Comparing and Ordering 2 11 Rational Numbers Warm

Comparing and Ordering 2 -11 Rational Numbers Warm Up Lesson Presentation Lesson Quizzes

Comparing and Ordering 2 -11 Rational Numbers Warm Up Write each mixed number as an improper fraction. 1. 1 3 7 4 2. 2 7 8 23 8 3. 1 5 6 11 6 1 4. 812 97 12 4

Comparing and Ordering 2 -11 Rational Numbers Learn to compare and order fractions and decimals.

Comparing and Ordering 2 -11 Rational Numbers Vocabulary rational number

Comparing and Ordering 2 -11 Rational Numbers 7 2 Which is greater, 9 or 9 ? When two fractions have the same denominator, just compare the numerators. 7 > 2 because 7 > 2. 9 9 =7 9 2 =9

Comparing and Ordering 2 -11 Rational Numbers Additional Example 1 A: Comparing Fractions Compare the fractions. Write < or >. 7 9 5 8 The LCM of the denominators 9 and 8 is 72. 7 =7· 8 56 = 9· 8 9 72 5 =5· 9 45 = 8· 9 8 72 5 56 45 , and so 7 > >. 9 8 72 72 Write equivalent fractions with 72 as the denominator. Compare the numerators.

Comparing and Ordering 2 -11 Rational Numbers Additional Example 1 B: Comparing Fractions Compare the fractions. Write < or >. – 2 5 – 3 7 Both fractions can be written with a denominator of 35. – 2 · 7 – 14 2 = – = 5 5· 7 35 – 15 3 = – 3 · 5 – = 7 7· 5 35 Write equivalent fractions with 35 as the denominator. Put the negative signs in the numerators. 3 – 14 > – 15 , and so – 2 > –. 5 7 35 35

Comparing and Ordering 2 -11 Rational Numbers Check It Out: Example 1 A Compare the fractions. Write < or >. 5 6 7 8 The LCM of the denominators 6 and 8 is 48. 5 =5· 8 40 = 6· 8 6 48 7 =7· 6 42 = 8· 6 8 48 7 40 42 , and so 5 < <. 6 8 48 48 Write equivalent fractions with 48 as the denominator. Compare the numerators.

Comparing and Ordering 2 -11 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.

Comparing and Ordering 2 -11 Rational Numbers Additional Example 2 A: Comparing Decimals Compare the decimals. Write < or >. 0. 427 7 0. 425 5 0. 425 Line up the decimal points. The tenths and hundredths are the same. Compare thousandths: 7 > 5. Since 0. 007 > 0. 005, 0. 427 > 0. 425.

Comparing and Ordering 2 -11 Rational Numbers Additional Example 2 B: Comparing Decimals Compare the decimals. Write < or >. 0. 734 _ 3 0. 73 = 0. 733… 0. 734 4 Line up the decimal points. The tenths and hundredths are the same. Compare thousandths: 3 < 4. Since 0. 003 is < 0. 004, 0. 73 < 0. 734.

Comparing and Ordering 2 -11 Rational Numbers A rational number is a number that can be written as a fraction with integers for its numerator and denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.

Comparing and Ordering 2 -11 Rational Numbers Remember! The values on a number line increase as you move from left to right.

Comparing and Ordering 2 -11 Rational Numbers Additional Example 3: Ordering Fractions and Decimals Order 4 , 0. 93, and 0. 9 from least to greatest. 5 Write as decimals with the same number of places. 4 = 0. 80 0. 93 = 0. 93 0. 9 = 0. 90 5 Graph the numbers on a number line. 0. 93 0 0. 2 0. 4 0. 6 0. 8 1 0. 80 < 0. 93 Compare the decimals in order. From least to greatest, the numbers are 4 , 0. 93. 5

Comparing and Ordering 2 -11 Rational Numbers Check It Out: Example 3 Order 3 , 0. 84, and 0. 7 from least to greatest. 5 Write as decimals with the same number of places. 3 = 0. 60 5 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 0. 60 < 0. 70 < 0. 84 Compare the decimals in order. From least to greatest, the numbers are 3, 0. 7, 0. 84. 5

Comparing and Ordering 2 -11 Rational Numbers Lesson Quizzes Standard Lesson Quiz

Comparing and Ordering 2 -11 Rational Numbers Lesson Quiz Compare the fractions. Write > or <. 3 and 4 > 2. 5 and 2 < 1. 7 10 8 3 Compare the decimals. Write < or >. 3. 0. 32 and 0. 312 > 4. Order 5 , 0. 826 from least to greatest. 6 0. 8, 0. 826, 5 6