Purpose
A good understanding of fractions is very important when
dealing with many everyday occurrences.
Retail stores use fractions in their sale advertisements to emphasize the
customer's savings. Recipes
for your favorite foods usually use fractional units. Can you name some other
daily instances where
fractions are used? This lesson will help you become more comfortable with
fractions.
Objectives
After completing this lesson, you should be able to
• identify terminology used when dealing with fractions;
• reduce, expand, and compare fractions;
• change proper fractions to mixed fractions;
• determine the greatest common factor (GCF) for
fractions; and
• change fractions into decimals and vice versa.
Reading As signment
Textbook, Chapter 5
Commentary
Section 1: Understanding Fractions
In order to clearly understand fractions, it may be necessary to construct
boxes or circles as
diagrams . Visualizing a problem and using hands-on experience can be a valuable
asset to you in
studying this mathematical process .
| Complete Ex press Yourself problems 1–13 on page
111. Complete Practice What You Know
problems 14–15 on page 111.
Check your answers with those provided in Appendix
A. |
Section 2: Finding Equivalent Fractions
In the process of comparing, adding, and subtracting
fractions , it is often necessary to find the
equivalent fraction. For example, changing fourths into eighths requires
multiplying the top
(numerator) and the bottom (denominator) by the same number, 2. Look at the
fol lowing example .
Diagram A
1 of the 4 equal parts: 1/4.
Diagram B
2 of the 8 equal parts: 2/8
Both equal the same portion of the whole: 
The two boxes are each the same size. One is divided into
four equal parts, and the other is divided
into eight equal parts. In looking at the 1/4 fraction only, one section would
be shaded in the first box.
This same-size portion in the other box would require shading in two sections.
Therefore, 
| Complete Think and Discuss problems 1–4 on pages
112–113. Complete Exercises 5–41 odd on page
113.
Check your answers with those provided in Appendix
A. |
If you feel that you need some additional practice finding
equivalent fractions, you may complete
the Extra Practice problems for this section on page 415 in your textbook
(answers are provided in
Appendix B).
Section 3: Writing Fractions and Mixed Numbers
The changing of whole numbers and mixed fractions into
improper fractions can be beneficial when
completing many mathematical problems, but it can also be helpful in
understanding the fractional
number in different ways. For example, the fraction 7/2 may not convey the
meaning that 
does,
even though they represent the same amount.
| Complete Think and Discuss problems 1–3 on page
115. Complete Exercises 5–29 odd and 30–34
on page 115.
Check your answers with those provided in Appendix
A. |
If you feel that you need extra practice writing fractions
and mixed numbers, you may complete the
Extra Practice problems for this section on page 416 in your textbook (answers
are provided in
Appendix B).
Section 4: Comparing Fractions and Mixed Numbers
When comparing fractions, it is vitally important to make
sure that each fraction has the same
denominator. Fractions with the same denominator can then be compared based on
their numerators.
| Complete Think and Discuss problems 1–4 on page
116.= Complete Exercises 5–43 odd on page
117.
Check your answers with those provided in Appendix
A. |
If you feel that you need additional practice comparing
fractions and mixed numbers, you may
complete the Extra Practice problems for this section on page 416 in your
textbook (answers are
provided in Appendix B).
Section 5: Factoring to Find the Greatest Common Factor
Finding the greatest common factor, or GCF, is very
important when working with fractions. The
word greatest in the term means the largest, and the word common means shared.
The word factor
has to do with part of a multiplication product . In other words, it means
looking for a number that
when multiplied by another number equals a common number. Finding the greatest
common factor,
therefore, is locating the largest number that is a factor of the numbers given.
Consider the numbers
20 and 12.
• The factors of 20 are 1, 2, 4, 5, 10, and 20.
• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• They share the factors 1, 2, and 4.
• The largest of these shared factors is 4.
• Therefore, the GCF is 4.
| Complete Think and Discuss problems 1–4 on page
119. Complete Exercises 5–35 odd and 36–40
on page 119.
Check your answers with those provided in Appendix
A. |
If you feel that you need some additional practice in
factoring to find the greatest common factor,
you may complete Extra Practice problems for this section on page 417 in your
textbook (answers
are provided in Appendix B).
Section 6: Writing Fractions in Lowest Terms
This process involves dividing the top (numerator) and the
bottom (denominator) by the same
number. By dividing in this manner, both parts of the fraction are reduced to
smaller numbers but
still represent the same portion. Look at the following example.
Diagram A
1/4
Diagram B
2/8
The fractions 
are the
same portion of the whole:
The reducing process will work nicely as long as the
divisor is the same number for the top as for the
bottom.
| Complete Think and Discuss problems 1–6 on page
120. Complete Exercises 7–53 odd and 55–62
on page 121.
Check your answers with those provided in Appendix
A. |
Is the process of writing fractions in lowest terms still
giving you problems? For additional practice,
complete the Extra Practice problems for this section on page 417 in your
textbook (answers are
provided in Appendix B).
Section 7: Writing Fractions and Decimals
The process of changing a fraction to a decimal involves
dividing the two numbers. I consider a
fraction just a division waiting to happen. The top number (numerator) is
waiting to be divided by
the bottom number (denominator). It is important to remember that the
denominator must always be
the divisor. The division process can result in three types of numbers: a whole
number, a terminating
decimal, or a repeating decimal. To change a decimal to a fraction, find the
place value of the
farthest digit to the right and place the digits of the decimal over that number
and reduce the fraction
if possible. A calculator can be invaluable in checking your work; however, it
is important that you
complete the divisions by hand, as you will not be allowed to use a calculator
on the exams.
| Complete Think and Discuss problems 1–4 on page
123. Complete Exercises 5–43 odd and 44–49
on page 123.
Check your answers with those provided in Appendix
A. |
If you feel that you need some additional practice writing
fractions and decimals, complete the Extra
Practice problems for this section on page 418 in your textbook (answers are
provided in Appendix
B).
Section 8: Finding Patterns with Fractions and
Repeating Decimals
One definition of mathematics is the study of patterns.
Throughout all aspects of your personal
experiences you will observe and interact with various patterns. The days of the
week and the music
scale are two common patterns to which you are constantly exposed.
| Complete problems 1–12 on pages 124–125.
Check your answers with those provided in Appendix A. |
