Comparing and Ordering Rational Numbers 3-10 Comparing and Ordering Rational Numbers Course 2 Warm Up Problem of the Day Lesson Presentation

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Warm Up Write each mixed number as an improper fraction. 1. 1 3. 1 3 4 7 4 7 8 23 8 2. 2 5 6 11 6 1 12 97 12 4. 8

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Problem of the Day Hot dogs are sold in packs of 6. Buns are sold in bags of 8. What is the least number of hot dog packages and the least number of bun packages you would need to buy in order to have the same number of hot dogs and buns? 4 packages of hot dogs and 3 packages of buns

Learn to compare and order fractions and decimals. Course 2 3-10 Comparing and Ordering Rational Numbers Learn to compare and order fractions and decimals.

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers 7 9 2 9 Which is greater, or ? When two fractions have the same denominator, just compare the numerators. 7 9 2 9 > because 7 > 2. 7 9 = 2 9 =

Additional Example 1A: Comparing Fractions Course 2 3-10 Comparing and Ordering Rational Numbers Additional Example 1A: Comparing Fractions Compare the fractions. Write < or >. 7 9 5 8 A. Both fractions can be written with a denominator of 72. 7 9 7 · 8 9 · 8 56 72 Write as fractions with common denominators. = = 5 8 5 · 9 8 · 9 45 72 = = 56 72 > 45 , and so . 7 9 > 5 8

Additional Example 1B: Comparing Fractions Course 2 3-10 Comparing and Ordering Rational Numbers Additional Example 1B: Comparing Fractions Compare the fractions. Write < or >. 2 5 B. 3 7 – – Both fractions can be written with a denominator of 35. 2 5 –2 · 7 5 · 7 –14 35 Write as fractions with common denominators. Put the negative signs in the numerators. – = = 3 7 –3 · 5 7 · 5 –15 35 – = = 14 35 15 35 2 5 3 7 – > – , and so – > . –

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Try This: Example 1A Compare the fractions. Write < or >. 5 6 7 8 A. Both fractions can be written with a denominator of 48. 5 6 5 · 8 6 · 8 40 48 Write as fractions with common denominators. = = 7 8 7 · 6 8 · 6 42 48 = = 40 48 < 42 , and so . 5 6 < 7 8

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Try This: Example 1B Compare the fractions. Write < or >. 6 8 B. 5 7 – – Both fractions can be written with a denominator of 56. 6 8 –6 · 7 8 · 7 –42 56 Write as fractions with common denominators. Put the negative signs in the numerators. – = = 5 7 –5 · 8 7 · 8 –40 56 – = = 42 56 40 56 6 8 5 7 – < – , and so – < . –

Course 2 3-10 Comparing and Ordering Rational Numbers To compare decimals, line up the decimal points and compare digits from left to right until you find the place where the digits are different.

Additional Example 2: Comparing Decimals Course 2 3-10 Comparing and Ordering Rational Numbers Additional Example 2: Comparing Decimals Compare the decimals. Write < or >. 0.427 0.425 0.427 7 Line up the decimal points. The tenths and hundredths are the same. 0.425 5 Compare the thousandths: 7 > 5. 0.427 > 0.425

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Try This: Example 2 Compare the decimals. Write < or >. 0.535 0.538 0.535 5 Line up the decimal points. The tenths and hundredths are the same. 0.538 8 Compare the thousandths: 5 < 8. 0.535 < 0.538

Additional Example 3: Ordering Fractions and Decimals Course 2 3-10 Comparing and Ordering Rational Numbers Additional Example 3: Ordering Fractions and Decimals Order the numbers from least to greatest. 4 5 , 0.93, and 0.9 Write as decimals with the same number of places. 4 5 = 0.80 0.93 = 0.93 0.9 = 0.90 Graph the numbers on a number line. 0.93 0 0.2 0.4 0.6 0.8 1

Additional Example 3 Continued Course 2 3-10 Comparing and Ordering Rational Numbers Additional Example 3 Continued Order the numbers from least to greatest. 4 5 , 0.93, and 0.9 The values on a number line increase as we move from left to right. 0.80 < 0.90 < 0.93 Place the decimals in order. 4 5 , 0.9, 0.93 0.93 0 0.2 0.4 0.6 0.8 1

Comparing and Ordering Rational Numbers Course 2 3-10 Comparing and Ordering Rational Numbers Try This: Example 3 Order the numbers from least to greatest. 3 5 , 0.84, and 0.7 Write as decimals with the same number of places. 3 5 = 0.60 0.84 = 0.84 0.7 = 0.70 Graph the numbers on a number line. 0.84 0 0.2 0.4 0.6 0.8 1

Try This: Example 3 Continued Course 2 3-10 Comparing and Ordering Rational Numbers Try This: Example 3 Continued Order the numbers from least to greatest. 3 5 , 0.84, and 0.7 The values on a number line increase as we move from left to right. 0.60 < 0.70 < 0.84 Place the decimals in order. 3 5 , 0.7, 0.84 0.84 0 0.2 0.4 0.6 0.8 1

Insert Lesson Title Here Course 2 3-10 Comparing and Ordering Rational Numbers Insert Lesson Title Here Lesson Quiz: Part 1 Choose the greater number. 1. Place the numbers in order from least to greatest 3. 0.3, 0.32, 0.312 3 7 4 10 3 7 5 8 2 3 2 3 or 2. or 0.3, 0.312, 0.32 4. 5 6 0.8, 0.826, 5 6 , 0.8, 0.826

Insert Lesson Title Here Course 2 3-10 Comparing and Ordering Rational Numbers Insert Lesson Title Here Lesson Quiz: Part 2 5. Dana’s cross-country team is getting ready for a big meet. On Monday they ran 3.7 miles, on Tuesday they ran 3 miles, and on Wednesday they ran miles. On which day did they run the greatest distance? 3 8 11 4 Monday