2. Warm Up Write each fraction as a decimal. 1. 1 3 2. 45 3. 4. 0.8 0.75 3 4 23 0.3 0.6
3. 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
5. 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.
6. Additional Example 1A: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. Multiply 6 and 10 to find a common denominator. 5 6 7 10 Write the fractions with a common denominator. Compare the fractions. Method 1: Multiply to find a common denominator. 6 10 = 60 > 5 10 6 10 = 5 6 10 10 = 50 60 7 6 10 6 = 7 10 6 6 = 42 60 50 60 5 6 > 42 60 ,so 7 10 >
7. Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.
8. Additional Example 1B: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. List multiples of 3 and 5. The LCM is 15. 2 3 4 5 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 = 2 3 5 5 = 10 15 4 3 5 3 = 4 5 3 3 = 12 15 10 15 2 3 < 12 15 ,so 4 5 <
9. Check It Out! Example 1A Compare. Write <, >, or =. Multiply 2 and 5 to find a common denominator. 1 2 2 5 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 = 1 2 5 5 = 5 10 2 2 5 2 = 2 5 2 2 = 4 10 5 10 1 2 > 4 10 ,so 2 5 >
10. Check It Out! Example 1B Compare. Write <, >, or =. List multiples of 3 and 4. The LCM is 12. 2 3 3 4 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 = 2 3 4 4 = 8 12 3 3 4 3 = 3 4 3 3 = 9 12 8 12 2 3 < 9 12 ,so 3 4 <
11. A. 5 5 Additional Example 2: Comparing by Using Decimals Compare. Write <, >, or =. 2 7 _ Write the fractions as decimals. Compare the decimals. < 2 9 _ 5 = 5.2 and 5 = 5.285714… 2 9 _ 2 7 _ _ 5.2 < 5.285714…, so 5 < 5 _ 2 9 _ 2 7 _
12. B. –0.44 – Additional Example 2: Comparing by Using Decimals Compare. Write <, >, or =. Compare the decimals. < C. 0.1 Compare the decimals. > 2 5 _ – = –0.4 2 5 _ – 0.44 < –0.4, so –0.44 < – 2 5 _ Write - as decimal. 2 5 _ 1 9 _ Write as decimal. 1 9 _ 1 9 _ = 0.1 0.1 > 0.1, so > 0.1 1 9 _
13. A. 4 4 Check It Out! Example 2 Compare. Write <, >, or =. 3 5 _ Write the fractions as decimals. Compare the decimals. < 2 9 _ 4 = 4.2 and 4 = 4.6 2 9 _ 3 5 _ _ 4.2 < 4.6, so 4 < 4 2 9 _ 3 5 _
14. B. –0.80 – Check It Out! Example 2 Compare. Write <, >, or =. Compare the decimals. = C. 0.8 Compare the decimals. > 4 5 _ – = –0.8 4 5 _ – 0.80 = –0.8, so –0.80 = – 4 5 _ Write – as decimal. 4 5 _ 5 6 _ Write as decimal. 5 6 _ 0.83 > 0.8, so > 0.8 5 6 _ _ 5 6 _ = 0.83
15. 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.
16. Additional Example 3: Social Studies Application – 2.5 6.0 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 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. __
17. Check It Out! Example 3 – 2.2 3.0 The numbers , 3.0, –2.2, and –3.9 represent the percent changes in populations for four states. List these numbers in order from least to greatest. 7 2 __ – 5 –4 –3 –2 –1 0 1 2 3 4 5 Place the numbers on a number line and read them from left to right. – 3.9 7 2 __ The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and . 7 2
18. Lesson Quiz Compare. Write <, >, or =. 1. 2. – –0.29 4. Sarah competed in a long-jump contest. Her first jump was 3.75 m, her second jump was 3 m, and her third jump was 3 m. Which jump was the longest? 3. –2 –2 > > 1 3 second jump < 1 4 2 9 6 7 7 8 8 9 9 11
