Chapter Audio Summary for McDougal Littell
Middle School Math, Course 1
Chapter 5 Number Patterns and Fractions
In Chapter 5 you saw how to use prime factorization to find the greatest common factor
and least common multiple of two or more numbers. You saw how to determine if
fractions are equivalent and how to order them. You also saw how to rewrite mixed
numbers as improper fractions and how to convert between decimals and fractions.
Turn to the lesson-by-lesson Notebook Review that starts on p. 233 of the textbook.
Review the Check Your Definitions section and the Use Your Vocabulary section, and
then look at the review sections that begin with lesson numbers.
Lessons 5.1 and 5.2 Can you use divisibility rules and find factors?
Important words and terms to know are: divisible, prime number, composite number,
prime factorization, factor tree, common factor, and greatest common factor.
The goals of lessons 5.1 and 5.2 are to find the prime factorization of a number and to
find the greatest common factor of two or more numbers.
Read the example.
“Test 574 for divisibility by 2, 3, 5, 6, 9, and 10.”
By using the divisibility rules, you can determine that 574 is divisible by 2 because it is
an even number. Adding the individual digits, 5, 7, and 4 gives us 16, which is not
divisible by 3 or 9, so 574 is not divisible by either. Because 574 is not divisible by 3, it
is also not divisible by 6. Because 574 does not end in a 5 or 0, it is not divisible by 5 or
10.
Now try Exercises 3, 4, 5, and 6. If you need help, go back to the worked-out examples
on pages 214-216.
Read the example.
“Find the greatest common factor of 90 and 126.”
To find the greatest common factor for 90 and 126, first find the prime factorization of
each number by creating a factor tree for both. The prime factors for 90 are 3, 3, 2, and
5. The prime factors of 126 are 2, 3, 3, and 7. The two numbers have 2, 3, and 3 in
common. If you multiply 2 by 3 by 3, you get 18 as the greatest common factor of 90 and
126.
McDougal Littell: Audio Summary
Number Patterns and Fractions
1
Chapter Audio Summary for McDougal Littell
Middle School Math, Course 1
Now try Exercises 7 and 8. If you need help, go back to the worked-out examples on
pages 222 and 223.
Lesson 5.3 Can you simplify fractions?
Important words and terms to know are: fraction, equivalent fraction, and simplest form.
The goal of lesson 5.3 is to write fractions in simplest form.
Read the example.
“Use the GCF to write the fraction in simplest form.”
To find the simplest form of 6/24, determine the greatest common factor of 6 and 24. 6 is
the greatest common factor of 6 and 24. Divide both the numerator and the denominator
by 6 to get the fraction, 1/4. The fraction 1/4 is called the simplest form of the fraction
6/24. The fractions are equivalent fractions.
To find the simplest form of 15/33, determine the greatest common factor of 15 and 33.
3 is the greatest common factor of 15 and 33. Divide both the numerator and the
denominator by 3 to get 5/11 as 15/33 in its simplest from.
Now try Exercises 9, 10,11 and 12. If you need help, go back to the worked-out
examples on pages 228 - 230.
Turn to the lesson-by-lesson Notebook Review that starts on p. 258 of the textbook.
Review the Check Your Definitions section and the Use Your Vocabulary section, and
then look at the review sections that begin with lesson numbers.
Lessons 5.4 and 5.5 Can you use the LCM to order fractions?
Important words to know are: multiple, common multiple, least common multiple, and
least common denominator.
The goals of lessons 5.4 and 5.5 are to find the least common multiple and then to
compare and order fractions.
Read the example.
“Order the fractions 2/3, 2/9, and 3/5 from least to greatest.”
McDougal Littell: Audio Summary
Number Patterns and Fractions
2
Chapter Audio Summary for McDougal Littell
Middle School Math, Course 1
Use the least common multiple of 45 as the least common denominator for each fraction.
Because 15 times 3 equals 45, multiply 2/3 by 15/15 to get 30/45. Because 9 times 5
equals 45, multiply 2/9 by 5/5 to get 10/45. Because 5 times 9 equals 45, multiply 3/5 by
9/9 to get 27/45. To order the fractions, 2/3, 2/9, and 3/5 from least to greatest, use their
equivalent fractions with their least common multiple in the denominator: 30/45, 10/45,
and 27/45. Now compare the numerators. 10/45 is less than both 30/45 and 27/45 and
27/45 is less than 30/45, so the order is: 10/45, 27/45, and 30/45. Reduce the fractions
back down to their original form, so that you can know that the fractions ordered from
least to greatest are: 2/9, 3/5, and 2/3.
Now try Exercise 3. If you need help, go back to the worked-out examples on pages
235 and 235 and 239 and 240.
Lesson 5.6 Can you rewrite improper fractions and mixed numbers?
Important words and terms to know are: least common denominator, improper fraction,
and proper fraction.
The goal of lesson 5.6 is to write mixed numbers as improper fractions.
Read the examples.
“a, write 2 and 7/8 as an improper fraction, and b, write 19/8 as a decimal.”
For example a, to write 2 7/8 as an improper fraction, multiply the 2 by the number in the
denominator which is 8 to get 16. Then add that 16 to the 7 in the numerator to get 23.
The final improper fraction is 23/8.
For example b, to write 19/8 as a decimal, divide 19 by 8 to get 2.375.
Now try Exercises 4 and 5. If you need help, go back to the worked-out examples on
pages 244-246.
Lessons 5.7 and 5.8 Can you rewrite decimals and fractions?
Important words and terms to know are: mixed number, terminating, and repeating
decimals.
The goals of lessons 5.7 and 5.8 are to convert decimals and fractions.
Read the examples.
“a, write 2.08 as a mixed number, and b, write 7/9 as a decimal.”
McDougal Littell: Audio Summary
Number Patterns and Fractions
3
Chapter Audio Summary for McDougal Littell
Middle School Math, Course 1
For example a, to write 2.08 as a mixed number, use 2 as the whole number and then
convert 0.08 into the fraction 8/100. Simplify 8/100 to 2/25. The final mixed number is 2
2/25.
For example b, To write 7/9 as a repeating decimal, divide 9 by 7 to get 0.77 and so on.
The 7/9 = 0.7 with a line over 7 to indicate that the 7 repeats.
Now try Exercises 6, 7, 8, and 9. If you need help, go back to the worked-out examples
on pages 253 and 254.
McDougal Littell: Audio Summary
Number Patterns and Fractions
4