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

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

Finding the LCM by Listing Multiples 1 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

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

Finding the LCM by Using Prime Factors 2 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

Using the LCM in an Application 3 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

4 You Try Find the LCM by listing several multiples of each number. a. 15 and 25 b. 4, 6, and 10 Slide 7

Find the LCM by using prime factors. 5 You Try Find the LCM by using prime factors. 9 and 24 b. 16 and 9 c. 36, 42, and 30 Slide 8

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. Slide 9

Writing Equivalent Fractions 6 Writing Equivalent Fractions Write the fraction with the indicated denominator. a. b. c. d. Slide 10

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

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

Comparing Two Fractions 8 Comparing Two Fractions Slide 13

Comparing Two Fractions 9 Comparing Two Fractions Fill in the blank with <, >, or =. b. c. Slide 14

Ranking Fractions in Order from Least to Greatest 10 Ranking Fractions in Order from Least to Greatest Rank the fractions from least to greatest. Slide 15

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

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

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