Chapter 2 Addition And Subtraction Fractions Point Out

Chapter 2

Fractions

Student Performance Objectives:

Section I Understanding and Working with Fractions

2-1 Distinguishing Among the Various Types of Fractions

2-2 Converting Improper Fractions to Whole or Mixed Numbers

Section II Addition and Subtraction of Fractions

2-6 Determining the Least Common Denominator, LCD, of Two or More Fractions

Section III Multiplication and Division of Fractions

2-9 Multiplying Fractions and Mixed Numbers

Chapter Notes, Teaching Tips and Lecture Launchers

• Remind students that the worked-out solutions, not just the answers, to all the Try-It

Exercises are located after the Chapter Summary Chart.

• As in Chapter 1, the Collaborative Learning Activity for this chapter, “Knowing Fractions is

Half the Battle” will get the students to think about and discuss the uses of math in business.

It is also another good opportunity for them to get to know each other early in the term.

• To get reluctant students motivated to learn fractions, ask if they cook, do construction

projects, or have pizza parties. Ask how an understanding of fractions might be helpful in

those situations.

• Point out that fractions represent a portion of a thing. For example, to find out how much

rock remains after using ¾ of a half ton of rock, one cannot subtract ¼ from ½ because the ¼

is a portion, and the ½ ton is the weight of a pile of rocks. This problem also makes a good

visual representation of fractions.

Section I Understanding and Working with Fractions

• Be sure students fully understand the types of fractions; proper, improper, and mixed

numbers.

• Make sure the students know the difference between the numerator and the denominator.

Stress the fact that fractions are a way of expressing parts of a whole, whereby the

denominator describes how many equal parts the whole is divided into and the numerator

describes how many parts we are describing or referring to.

• Spotlight: Sometimes students have difficulty determining which of two fractions is the

larger or smaller number. By having the students convert them to like fractions (same

denominator), the answer will become evident.

• Classroom Activity: Frequently fractions are used to express a given quantity as a part of a

whole, such as 4 months equals

4

12

1

3

or

of a year. Ask students to write the following as a

fractional part of the whole, reduced to lowest terms:

7

• When converting mixed numbers to improper fractions draw an arrow going in a clockwise

direction starting at the denominator, around the whole number and ending at the numerator

to help students remember the order of the steps.

• Show students that raising fractions is simply cutting the pie into smaller pieces; the amount

of pie, or the value of the number, remains the same. Reducing fractions is just the opposite.

Section II Addition and Subtraction of Fractions

• Point out that a common denominator must be found before fractions can be added or

subtracted. The “least” common denominator, LCM, is the most desirable to use since it

simplifies the calculation.

• Be sure students understand that when they borrow 1 in subtraction, they are borrowing a

whole unit, expressed in terms of the common denominator.

• Ask students to express a whole unit in terms of fourths, fifths, sixths, and twenty-

fourths. (

4

4, 5

5, 6

6, 24

24

)

complement of that fraction, i.e. what we have or what we don’t have, this or not this? Can

the students use the fraction given, or must they subtract the fraction from 1?

• When raising fractions, show the fraction by which to multiply.

Section III Multiplication and Division of Fractions

• Spotlight: Show students that fractions raised to higher terms or reduced to lower terms are

still the same number. This can be demonstrated by having the students multiply a number,

1

2

1

4

1

2

1

2

1

2

• Point out to students that cancellation can be done in any order.

• Demonstrate that sometimes fractions can be solved mentally, without pencil and paper.

• Spotlight: Ask students to divide a fraction, say

7

8

, by

5

7

8

. When the quotient turns out to be

1

4

• Classroom Activity: In division of fractions, be sure students invert the divisor, not the

dividend. Point out that the divisor is the fraction after the term “divided by.” Ask the

students to identify the divisor and the dividend and then solve the following:

•

3

8 divided by 9

16

(Answer:

2

3

)

16

Questions Students Always Ask

“When raising fractions to higher terms, why do I have to multiply the numerator?”

• Fractions are raised to higher numbers so that we can add and subtract like numbers,

apples to apples, so to speak. However, we don’t want to change the value of the

3

4

“To solve the equation 3 ½ – 1 ¾, why do I add 4/4 to the top fraction?

• First, you must raise all fractions to a common denominator. Then you will notice that

the top fraction,

2

1

raised to

4

2

, is less than the fraction you are subtracting from it.

“When adding and subtracting mixed fractions, should I convert them into improper fractions?”

“Do I have to cancel when multiplying fractions?”

“I don’t understand the concept of dividing by a fraction.”

“Does it matter which number I invert when dividing fractions?”

4

2

4

2

4

6