Chapter 2: Multiplying and Dividing Fractions

1.2Fractions!!!Write fractions for the shaded and unshaded portions of each figure.

a.

b. Slide 2.1- 2ParallelExample 1Identifying Fractions

The figure has 8 equal parts.There are 5 shaded parts.

shaded portion

unshaded portionThe figure has 12 equal parts.There are 6 shaded parts.

shaded portion

unshaded portionUse a fraction to represent the shaded part of each figure. a.

b. Slide 2.1- 3ParallelExample 2Representing Fractions Greater Than 1An area equal to 7 of the parts is shaded. Write this as

An area equal to 8 of the 1/6 parts is shaded. Write this as

In the fraction , the number 3 is the numerator and the 4 is the denominator. The bar between the numerator and the denominator is the fraction bar.

Slide 2.1- 4

NumeratorDenominatorFraction bar

Identify the numerator and denominator in each fraction. a.

b. Slide 2.1- 5ParallelExample 3Identifying Numerators and Denominators

NumeratorDenominator

NumeratorDenominator

Proper FractionsImproper Fractions

Slide 2.1- 6a. Identify all proper fractions in this list.

Proper fractions have a numerator that is smaller than the denominator. The proper fractions are shown below.

b. Identify all the improper fractions in the list above. Slide 2.1- 7ParallelExample 4Classifying Types of Fractions

A proper fraction is less than 1.An improper fraction is equal to or greater than 1.Mixed NumbersSlide 1- 8Writing a Mixed Number as an Improper Fraction

Slide 2.2- 9Change 3 to an improper fraction.Use the following steps to write a mixed number as an improper fraction.

Slide 2.2- 10Write as an improper fraction (numerator greater than denominator).

Slide 2.2- 11ParallelExample 1Writing a Mixed Number as an Improper Fraction

Step 1Multiply 5 and 9.

Step 2

45 + 8 = 53Add 8. The numerator is 53. Step 3

Use the same denominator. Write each improper fraction as a mixed number.

a. Slide 2.2- 12ParallelExample 2Writing Improper Fractions as Mixed Number

Divide 14 by 3.RemainderWhole number part

12 2The quotient 4 is the whole number part of the mixed number. The remainder 2 is the numerator of the fraction, and the denominator stays as 3.

RemainderWrite each improper fraction as a mixed number.

b. Slide 2.2- 13ParallelExample 2continuedWriting Improper Fractions as Mixed Number

Divide 48 by 6.RemainderWhole number part

48 0

Slide 2.5- 14Multiply. Write answers in lowest terms.

a.

b.Slide 2.5- 15ParallelExample 1Multiplying FractionsMultiply the numerators and multiply the denominators.

Lowest terms

Lowest termsMultiply Write answers in lowest terms.

Slide 2.5- 16ParallelExample 2Using the Multiplication ShortcutThe numerator and denominator have a common factor other than 1, so write the prime factorization of each number.Not in lowest terms

Multiply Write answers in lowest terms.

Slide 2.5- 17ParallelExample 2Using the Multiplication Shortcut

Divide by the common factors 2 and 7.

Or divide out common factors.

Use the multiplication shortcut to find each product. Write the answers in lowest terms and as mixed numbers where possible.

a.

Slide 2.5- 18ParallelExample 3Using the Multiplication Shortcut

Divide 8 and 6 by their common factor 2. Notice that 5 and 13 have no common factor. Then, multiply.

43

Lowest termsUse the multiplication shortcut to find each product. Write the answers in lowest terms and as mixed numbers where possible.

b.

c.

Slide 2.5- 19ParallelExample 3Using the Multiplication Shortcut

Divide 9 and 18 by 9, and divide 10 and 16 by 2.

12

Lowest terms58

6537

12

Slide 2.5- 20Multiply. Write answers in lowest terms and as whole numbers where possible.

a.

b.

Slide 2.5- 21ParallelExample 4 Multiplying by Whole Numbers

Write 9 as 9/1 and multiply.

31

52

Slide 2.7- 22

ReciprocalFind the reciprocal of each fraction.

a.

b.

c.

d. 2 Slide 2.7- 23ParallelExample 1Finding ReciprocalsThe reciprocal is

The reciprocal is

The reciprocal is

The reciprocal is

Slide 2.7- 24

Divide. Write answers in lowest terms and as mixed numbers where possible.

Slide 2.7- 25ParallelExample 2Dividing One Fraction by AnotherThe reciprocal of

ReciprocalsChange division to multiplication

21

Divide

Slide 2.7- 26ParallelExample 2

Dividing One Fraction by Another

14

Divide. Write all answers in lowest terms and as whole or mixed numbers where possible.

a.

Slide 2.7- 27ParallelExample 3Dividing with a Whole Number

Write 9 as 9/1. Use the reciprocal of which is 4/1.

Divide. Write all answers in lowest terms and as whole or mixed numbers where possible.

b.

Slide 2.7- 28ParallelExample 3Dividing with a Whole Number

Write 4 as 4/1. The reciprocal of 4/1 is .

(+ and -) Fractions29Slide 3.3- 30To add unlike fractions, we must first change them to like fractions (fractions with the same denominator.)

Add Slide 3.3- 31ParallelExample 1Adding Unlike FractionsThe least common multiple of 6 and 12 is 12.Write the fractions as like fractions with a denominator of 12. This is the least common denominator (LCD).

Step 1

Step 2

Step 3Step 3 is not needed because the fraction is in lowest terms.Add the fractions using the three steps. Simplify all answers. Slide 3.3- 32ParallelExample 2Adding FractionsThe least common multiple of 4 and 8 is 8. Step 1Step 2

Step 3Step 3 is not needed because the fraction is in lowest terms.

Rewritten as like fractionsSubtract. Simplify all answers. Slide 3.3- 33ParallelExample 4Subtracting Unlike Fractions

Step 1

Step 2Step 3Step 3 is not needed because the fraction is in lowest terms.

Rewritten as like fractions

Subtract numerators.Subtract. Simplify all answers. Slide 3.3- 34ParallelExample 4Subtracting Unlike Fractions

Step 1

Step 2Step 3

Rewritten as like fractions

Subtract numerators.

ExampleSlide 1- 35Try these:Slide 1- 36Hw Section 1.2 Pg 331-5,7-11Slide 1- 37