Section

Objectives

2.4 Least Common Multiple and Equivalent Fractions

Slide 1

1. Least Common Multiple (LCM)2. Writing Equivalent Fractions3. Ordering Fractions

Section 2.4 Least Common Multiple and Equivalent Fractions

1. Least Common Multiple

Slide 2

When we multiply a number by the whole numbers 1, 2, 3, and so on, we form the multiples of the number.

The least common multiple (LCM) of two given numbers is the smallest whole number that is a multiple of each given number.

Example 1 Finding the LCM by Listing Multiples

Slide 3

Find the LCM of the given numbers by listing several multiples of each number.

a. 15 and 12 b. 10, 15, and 8

PROCEDURE Using Prime Factors to Find the LCM of Two Numbers

Slide 4

Step 1 Write each number as a product of prime factors.

Step 2 The LCM is the product of unique prime factors from both numbers. Use repeated factors the maximum number of times they appear in either factorization.

Example 2 Finding the LCM by Using Prime Factors

Slide 5

Find the LCM.

a. 14 and 12 b. 50 and 24 c. 45, 54, and 50

Example 3 Using the LCM in an Application

Slide 6

A tile wall is to be made from 6-in., 8-in., and 12-in. square tiles. A design is made by alternating rows with different-size tiles. The first row uses only 6-in. tiles, the second row uses only 8-in. tiles, and the third row uses only 12-in. tiles. Neglecting the grout seams, what is the shortest length of wall space that can be covered using only whole tiles?

Example

a. 15 and 25 b. 4, 6, and 10

Find the LCM by listing several multiples of eachnumber.

4 You Try

Slide 7

Example

Find the LCM by using prime factors.

a. 9 and 24 b. 16 and 9

c. 36, 42, and 30

5 You Try

Slide 8

Section 2.4 Least Common Multiple and Equivalent Fractions

2. Writing Equivalent Fractions

Slide 9

A fractional amount of a whole may be represented by many fractions.

Expressing a fraction in an equivalent form is important for several reasons. We need this skill to order fractions and to add and subtract fractions.

Example 6 Writing Equivalent Fractions

Slide 10

Write the fraction with the indicated denominator.

11

8 56a. b.

5

6 30

9

4 8

c. d.

Example

Write the fraction with the indicated denominator.

7 You Try

2

3 15 5

6 54

10

3 12

3

8 16

a. b.

c. d.

Slide 11

Section 2.4 Least Common Multiple and Equivalent Fractions

3. Ordering Fractions

Slide 12

To order fractions, our first step is to write the fractions as equivalent fractions with the same denominator, called a common denominator.The least common denominator (LCD) of two fractions is the LCM of the denominators of the fractions. Once we have the same denominators, just compare the numerators. For example the LCD of is 35, because this is the LCM of 5 and 7.

3 4

5 7and

Example 8 Comparing Two Fractions

Slide 13

Example

a. b.

c.

Fill in the blank with <, >, or =.

9 Comparing Two Fractions

Slide 14

3

12 2

81

42

9

5

8

15

24

Example 10 Ranking Fractions in Order from Least to Greatest

Slide 15

Rank the fractions from least to greatest.

Example

a. b.

11 Ranking Fractions in Order from Least to Greatest

Slide 16

5 9 13, ,8 16 32

9 4 5, ,

10 5 6

Example

Rank the fractions from least to greatest.

Fill in the blank with <, >, or =.

12 You Try

a. b.

c.

3

84

20

5 8 3, ,9 15 5

and

Slide 15

4

9

6

30

1. Least Common Multiple2. Writing Equivalent Fractions3. Ordering Fractions

A review of the objectives you are responsible for learning

Slide 18