 # EXAMPLE 1 Comparing Fractions Using the LCD 7 10 3 4

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EXAMPLE 1 Comparing Fractions Using the LCD 7 10 3 4 Julie kayaks a distance of mile, and Seth kayaks mile. Who kayaks the greater distance? Kayaking SOLUTION Find the LCD of the fractions, to compare and Because the LCM of 10 and 4 is 20, the LCD of the fractions is 20. STEP 1 3 4 7 10 Use the LCD to write equivalent fractions. STEP 2 Julie: 7 10 = 7 10 2 = 14 20 Seth: 3 4 = 3 4 5 = 15 20

EXAMPLE 1 Comparing Fractions Using the LCD STEP 3 < Compare the numerators: 14 20 15 3 4 7 10 , so ANSWER Seth kayaks the greater distance. Graph the numbers on a number line. Check : Because 14 20 is to the left of < 15 3 4 7 10 ,

EXAMPLE 2 Standardized Test Practice SOLUTION STEP 1 Find the LCD. The LCD is the LCM of 3, 4, 8, and 6, which is 24.

EXAMPLE 2 Standardized Test Practice STEP 2 Use the LCD to write equivalent fractions. 2 3 = 2 3 8 = 16 24 3 8 = 3 8 = 9 24 1 6 6 = 1 4 = 4 24 3 4 = 3 4 6 = 18 24 STEP 3 Compare the numerators: 4 24 9 16 18 < , so 1 6 3 8 2 4 < The order of the fractions from least to greatest is ANSWER The correct answer is B. 1 6 3 8 2 4 , , and .

EXAMPLE 3 Comparing Fractions Using Approximations Use approximation to tell which portion in each package is greater 13 24 17 36 or . , Notice that the numerator of each fraction is about half the denominator. You know that 12 24 ,so 1 2 = 13 > . < You know that 18 36 ,so 1 2 = 17 .

EXAMPLE 3 Comparing Fractions Using Approximations 13 24 17 36 ANSWER You can conclude that so the package with package with has a greater portion of pencils in it. so the >

GUIDED PRACTICE EXAMPLE 3 Comparing Decimals for Examples 1, 2, and 3 1. Copy and complete the statement using <, >, or =: 5 8 7 12 ? SOLUTION STEP 1 8 Find the LCD of the fractions, to compare and Because the LCM of 8 and 12 is 24, the LCD of the fractions is 24. 7 12 5 Use the LCD to write equivalent fractions. STEP 2 5 8 = 5 8 3 = 15 24 7 12 = 7 12 2 = 14 24

EXAMPLE 3 GUIDED PRACTICE Comparing Decimals for Examples 1, 2, and 3 24 > , 15 14 > 12 8 so 7 5 STEP 3 Compare the numerators:

EXAMPLE 3 GUIDED PRACTICE Comparing Decimals for Examples 1, 2, and 3 2. Order the fractions from least to greatest: 9 14 3 4 5 28 7 , SOLUTION STEP 1 Find the LCD. The LCD is the LCM of 15, 7, 4, and 28, which is 28. STEP 2 Use the LCD to write equivalent fractions. 9 14 = 9 14 2 = 18 28 5 7 = 5 7 4 = 20 28 3 4 = 3 4 7 = 21 28 5 28 = 5 28 1 = 5 28

EXAMPLE 3 GUIDED PRACTICE Comparing Decimals for Examples 1, 2, and 3 STEP 3 Compare the numerators: 5 28 18 20 21 < , so 5 28 9 14 7 3 4 < The order of the fractions from least to greatest is ANSWER 5 28 15 7 3 4 , . 9

GUIDED PRACTICE EXAMPLE 3 Comparing Decimals for Examples 1, 2, and 3 Use approximation to tell which fraction is greater. 8 15 11 24 , Notice that the numerator of each fraction is about half the denominator. You know that 8 16 1 2 = ,so 8 15 > 1 2 . You know that 12 24 1 2 = < ,so 11 24 1 2 . 8 15 ANSWER

GUIDED PRACTICE EXAMPLE 3 Comparing Decimals for Examples 1, 2, and 3 Use approximation to tell which fraction is greater. 16 33 11 18 , Notice that the numerator of each fraction is about half the denominator. You know that 16 32 1 2 = ,so 16 33 < 1 2 . You know that 9 18 1 2 = > ,so 11 18 1 2 . 11 18 ANSWER

GUIDED PRACTICE EXAMPLE 3 Comparing Decimals for Examples 1, 2, and 3 Use approximation to tell which fraction is greater. 23 48 31 56 , Notice that the numerator of each fraction is about half the denominator. You know that 24 48 1 2 = ,so 23 48 < 1 2 . You know that 28 56 1 2 = > ,so 31 56 1 2 . 31 56 ANSWER

GUIDED PRACTICE EXAMPLE 3 Comparing Decimals for Examples 1, 2, and 3 Use approximation to tell which fraction is greater. 16 30 60 130 , Notice that the numerator of each fraction is about half the denominator. You know that 15 30 1 2 = ,so 16 30 > 1 2 . You know that 65 130 1 2 = < ,so 60 130 1 2 . 16 30 ANSWER

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