* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Powerpoint of Notes
Survey
Document related concepts
History of mathematics wikipedia , lookup
History of logarithms wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Location arithmetic wikipedia , lookup
Approximations of π wikipedia , lookup
Large numbers wikipedia , lookup
Real number wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Continued fraction wikipedia , lookup
Transcript
LESSON 4-5 Warm Up ALGEBRA READINESS LESSON 4-4 Warm Up ALGEBRA READINESS “Comparing and Ordering Rational Numbers” (4-5) How do you order rational numbers? To order rational numbers, put them all into decimal form. Then, put the decimals in order by: 1. graphing them on a number line, or 2. changing them to decimal form and lining the numbers up vertically by the decimal points, adding zeroes in blank spaces, and comparing the place values from the left (largest place values) to the right (smallest place values) [In the result of a tie, go to the next largest place value until there is no longer a tie]. Example: Write each fraction as a decimal by dividing the bottom into the top. Graph each decimal on a number line. Change the decimals back to their original form. ALGEBRA READINESS Comparing and Ordering Rational Numbers LESSON 4-5 Additional Examples Order –0.175, 2 , – 5 , 1.7, –0.95 from least to greatest. 3 8 Write each fraction as a decimal. 2 3 – 0.667 5 = –0.625 8 Then graph each decimal on a number line. The number line shows that –0.95 < –0.625 < –0.175 < 0.667 < 1.7 So, –0.95 < – 5 < –0.175 < 2 < 1.7. 8 3 Turn the decimals that were changed back into fractions (original form). ALGEBRA READINESS “Comparing and Ordering Rational Numbers” (4-5) How do you compare fractions? To compare fractions, you can 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: One way you find a common denominator is to multiply the two original denominators. 2 3 Example: Recipe A uses 3 cups sugar and Recipe B uses 4 cups sugar. Which recipe uses more sugar? 3 • 4 = 12 2 • 4 = 8_ 3 • 4 = 12 3 • 3 = 9_ 4 • 3 = 12 Since Multiply the denominators together to find a common denominator Write equivalent fractions with a denominator of 12 (Hint: Notice that you multiply the each fraction by the other fractions denominator) 8 9 , then 3 2 , so Recipe B uses more sugar. 12 12 4 3 ALGEBRA READINESS “Comparing and Ordering Rational Numbers” (4-5) Method 2: Another way to find a common denominator is to use the Least Common Denominator (LCD). The advantage of this method is that you will not need to reduce the answer later. What is the “least common multiple” (LCM) and “least common denominator” (LCD)? Least Common Multiple (LCM): the smallest multiple shared by all of the numbers 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. 5 Since 16 15 , then 4 ,. 12 36 36 9 ALGEBRA READINESS Comparing and Ordering Rational Numbers LESSON 4-5 Additional Examples The Eagles won 7 out of 11 games, while the Seals won 8 out of 12 games. Which team has the better record? A common denominator of 11 and 12 is 11 • 12, or 132. 7 7 • 12 84 Eagles: 11 = 11 • 12 = 132 8 • 11 88 8 Seals: 12 = 12 • 11 = 132 Because Write equivalent fractions with a denominator of 132. 84 88 7 > , 8 > . The Seals have the better record. 132 12 132 11 ALGEBRA READINESS Comparing and Ordering Rational Numbers LESSON 4-5 Additional Examples Compare 5 7 and 12 using their LCD. Use <, =, >. 18 List multiples of each denominator to find their LCD. Multiples of 18: 18, 36 Multiples of 12: 12, 24, 36 Stop when you find a multiple that is shared by both numbers. The LCM of 18 and 12 is 36. So the LCD of the fractions is 36. 14 7 7•2 = 36 = 18 18 • 2 5 5•3 15 = = 12 12 • 3 36 Use the LCD to write equivalent fractions. 15 14 so 5 > 7 . > , 36 36 12 18 ALGEBRA READINESS Comparing and Ordering Rational Numbers LESSON 4-5 Lesson Quiz Compare. Use <, >, or =. 1. 5 < 3. 15 = 12 50 8 15 2. 4 > 36 120 4. 7 = 0.35 5 20 8 11 5. Order 0.17, 1 , –0.3, 0, and – 1 from least to greatest. 5 4 –0.3, – 1 , 0, 0.17, 1 4 5 6. A survey found that 75 out of 125 men and 88 out of 136 women prefer comedy films over action films. Which group prefers comedy over action films more? women ALGEBRA READINESS