Download Chapter Audio Summary for McDougal Littell

Chapter Audio Summary for McDougal Littell
Pre-Algebra
Chapter 4 Factors, Fractions, and Exponents
In Chapter 4 you learned to factor whole numbers and monomials and to write prime
factorizations. You saw how to use the greatest common factor to write equivalent fractions. You
also used the least common multiple to compare fractions. You used rules of exponents with
whole number, negative, and zero exponents. Finally, you wrote numbers in scientific notation.
Turn to the lesson-by-lesson Chapter Review that starts on p. 210 of the textbook.
Read the Vocabulary Review and answer the vocabulary questions. Now look at the review
sections that begin with lesson numbers.
Lesson 4.1 Factors and Prime Factorization
Important words and terms to know are: prime number, composite number, prime factorization,
factor tree, and monomial.
The goal of Lesson 4.1 is to factor numbers and monomials.
Read the first example.
“Write the prime factorization of 240.”
Use a factor tree to express 240 as a product of all prime numbers. Begin by writing the original
number. Then write 240 as 12 • 20. Then write 12 as 3 • 4, and 20 as 4 • 5. Finally write each 4 as
2 • 2. So, the prime factorization of 240 is 24 • 3 • 5.
Now read the second example.
“Factor the monomial 42x4y.”
To factor the monomial 42x4y, write 42 as 2 • 3 • 7 and write x4 as x • x • x • x. So, the prime
factorization of 42x4y is 2 • 3 • 7 • x • x • x • x • y.
Now try Exercises 5 through 12. If you need help, go back to the worked-out examples on
pages 172 through 174.
Lesson 4.2 Greatest Common Factor
Important terms to know are: common factor, greatest common factor (GCF), and relatively
prime.
The goal of Lesson 4.2 is to find the GCF of numbers and monomials.
Read the example.
“Find the greatest common factor of 45, 18, and 90.”
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Begin by writing the prime factorization of each number: 45 = 3 • 3 • 5; 18 = 2 • 3 • 3; and 90 = 2
• 3 • 3 • 5. Remember that if the same number appears twice in the prime factorization of each
number, include it twice when finding the GCF. The common prime factors are 3 and 3, so the
GCF of 45, 18, and 90 is 3 • 3, or 9.
Now try Exercises 13 through 16. If you need help, go back to the worked-out examples on
pages 177 and 178.
Lesson 4.3 Equivalent Fractions
Important terms to know are: equivalent fractions and simplest form.
The goal of Lesson 4.3 is to write fractions in simplest form.
Read the first example.
“Write
60
in simplest form.”
75
Remember that a fraction is in simplest form when the numerator and denominator have 1 as their
GCF. So to write
60
in simplest form, first write the prime factorizations of the numerator and
75
the denominator. 60 = 22 • 3 • 5 and 75 = 3 • 5 • 5. The GCF of 60 and 75 is 15, so divide both the
numerator and denominator by 15, to get
4
.
5
Now read the second example.
“Write
21a2
in simplest form.”
49ab
Begin by factoring the numerator and denominator and dividing out common factors. Then
simplify to
3a
.
7b
Now try Exercises 17 through 24. If you need help, go back to the worked-out examples on
pages 182 through 184.
Lesson 4.4 Least Common Multiple
Important words and terms to know are: multiple, common multiple, least common multiple
(LCM), and least common denominator (LCD).
The goal of Lesson 4.4 is to use the LCD to compare fractions.
Read the example.
2
“Use the LCD to compare
5
17
and
.”
36
90
First factor the denominators to find their least common multiple. Use the common factors, 2, 3,
and 3 only once. Multiply all the factors, 2 • 3 • 3 • 2 • 5, to get the LCM, 180. So, the LCD is
180. Write equivalent fractions using the LCD. Then compare the numerators.
25
34
<
, so
180 180
5
17
<
.
36
90
Now try Exercises 25 through 29. If you need help, go back to the worked-out examples on
pages 187 through 189.
Lesson 4.5 Rules of Exponents
The goal of Lesson 4.5 is to use rules of exponents to simplify products and quotients.
Read the example.
“Find the product. Write your answer using exponents.”
For part (a), 58 • 56, use the product of powers property to multiply powers with the same base.
Add the exponents, 8 and 6, to get 14. The product is 514.
For part (b), 7a2 • a6, use the associative property of multiplication to group the powers of a. Add
the exponents of a, 2 + 6, to get the product 7a8. Notice that in the expression 7a2, the exponent 2
applies to only the variable a. The 7 is not squared.
Now try Exercises 30 through 37. If you need help, go back to the worked-out examples on
pages 194 through 196.
Lesson 4.6 Negative and Zero Exponents
The goal of Lesson 4.6 is to rewrite expressions containing negative or zero exponents.
Read the example.
“Write 80b–5 using only positive exponents.”
Use the definition of zero exponent: For any nonzero number a, a0 = 1. So, 80 = 1 and 80b–5 = 1 •
b–5. Then use the definition of a negative exponent to write b–5 as
1
1
0 –5
5 . So, 8 b is written
5 .
b
b
Now try Exercises 38 through 41. If you need help, go back to the worked-out examples on
pages 199 through 201.
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Lesson 4.7 Scientific Notation
An important term to know is: scientific notation.
The goal of Lesson 4.7 is to write numbers in scientific notation.
Read the first example.
“Write the number in scientific notation.”
For part (a), to write 41,800,000 in scientific notation, first write it in product form. Move the
decimal point 7 places to the left, so that the first factor, 4.18, is greater than or equal to 1 and less
than 10. The second factor is 10,000,000. Then write 10,000,000 as 107, so the number is written
in scientific notation as 4.18 × 107. Notice that the number 41.8 × 106 is not written in scientific
notation because 41.8 > 10.
Now read the second example.
“Order 4.7 × 10–5, 0.000056, and 3.2 × 10–6 from least to greatest.”
In step 1, rewrite 0.000056 as 5.6 × 10–5 because all of the numbers need to be in scientific
notation. In step 2, order the numbers with different powers of 10. You see that
3.2 × 10–6 is smaller than the other numbers because 10–6 < 10–5. In step 3, you then order the
numbers with the same power of 10. Because 4.7 < 5.6, 4.7 × 10–5 < 5.6 × 10–5. In step 4, write
the original numbers in order from least to greatest: 3.2 × 10–6; 4.7 × 10–5; 0.000056.
Now try Exercises 42 through 47. If you need help, go back to the worked-out examples on
pages 204 through 206.
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