1. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general. Also covered: NS1.3 California Standards

2. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers least common denominator (LCD) Vocabulary

3. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers To compare fractions with unlike denominators, you can find a common denominator. This could be the least common denominator (LCD), which is the least common multiple of the denominators.

4. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.

5. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Additional Example 1B: Comparing Fractions by Finding a Common Denominator Compare. Write, or =. List multiples of 3 and 5. The LCM is 15. 2323 4545 Write the fractions with a common denominator. Compare the fractions. Method 2: Find the least common denominator. 3; 3, 6, 9, 12, 15… 5; 5, 10, 15 2  5 3  5 = 2323  5 = 10 15 4  3 5  3 = 4545  3 = 12 15 10 15 2323 < 12 15,so 4545 < >

6. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Check It Out! Example 1A Compare. Write, or =. Multiply 2 and 5 to find a common denominator. 1212 2525 Write the fractions with a common denominator. Compare the fractions. Method 1: Multiply to find a common denominator. 2  5 = 10 1  5 2  5 = 1212  5 = 5 10 2  2 5  2 = 2525  2 = 4 10 5 10 1212 > 4 10,so 2525 > >

7. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Check It Out! Example 1B Compare. Write, or =. List multiples of 3 and 4. The LCM is 12. 2323 3434 Write the fractions with a common denominator. Compare the fractions. Method 2: Find the least common denominator. 3; 3, 6, 9, 12, … 4; 4, 8, 12… 2  4 3  4 = 2323  4 = 8 12 3  3 4  3 = 3434  3 = 9 12 8 12 2323 < 9 12,so 3434 < >

8. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers A. 5 5 Additional Example 2: Comparing by Using Decimals Compare. Write, or =. 2929 _ 2727 _ Write the fractions as decimals. 5 = 5.2 and 5 = 5.285714… 2929 _ 2727 _ _ 5.2 < 5.285714…, so 5 < 5 _ 2929 _ 2727 _ Compare the decimals. <

9. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers B. –0.44 – Additional Example 2: Comparing by Using Decimals Compare. Write, or =. 2525 _ – = –0.4 2525 _ –0.44 < –0.4, so –0.44 < – 2525 _ Compare the decimals. < Write - as decimal. 2525 _ C. 0.1 1919 _ Compare the decimals. Write as decimal. 1919 _ > 1919 _ = 0.1 0.1 > 0.1, so > 0.1 1919 _

10. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers A. 4 4 Check It Out! Example 2 Compare. Write, or =. 2929 _ 3535 _ Write the fractions as decimals. 4 = 4.2 and 4 = 4.6 2929 _ 3535 _ _ Compare the decimals. < 4.2 < 4.6, so 4 < 4 2929 _ 3535 _

11. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers B. –0.80 – Check It Out! Example 2 Compare. Write, or =. 4545 _ – = –0.8 4545 _ –0.80 = –0.8, so –0.80 = – 4545 _ Compare the decimals. = Write – as decimal. 4545 _ C. 0.8 5656 _ Compare the decimals. Write as decimal. 5656 _ > 0.83 > 0.8, so > 0.8 5656 _ _ 5656 _ = 0.83

12. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers To order fractions and decimals, you can either write them all in the same form and then compare them, or place them on a number line. Recall that numbers increase in value as you move from left to right along a number line.

13. Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Additional Example 3: Social Studies Application The numbers, –3.4, 6.0, and –2.5 represent the percent changes in populations for four states. List these numbers in order from least to greatest. 14 4 __ –4 –3 –2 –1 0 1 2 3 4 5 6 –2.5  6.0  Place the numbers on a number line and read them from left to right.  –3.4  14 4 __ 14 4 The percent changes in population from least to greatest are –3.4, –2.5,, and 6.0. __