1. PRE-ALGEBRA

2. Lesson 5-1 Warm-Up

3. PRE-ALGEBRA “Comparing and Ordering Rational Numbers” (5-1) What is the a “multiple”? What is the the “least common multiple” or LCM? How do you find the LCM? Multiple: The multiple of a number is the product of that number and any nonzero number (when you count by a number, you are finding its multiples) Example: Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36,…. Example: Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54,…. Least Common Multiple (LCM): the smallest multiple shared by all of the numbers Example: Common Multiples of 4 are 6 are 12, 24, and 36. The smallest multiple of both numbers, or Least Common Multiple (LCM) is 12. To find the LCM: 1. list the multiples of both numbers until you find the first one that they share in common, or 2. multiply the greatest power of the factors the numbers. Example: Find the LCM of 18, 27, and 36. Method 1: List the multiples of each number until you find a common one. Multiples of 18 are 18, 36, 54, 72, 90, 108,…. Multiples of 27 are 27, 54, 81, 108,… Multiples of 36 are 36, 72, 108,…. The LCM of 18, 27, and 36 is 108. Find the multiple of each number. Stop when you find a multiple the numbers share in common.

4. PRE-ALGEBRA “Comparing and Ordering Rational Numbers” (5-1) Method 2: Multiply the greatest power of all factors together. Example: Find the LCM of 18, 27, and 36. 18 = 3 3 2 = 3 2 2 27 = 3 3 3 = 3 3 36 = 3 3 2 2 = 3 2 2 2 3 3 2 2 = 27 4 = 108 Example: Find the LCM of 6a 2 and 18a 3. LCM of 6a 2 and 18a 3 is 18a 3. Create a factor tree number to find the prime factors of each number. Write each number in prime factorization. form Multiply the greatest powers of all factors together.

5. PRE-ALGEBRA Today, the school’s baseball and soccer teams had games. The baseball team plays every 7 days. The soccer team plays every 3 days. When will the teams have games on the same day again? 7, 14, 21, 28, 35, 42,...List the multiples of 7. 3, 6, 9, 12, 15, 18, 21,...List the multiples of 3. The LCM is 21. In 21 days both teams will have games again. Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

6. PRE-ALGEBRA Find the LCM of 16 and 36. = 144Multiply. 16 = 2 4 36 = 2 2 3 2 Write the prime factorizations. The LCM of 16 and 36 is 144. LCM = 2 4 3 2 Use the greatest power of each factor. Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

7. PRE-ALGEBRA Find the LCM of 5a 4 and 15a. 5a 4 = 5 a 4 15a = 3 5 aWrite the prime factorizations. = 15a 4 Multiply. The LCM of 5a 4 and 15a is 15a 4. LCM = 3 5 a 4 Use the greatest power of each factor. Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

8. PRE-ALGEBRA “Comparing and Ordering Rational Numbers” (5-1) How do you compare fractions? To compare fractions, you can: 1. use a number line (numbers to the right are greater than numbers to the left), or 2. compare the numerators (number of parts) if the denominator (size of the parts) are equal. So, if the denominators aren’t the same, you need to change one or more of the fractions into equivalent fractions with a common denominator. Method 1: Use a number line. Example: Compare and. is on the left of, so . Method 1: Compare the numerators. Example: Compare and. 3 4 = 12Multiply the denominators together to find a common denominator Write equivalent fractions with a denominator of 12 and compare the numerators (Hint: Notice that you multiply the each fraction by the other fractions denominator) Since , then . 2 3 4 2 4 = 8_ 3 4 = 12 3 3 = 9_ 4 3 = 12 9 12 8 12 3 4 2 3 - 1 2 - 1 10 - 1 2 - 1 10 - 1 10 - 1 2

9. PRE-ALGEBRA Graph and compare the fractions in each pair. is on the left, so <. 3838 3838 7878 b. – 1313, – 1616 is on the right, so >.– 1616 – 1616 – 1313 a. 7878 3838, 3838 7878 – 1313 – 1616 Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

10. PRE-ALGEBRA “Comparing and Ordering Rational Numbers” (5-1) What is the “least common denominator” (LCD)? Least Common Denominator (LCD): the LCM of two or more denominators (in other words, the smallest common denominator) Example: List the multiples of each denominator until you find a multiple that is shared by both numbers (LCM). LCM = 36 Rewrite the fractions into equivalent fractions with a denominator of 36 (The LCD is 36). Then, compare the numerators. Since , then . 16 36 15 36 4949 5 12

11. PRE-ALGEBRA The softball team won of its games and the hockey team won of its games. Which team won the greater fraction of its games? 6767 7979 Step 1 Find the LCM of 7 and 9. 7 = 7 and 9 = 3 2 LCM = 7 3 2 = 63 Step 2 Write equivalent fractions with a denominator of 63. 6 9 7 9 7 9 7 = 54 63 49 63 = Step 3 Compare the fractions. 54 63 49 63 6767 7979 > >, so The softball team won the greater fraction of its games. Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

12. PRE-ALGEBRA Order,, and from least to greatest. 3737 1414 2323 3737 1414 2323 3 12 7 12 1 21 4 21 2 28 3 28 36 84 21 84 56 84 = = = = = = The LCM of 7, 4, and 3 is 84. Use 84 as the common denominator. 21 84 36 84 56 84 1414 3737 2323 <<, so<<. Comparing and Ordering Rational Numbers LESSON 5-1 Additional Examples

13. PRE-ALGEBRA Find the LCM of each pair of numbers. 1.8, 62.12, 16 3.Compare and order, –, and – from least to greatest. 3 16 8 10 3 16 2448 8 10 –– << 3 16 3 16 Lesson Quiz Comparing and Ordering Rational Numbers LESSON 5-1