1. 1.3 2.4 Least Common Multiple and Equivalent Fractions Slide 1
Addition of Real Numbers 1.
Least Common Multiple (LCM) 2.
Writing Equivalent Fractions 3.
Ordering Fractions
Slide 1

2. Least Common Multiple and Equivalent Fractions
2.4
Least Common Multiple and Equivalent Fractions 1.
Least Common Multiple
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.
Slide 2

3. Finding the LCM by Listing Multiples1
Finding the LCM by Listing Multiples
Find the LCM of the given numbers by listing several multiples of each number.
a. 15 and 12 b. 10, 15, and 8
Slide 3

4. Using Prime Factors to Find the LCM of Two Numbers
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.
Slide 4

5. Finding the LCM by Using Prime Factors2
Finding the LCM by Using Prime Factors
Find the LCM.
a. 14 and 12 b. 50 and 24 c. 45, 54, and 50
Slide 5

6. Using the LCM in an Application3
Using the LCM in an Application
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?
Slide 6

7. 4
You Try
Find the LCM by listing several multiples of each
number.
a. 15 and b. 4, 6, and 10
Slide 7

8. Find the LCM by using prime factors.5
You Try
Find the LCM by using prime factors.
9 and b and 9
c. 36, 42, and 30
Slide 8

9. Least Common Multiple and Equivalent Fractions
2.4
Least Common Multiple and Equivalent Fractions 2.
Writing Equivalent Fractions
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.
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10. Writing Equivalent Fractions6
Writing Equivalent Fractions
Write the fraction with the indicated denominator.
a b.
c d.
Slide 10

11. Write the fraction with the indicated denominator.7
You Try
Write the fraction with the indicated denominator.
a b.
c d.
Slide 11

12. Least Common Multiple and Equivalent Fractions
2.4
Least Common Multiple and Equivalent Fractions 3.
Ordering Fractions
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.
Slide 12

13. Comparing Two Fractions8
Comparing Two Fractions
Slide 13

14. Comparing Two Fractions9
Comparing Two Fractions
Fill in the blank with <, >, or =. b. c.
Slide 14

15. Ranking Fractions in Order from Least to Greatest10
Ranking Fractions in Order from Least to Greatest
Rank the fractions from least to greatest.
Slide 15

16. 11
Ranking Fractions in Order from Least to Greatest
a b.
Slide 16

17. Fill in the blank with <, >, or =.12
You Try
Fill in the blank with <, >, or =.
a b.
Rank the fractions from least to greatest. c.
Slide 15

18. A review of the objectives you are responsible for learning 1.
Least Common Multiple 2.
Writing Equivalent Fractions 3.
Ordering Fractions
Slide 18