Chapter 4: Summary Definition/Procedure Example 4.1 Adding and Subtracting Like Fractions Adding Like Fractions To add like fractions: 1) Add the numerators. 2) Use the denominator of the like fractions as the denominator of the sum. 3) Write the answer in lowest terms. (p. 224) 4 11 3 11 4 3 11 7 11 The answer is in lowest terms. Subtracting Like Fractions To subtract like fractions: 1) Subtract the numerators. 2) Use the denominator of the like fractions as the denominator of the difference. 3) Write the answer in lowest terms. (p. 226) 9 10 3 10 9 3 10 6 10 3 5 Write the answer in lowest terms. The least common multiple, or LCM, of a group of natural numbers is the smallest natural number divisible by each number in the group. (p. 230) The LCM of 4 and 5 is 20 because 20 is the smallest number divisible by both 4 and 5. Make a List of Multiples to Find the LCM To fi nd the LCM of a group of numbers, begin by listing some multiples of each number. Then, the least common multiple (LCM) is the smallest number that appears on each list. (p. 230) Find the least common multiple of 6 and 8. List some multiples of 6 and 8. Multiples of 6: 6, 12, 18, 24, 30, 36, … Multiples of 8: 8, 16, 24, 32, 40, 48, … The LCM of 6 and 8 is 24. Find the LCM by Inspection If the numbers are easy to work with, we should be able to fi nd the LCM without making a list or writing anything on paper. (p. 231) Find the least common multiple of 2 and 10. Ask yourself, “What is the smallest number that is divisible by both 2 and 10?” That number is 10. The LCM of 2 and 10 is 10. Make a List of Multiples of the Largest Number to Find the LCM We can also fi nd the LCM by fi rst fi nding multiples of the larger number and then fi nding the smallest of those that is divisible by the other numbers in the group. (p. 231) Find the least common multiple of 5, 6, and 20 by fi rst making a list of multiples of the largest number. The largest number in the group is 20, so make a list of some multiples of 20. Multiples of 20: 20, 40, 60, 80, 100, … Are any of the numbers on the list divisible by 5 and 6? Yes! 60 is divisible by 5 and 6. The LCM of 5, 6, and 20 is 60. 4.2 Least Common Multiples 280 CHAPTER 4 Adding and Subtracting Fractions www.mhhe.com/messersmith
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