the numerator and the denominator by the GCF.
138150
138 ÷ 6150 ÷ 6=
Simplify. The numbers 23 and 25 are relatively prime.
=2325
The GCF of 138 and 150 is 6.
Quick Check
Additional Examples
2-2
FeatureLesson
Course 3Course 3
LessonMain
Write in simplest form using prime factorization.
Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersLESSON 2-2LESSON 2-2
60126
Divide the common factors. 2 • 2 • 3 • 52 • 3 • 3 • 7
1 1
1 1
=
Simplify.1021=
Write the prime factorizations of the numerator and denominator.
60126
2 • 2 • 3 • 52 • 3 • 3 • 7=
Quick Check
Additional Examples
2-2
FeatureLesson
Course 3Course 3
LessonMain
Write each batting average as a decimal.
Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersLESSON 2-2LESSON 2-2
a. Joe made 4 hits in 20 times at bat.
Joe’s batting average was .200.
b. Pat made 6 hits in 33 times at bat.
Pat’s batting average was about .182.
Write the batting average as a fraction.4
20
Divide the numerator by the denominator. This is a terminating decimal.
0.2
Write the batting average as a fraction.6
33
Use a calculator. This is a repeating decimal.0.18181818
Quick Check
Additional Examples
2-2
FeatureLesson
Course 3Course 3
LessonMain
Write 3.225 as a mixed number.
Equivalent Forms of Rational NumbersEquivalent Forms of Rational NumbersLESSON 2-2LESSON 2-2
3.225 = Write as a fraction with the denominator 1. 3.225
1
Since there are 3 digits to the right of the decimal, multiply the numerator and denominator by 103 or 1,000.
=3,2251,000
Simplify using the GCF, 25.=3,225 ÷ 251,000 ÷ 25 =
12940
Write as a mixed number.= 39
40
Quick Check
Additional Examples
2-2
FeatureLesson
Course 3Course 3
LessonMain
Equivalent Forms of Rational NumbersEquivalent Forms of Rational Numbers
Write each as a fraction in simplest form.
1. 2. –
3. Write as a decimal.
Write each decimal as a mixed number or fraction insimplest form.
4. 2.75 5. 0.4
57
LESSON 2-2LESSON 2-2
3042
23
–
34
2
1218
216
0.125
25
Lesson Quiz
2-2
FeatureLesson
Course 3Course 3
LessonMain
Express 4 days, 12 hours in minutes.
6,480 min
LESSON 2-3LESSON 2-3
Comparing and Ordering Rational NumbersComparing and Ordering Rational Numbers
Problem of the Day
2-3
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-3LESSON 2-3
Comparing and Ordering Rational NumbersComparing and Ordering Rational Numbers
(For help, go to Lesson 2-2.)
Use the GCF to write each fraction in simplest form.
2. 3. 4. 5.1220
1555
1664
50550
1. Vocabulary Review Explain what the numerator of a fraction represents.
Check Skills You’ll Need
Check Skills You’ll Need
2-3
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. The numerator represents a part of the whole.
2. 3.
4. 5.
Comparing and Ordering Rational NumbersComparing and Ordering Rational NumbersLESSON 2-3LESSON 2-3
12 ÷ 420 ÷ 4
= 35
16 ÷ 1664 ÷ 16
= 14
15 ÷ 555 ÷ 5
= 311
50 ÷ 50550 ÷ 50
= 111
Check Skills You’ll Need
2-3
FeatureLesson
Course 3Course 3
LessonMain
Which is greater, or ?
Comparing and Ordering Rational NumbersComparing and Ordering Rational NumbersLESSON 2-3LESSON 2-3
718
512
Since the LCM of 18 and 12 is 36, the LCD of the fractions is 36.
Multiples of 18: 18, 36
Multiples of 12: 12, 24, 36
List multiples of each denominator to find their LCD.
Multiply the numerator and denominator by 2.7
187 • 2
18 • 2=
Simplify.1436=
Additional Examples
2-3
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Comparing and Ordering Rational NumbersComparing and Ordering Rational NumbersLESSON 2-3LESSON 2-3
Multiply the numerator and denominator by 3.5
125 • 3
12 • 3=
Simplify.1536=
Since1536
1436> , >
718 .
512
Quick Check
Additional Examples
2-3
FeatureLesson
Course 3Course 3
LessonMain
The Eagles won 7 out of 11 games while the Seals won 8
out of 12 games. Which team has the better record?
Comparing and Ordering Rational NumbersComparing and Ordering Rational NumbersLESSON 2-3LESSON 2-3
Change each fraction to a decimal. Compare the two decimals.
Since 0.666 > 0.636, the Seals have the better record.
Divide. Use a calculator.Eagles:
711 0.636363
Seals:8
12 0.666667
Quick Check
Additional Examples
2-3
FeatureLesson
Course 3Course 3
LessonMain
Order –0.175, , – , 1.7, –0.95 from least to greatest.
Comparing and Ordering Rational NumbersComparing and Ordering Rational NumbersLESSON 2-3LESSON 2-3
23
58
Then graph each decimal on a number line.
The order of the points from left to right gives the order of the numbers from least to greatest.
–0.95 < –0.625 < –0.175 < 0.667 < 1.7
So, –0.95 < – < –0.175 < < 1.7.23
58
Write each fraction as a decimal.
23 0.667
58 = –0.625–
Quick Check
Additional Examples
2-3
FeatureLesson
Course 3Course 3
LessonMain
Comparing and Ordering Rational NumbersComparing and Ordering Rational Numbers
Compare. Use <, >, or =.
1. 2.
3. 4. 0.35
5. Order 0.17, , –0.3, 0, and – from least to greatest.
6. A survey found that 75 out of 125 men and 88 out of 136 women prefer comedy films over action films. Which group prefers comedy over actions films more?
< >
LESSON 2-3LESSON 2-3
= =
–0.3, – , 0, 0.17, 14
15
5 12
8 15
45
8 11
1550
36 120
7 20
15
14
women
Lesson Quiz
2-3
FeatureLesson
Course 3Course 3
LessonMain
Four divers competed in the belly-flop contest. The bigger the splash the better they do. John made a bigger splash than Bo. Allison came in third. Jennifer came in first with the biggest splash. In what order did the divers finish?
Jennifer, John, Allison, Bo
LESSON 2-4LESSON 2-4
Adding and Subtracting Rational NumbersAdding and Subtracting Rational Numbers
Problem of the Day
2-4
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-4LESSON 2-4
(For help, go to Lesson 1-3.)
1. Vocabulary Review Which numbers are integers: 2, 4.5, 0, –6, ?
Simplify each expression.
2. –9 – 1 3. 10 – 100 4. 12 + (– 2)
Adding and Subtracting Rational NumbersAdding and Subtracting Rational Numbers
13
Check Skills You’ll Need
Check Skills You’ll Need
2-4
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. 2, 0, –6 2. – 10 3. – 90 4. 10
LESSON 2-4LESSON 2-4
Adding and Subtracting Rational NumbersAdding and Subtracting Rational Numbers
Check Skills You’ll Need
2-4
FeatureLesson
Course 3Course 3
LessonMain
A recipe calls for cup white flour and cup wheat flour.
How many total cups of flour are used?
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
13
34
You need , or 1 , cups of flour.1312
112
13
1 • 43 • 4+
34 = +
3 • 34 • 3
Write equivalent fractions with the same denominator.
412= +
912 Simplify.
=1312 Add the numerators.
Quick Check
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
Find – .
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
34
910
The LCM of 10 and 4 is 20, so the LCD of and is 20.9
1034
910 Write equivalent fractions using
the LCD.
34– =
1820
1520–
Subtract the numerators.18 – 15
203
20==
Quick Check
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
Find 6 + 8 .
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
34
23
Method 1 Use improper fractions.
Write each mixed number as an improper fraction.
6 + 8 = +274
34
23
263
Write equivalent fractions using the LCD, 12.= +8112
10412
Add the numerators.=18512
Change the improper fraction to a mixed number.
= 155
12
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
Method 2 Rewrite the mixed numbers using common denominators.
912
34
236 + 8 = 6 + 8
812
Rewrite each mixed number using the LCD, 12.
1712= 14 + Add the integers and the fractions.
512= 14 + 1
Change the improper fraction to a mixed number.
Add the integers.5
12= 15
Quick Check
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
On a 50-foot roll of cable, 15 ft are left. How many feet of
cable were used?
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
34
Let t = the amount used.
Words amount left + amount used = original amount
34Equation 15 + t = 50
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
(continued)
Adding and Subtracting Rational NumbersAdding and Subtracting Rational NumbersLESSON 2-4LESSON 2-4
Subtract 15 from each side.t = 50 – 1534
34
The amount of cable used was 34 ft.14
15 + t = 5034
Rewrite 50 as 49 + , or 1. Subtract. t = 49 – 15 = 3444
34
44
14
Quick Check
Additional Examples
2-4
FeatureLesson
Course 3Course 3
LessonMain
Adding and Subtracting Rational NumbersAdding and Subtracting Rational Numbers
Find each sum or difference.
1. – 2. + 3. – 4. 4
5. It snowed 2 in. on top of 4 in. of snow already on the ground.
How deep is the snow now?
13
7 in.
LESSON 2-4LESSON 2-4
89
59
45
23
7838
7 15
1 7 12
3
12
56
12
12
– 114
Lesson Quiz
2-4
FeatureLesson
Course 3Course 3
LessonMain
Express 106,457,086,299 in words.
one hundred six billion, four hundred fifty-seven million, eighty-six thousand, two hundred ninety-nine
LESSON 2-5LESSON 2-5
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational Numbers
Problem of the Day
2-5
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-5LESSON 2-5
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational Numbers
(For help, go to Lesson 2-2.)
Simplify each expression.
2. 3. 4. 5.1220
7 21
3666
9 81
1. Vocabulary Review A rational number can be written in the form ? , where a and b are integers, and b = 0.
Check Skills You’ll Need
Check Skills You’ll Need
2-5
FeatureLesson
Course 3Course 3
LessonMain
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational NumbersLESSON 2-5LESSON 2-5
Solutions
1. 2. = 3. =
4. = 5. =
7 ÷ 7 21 ÷ 7
13
9 ÷ 9 81 ÷ 9
19
12 ÷ 420 ÷ 4
35
ab
36 ÷ 6 66 ÷ 6
6 11
Check Skills You’ll Need
2-5
FeatureLesson
Course 3Course 3
LessonMain
Find • – .
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational NumbersLESSON 2-5LESSON 2-5
47
512
Multiply the numerators and multiply the denominators.
47
512 • – = –
5 • 412 • 7
Divide the numerator and demoninator by their GCF, 4.
= –5 • 4
12 • 7
1
3
Simplify.= –5
21
Quick Check
Additional Examples
2-5
FeatureLesson
Course 3Course 3
LessonMain
Find the product –3 • –2 .
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational NumbersLESSON 2-5LESSON 2-5
13
56
Estimate: –3 • –2 –3 • (–3) = 913
56
Write as improper fractions.–3 • –2 = – • –13
56
103
176
Divide the numerator and denominator by their GCF, 2.
= 10 • 173 • 6
5
3
Simplify. Write as a mixed number.=859 = 9
49
Check Since 9 is close to 9, the answer is reasonable.49
Quick Check
Additional Examples
2-5
FeatureLesson
Course 3Course 3
LessonMain
One bow takes yards of ribbon. How many bows could
you make from a roll of ribbon that is 12 yards long?
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational NumbersLESSON 2-5LESSON 2-5
34
12
You can use logical reasoning to solve this problem. You need to find
how many -yd pieces there are in 12 yards.34
12
Divide 12 by .34
12
Write the mixed number as an improper fraction.
25212 ÷ = ÷
34
12
34
Multiply by the reciprocal of .252
43= •
34
Additional Examples
2-5
FeatureLesson
Course 3Course 3
LessonMain
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational NumbersLESSON 2-5LESSON 2-5
(continued)
Divide numerator and denominator by the GCF, 2.
252
43= •
1
2
Multiply. Write the fraction as a mixed number.
= = 16503
23
Since you cannot make of a bow, you can make 16 bows. 23
Quick Check
Additional Examples
2-5
FeatureLesson
Course 3Course 3
LessonMain
Multiplying and Dividing Rational NumbersMultiplying and Dividing Rational Numbers
1. • (– ) 2.
3. ÷ ( ) 4.
5. Solve the equation. 1 r =
6. Megan has 3 quarts of punch. One serving is quart. Does she have enough to serve 15 guests?
LESSON 2-5LESSON 2-5
29
12
– 58
–2
14
–1
58
45
23
56
12
14
12
No
– 16
– 34
2 • (–1 )13
18
(–1 ) ÷ (1 )78
12
Lesson Quiz
2-5
FeatureLesson
Course 3Course 3
LessonMain
Twin primes are pairs of prime numbers who have a difference of 2. For example, 43 – 41 = 2. Name the twin primes between 2 and 35.
5, 3; 5, 7; 11, 13; 17, 19; 29, 31
LESSON 2-6LESSON 2-6
FormulasFormulas
Problem of the Day
2-6
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-6LESSON 2-6
FormulasFormulas
(For help, go to Lesson 1-1.)
Evaluate each expression for w = 2 and t = –3.
2. 4w + t 3. 4(w + t)
4. 4w + 4t 5. – 4t –w
1. Vocabulary Review According to the order of operations, you multiply and divide before you ? and ? .
Check Skills You’ll Need
Check Skills You’ll Need
2-6
FeatureLesson
Course 3Course 3
LessonMain
Solutions
1. add; subtract
2. 4(2) + (–3) = 8 + (–3) = 5 3. 4[2 + (–3)] = 4(–1) = –4
4. 4(2) + 4(–3) = 8 + (–12) = –4 5. –4(–3) – 2 =12 – 2 =10
FormulasFormulasLESSON 2-6LESSON 2-6
Check Skills You’ll Need
2-6
FeatureLesson
Course 3Course 3
LessonMain
Find the area of a trapezoid with height of 6 cm and bases
of 5.2 cm and 7.5 cm.
FormulasFormulasLESSON 2-6LESSON 2-6
A = h (b1 + b2)Use the formula for the area of a trapezoid.
12
= (6.0) (5.2 + 7.5) Substitute.12
Additional Examples
2-6
FeatureLesson
Course 3Course 3
LessonMain
(continued)
FormulasFormulasLESSON 2-6LESSON 2-6
The area of the trapezoid is 38.1 cm2.
12= (6.0)(12.7) Add within the parentheses.
= 3(12.7) Multiply from left to right.
= 38.1 Simplify.
Quick Check
Additional Examples
2-6
FeatureLesson
Course 3Course 3
LessonMain
Find the time it takes a sled-dog team to go 95 miles if their
average rate is 19 mph.
FormulasFormulasLESSON 2-6LESSON 2-6
The problem gives distance and rate. Use the distance formula, d = rt where d is the distance traveled, r is the rate of travel, and t is the time spent traveling.
It took the sled-dog team 5 hours to go 95 miles.
d = rt Use the distance formula.
5 = t
Simplify.9519 t=
95 = 19 • t Substitute 95 for d and 19 for r.
Divide each side by 19 to isolate t on the right.9519
19 • t19=
Quick Check
Additional Examples
2-6
FeatureLesson
Course 3Course 3
LessonMain
FormulasFormulasLESSON 2-6LESSON 2-6
Which formula can be used to find the diameter d of a circle, given the circumference C?
C Divide each side by to isolate the variable d.
d=
= d Simplify. C
The formula for the diameter of a circle is d = . C
Quick Check
Use the circumference formula for a circle.C = d
Additional Examples
2-6
FeatureLesson
Course 3Course 3
LessonMain
FormulasFormulas
27 cm2
LESSON 2-6LESSON 2-6
126.75 square inches
392.5 miles
1. Find the area of a triangle whose base is 18 cm and height is 3 cm.
2. Amina purchased a circular glass tabletop. The radius of the tabletop is 6.5 inches. Find the area of the tabletop. Use A = r 2 and let = 3.
3. Solve for w in the formula V = wh.
4. Tyrone drove 1570 miles in 4 days. Find the average distance he drove each day.
w = v h
Lesson Quiz
2-6
FeatureLesson
Course 3Course 3
LessonMain
Formulate a set of 5 different numbers whose median is 95 and whose mean is 100.
Sample Answer90, 92, 95, 110, 113
LESSON 2-7LESSON 2-7
Powers and ExponentsPowers and Exponents
Problem of the Day
2-7
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-7LESSON 2-7
(For help, go to Lesson 2-1.)
1. Vocabulary Review A ? is an integer that divides another integer with a remainder of 0.
Find the GCF.
2. 12, 16 3. 24, 30 4. 32, 48
5. 120, 144 6. 80, 256
Powers and ExponentsPowers and Exponents
Check Skills You’ll Need
Check Skills You’ll Need
2-7
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-7LESSON 2-7
Solutions
1. factor 2. 4 3. 6 4. 16 5. 24 6. 16
Powers and ExponentsPowers and Exponents
Check Skills You’ll Need
2-7
FeatureLesson
Course 3Course 3
LessonMain
Powers and ExponentsPowers and ExponentsLESSON 2-7LESSON 2-7
Write using exponents.
2 • 2 • 2 • 7 • 7
2 is a factor 3 times, and 7 is a factor 2 times. 23 • 72
Quick Check
Additional Examples
2-7
FeatureLesson
Course 3Course 3
LessonMain
Powers and ExponentsPowers and ExponentsLESSON 2-7LESSON 2-7
(–2)6
Multiply. = 64
(–2)6 = (–2)(–2)(–2)(–2)(–2)(–2) The base is –2.
Quick Check
Simplify the expression.
Additional Examples
2-7
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-7LESSON 2-7
Powers and ExponentsPowers and Exponents
–(2)6
The base is 2. –26 = –(2 • 2 • 2 • 2 • 2 • 2)
Multiply. = –64
Quick Check
Simplify the expression.
Additional Examples
2-7
FeatureLesson
Course 3Course 3
LessonMain
Powers and ExponentsPowers and ExponentsLESSON 2-7LESSON 2-7
38 – (3 • 2)2
38 – (3 • 2)2 = 38 – (6)2 Work inside the grouping symbols.
= 38 – 36 Simplify the power.
= 2 Subtract.
Quick Check
Simplify the expression.
Additional Examples
2-7
FeatureLesson
Course 3Course 3
LessonMain
Powers and ExponentsPowers and ExponentsLESSON 2-7LESSON 2-7
Use the expression to find the radius of a doorway that
has the dimensions s = 3 ft and h = 1 ft.
s2 + h2
2h
s2 + h2
2h32 + 12
2 • 1= Substitute 3 for s and 1 for h.
9 + 12 • 1
= The fraction bar acts as a grouping symbol. Simplify the powers.
102
= Simplify above and below the fraction bar.
Divide.= 5
The radius of the doorway is 5 ft.
Quick Check
Additional Examples
2-7
FeatureLesson
Course 3Course 3
LessonMain
Powers and ExponentsPowers and Exponents
1. Write a • a • a • b • b using exponents.
2. Simplify (–4)3. 3. Simplify –25.
4. Simplify (–8 • 5)2 – 92. 5. Evaluate 10 – (5x)2 for x = –2.
6. Find the volume of a child’s wading pool that has a diameter of 6 feet and a height of 1 foot. Use the formula V = r 2h. Use = 3.
LESSON 2-7LESSON 2-7
a3b2
–64 –32
1,519 –90
27 cubic feet
Lesson Quiz
2-7
FeatureLesson
Course 3Course 3
LessonMain
Evaluate the following expressions. Write the answers in lowest terms.
a. – = ? b. + = ?
LESSON 2-8LESSON 2-8
910
110
25
1720
12
34
Scientific NotationScientific Notation
Problem of the Day
2-8
FeatureLesson
Course 3Course 3
LessonMain
LESSON 2-8LESSON 2-8
Scientific NotationScientific Notation
(For help, go to Skills Handbook page 634.)
Multiply.
2. 2 10 3. 4.51 100
4. 1.5 1,000 5. 1.803 10,000
6. 2.39 1,000,000
1. Vocabulary Review An expression using a base and an exponent is a ? .
Check Skills You’ll Need
Check Skills You’ll Need
2-8
FeatureLesson
Course 3Course 3
LessonMain
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
2. 20.0 3. 451.0 4. 1,500.0
5. 18,030.0 6. 2,390,000.0
Solutions
1. power
Check Skills You’ll Need
2-8
FeatureLesson
Course 3Course 3
LessonMain
At one point, the distance from Earth to the moon is
1.513431 1010 in. Write this number in standard form.
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
= 15,134,310,000
At one point, the distance from Earth to the moon is 15,134,310,000 in.
1.513431 1010 = 1.5134310000Move the decimal 10 places to the right. Insert zeros as necessary.
.
Quick Check
Additional Examples
2-8
FeatureLesson
Course 3Course 3
LessonMain
The diameter of the planet Jupiter is about 142,800 km.
Write this number in scientific notation.
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
142,800 = 1 42,800.
The diameter of the planet Jupiter is about 1.428 105 km.
The decimal point moves 5 places to the left..
= 1.428 105 Use 5 as the exponent of 10.
Quick Check
Additional Examples
2-8
FeatureLesson
Course 3Course 3
LessonMain
Write 4.86 x 10–3 in standard form.
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
= 0.00486
4.86 x 10–3 = 0.004.86 Move the decimal point 3 places to the left to make4.86 less than 1.
Quick Check
Additional Examples
2-8
FeatureLesson
Course 3Course 3
LessonMain
Write 0.0000059 using scientific notation.
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
0.0000059 = 0.000005.9 Move the decimal point 6 places to the right to geta factor greater than 1 butless than 10.
= 5.9 x 10–6 Use 6 as the exponent of 10.
Quick Check
Additional Examples
2-8
FeatureLesson
Course 3Course 3
LessonMain
Scientific NotationScientific NotationLESSON 2-8LESSON 2-8
1. Write 7.304 102 in standard form.
2. Write 41,700,000,000 in scientific notation.
3. Write 3.03 x 10–5 in standard form.
4. Write 0.00000127 using scientific notation.
730.4
4.17 1010
0.0000303
1.27 10–6
Lesson Quiz
2-8