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# Multiplying and Dividing Fractions and Mixed Numbers

PURPOSE

The knowledge of multiplying and dividing fractions will be used often in your daily life. Whether
you are purchasing floor covering, material for four bridesmaids' dresses, or figuring out the amount
and size of lumber for a particular project, there are many activities that require the multiplication
and division of fractions.

OBJECTIVES

After completing this lesson, you should be able to

• multiply fractions and mixed fractions;

• divide fractions and mixed fractions; and

•use multiplication and division of fractions in real-life situations.

Textbook, Chapter 6

COMMENTARY

Section 1: Multiplying Fractions

To multiply fractions, you must multiply the numerators and denominators, respectively. The new
fraction must then be reduced into its lowest terms.

 Complete Think and Discuss problems 1–5 on page 130. Complete exercises 7–59 odd and 61–77 on page 131. Check your answers with those provided in Appendix A.

If you feel that you need additional practice multiplying fractions, you may complete the Extra
Practice problems for this section on page 418 in your textbook (answers are provided in Appendix
B).

Section 2: Multiplying Fractions: A Shortcut

My guess is that you have probably already been using this shortcut. If not, I encourage you to use it
faithfully. The process will reduce the effort required to do these problems and make them more
enjoyable. I love this section for just that reason. The procedure requires the reduction of the
numerator and the denominator with a common factor to its lowest terms before multiplying the
numerators and denominators together.

 Complete Think and Discuss problems 1–4 on page 132. Complete Exercises 5–49 odd and 50–66 on page 133. Check your answers with those provided in Appendix A.

If you feel that you need some additional practice using the shortcut when multiplying fractions, you
may complete the Extra Practice problems for this section on page 419 in your textbook (answers are
provided in Appendix B).

Section 3: Using Guess and Check to Solve Problems

By focusing on specific mathematical procedures in math class, teachers often forget that trial and
error is a perfectly good skill and should be stressed more. At times it takes longer to solve the
problem, but more often than not trial and error is a valid technique.

 Complete problems 1–9 on page 135. Check your answers with those provided in Appendix A.

Section 4: Multiplying Mixed Numbers

The first step in multiplying mixed numbers is to adjust each number to an improper fraction. Next,
use the multiplication process discussed in previous sections. Remember to reduce the fractions
before multiplying.

 Complete Think and Discuss problems 1–5 on page 136. Complete Exercises 7–39 odd and 40–51 on page 137. Check your answers with those provided in Appendix A.

If you feel that you need more practice multiplying mixed numbers, you may complete the Extra
Practice problems for this section on page 419 in your textbook (answers are provided in Appendix
B).

Section 5: Estimating Products of Fractions and Mixed Numbers

No doubt you have been in a store and discovered the need to multiply fractions but had no paper
and pencil. In this instance, the process of estimating becomes invaluable. There are two methods
that can be used when estimating. The first involves rounding the top multiplication and the bottom
product into multiples of 10, making the reducing easier. The second method involves estimating a
simpler fraction—such as one-half or one-fourth the whole number—and completing the
computation with the simpler approximation.

 Complete problems 1–6 on pages 138–139. Complete Exercises 7–21 odd and 22–33 on page 139. Check your answers with those provided in Appendix A.

Section 6: Dividing Fractions

When dividing one fraction by another, it is important to multiply the fraction to the left by the
reciprocal of the divisor (the fraction to the right). Dividing fractions is really just multiplying them
after flipping the divisor. As you work through this process, remember that when dividing by a
fraction less than 1 you will get a bigger number. For example, if you have a candy bar and divide it
into halves, you would have two pieces.

 Complete Think and Discuss problems 1–6 on pages 140–141. Complete Exercises 7–43 odd and 45–51 on page 141. Check your answers with those provided in Appendix A.

If you feel that you need additional practice dividing fractions, you may complete the Extra Practice
problems for this section on page 420 in your textbook (answers are provided in Appendix B).

Section 7: Dividing Mixed Numbers

Just as in multiplication, the first step in dividing mixed numbers is to rewrite each mixed fraction as
an improper fraction. Next, flip the right fraction, reduce, and multiply. In problems in which you
begin with mixed fractions, your answer should, in most cases, be converted to a mixed fraction.

 Complete Think and Discuss problems 1–5 on page 142. Complete Exercises 7–49 odd and 51–64 on page 143. Check your answers with those provided in Appendix A.

If you feel that you need extra practice in dividing mixed numbers, you may complete Extra Practice
problems for this section on page 420 in your textbook (answers are provided in Appendix B).

Section 8: Fractions: A Business Application

Fractions are commonly used in the business world. Some of the processes that are used include
multiplying decimals and whole numbers, rounding quotients, rounding to the nearest cent, and
multiplying fractions by decimals. The example below illustrates the process of multiplying fractions
by decimals. Place decimal over 1: Multiply numerators and denominators: Then divide:
. Finally, round to nearest cent:
.45.

 Complete Think and Discuss problems 1–14 on pages 144–145. Complete Review problems 15–22 on page 145. Check your answers with those provided in Appendix A. 