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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 0.3. 0.6. Warm Up Write each fraction as a decimal. 1 3. 45. 2. 0.8. 1. 3 4. 23. 3. 0.75. 4. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 0.3 0.6 Warm Up Write each fraction as a decimal. 1 3 45 2. 0.8 1. 3 4 23 3. 0.75 4.

  3. California Standards 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

  4. Vocabulary least common denominator (LCD)

  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. 50 60 42 60 10 10 6 6 7 10 5 6 7  6 10  6 5  10 6  10   = = = = 50 60 42 60 5 6 7 10 > ,so > Additional Example 1A: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. 5 6 7 10 > Method 1: Multiply to find a common denominator. Multiply 6 and 10 to find a common denominator. 6  10 = 60 Write the fractions with a common denominator. Compare the fractions.

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

  9. 5 10 4 10 5 5 2 2 2 5 1 2 2  2 5  2 1  5 2  5   = = = = 5 10 4 10 1 2 2 5 > ,so > Check It Out! Example 1A Compare. Write <, >, or =. 1 2 2 5 > Method 1: Multiply to find a common denominator. Multiply 2 and 5 to find a common denominator. 2  5 = 10 Write the fractions with a common denominator. Compare the fractions.

  10. 8 12 9 12 4 4 3 3 3 4 2 3 3  3 4  3 2  4 3  4   = = = = 8 12 9 12 2 3 3 4 < ,so < Check It Out! Example 1B Compare. Write <, >, or =. 2 3 3 4 > Method 2: Find the least common denominator. List multiples of 3 and 4. The LCM is 12. 3; 3, 6, 9, 12, … 4; 4, 8, 12… Write the fractions with a common denominator. Compare the fractions.

  11. _ _ _ _ _ 2 9 2 9 2 7 2 7 2 9 _ 5 = 5.2 and 5 = 5.285714… _ 5.2 < 5.285714…, so 5 < 5 Additional Example 2: Comparing by Using Decimals Compare. Write <, >, or =. _ 2 7 < A. 5 5 Write the fractions as decimals. Compare the decimals.

  12. _ _ _ _ _ _ _ _ 1 9 2 5 2 5 1 9 2 5 2 5 1 9 1 9 Write - as decimal. Write as decimal. – = –0.4 –0.44 < –0.4, so –0.44 < – = 0.1 0.1 > 0.1, so > 0.1 Additional Example 2: Comparing by Using Decimals Compare. Write <, >, or =. < B. –0.44 – Compare the decimals. C. 0.1 > Compare the decimals.

  13. _ _ _ _ _ 2 9 3 5 3 5 2 9 2 9 _ 4 = 4.2 and 4 = 4.6 4.2 < 4.6, so 4 < 4 Check It Out! Example 2 Compare. Write <, >, or =. _ 3 5 < A. 4 4 Write the fractions as decimals. Compare the decimals.

  14. _ _ _ _ _ _ _ _ 5 6 4 5 4 5 5 6 5 6 5 6 4 5 4 5 Write – as decimal. Write as decimal. – = –0.8 –0.80 = –0.8, so –0.80 = – = 0.83 _ 0.83 > 0.8, so > 0.8 Check It Out! Example 2 Compare. Write <, >, or =. = B. –0.80 – Compare the decimals. C. 0.8 > Compare the decimals.

  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. 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. Place the numbers on a number line and read them from left to right. The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. 14 4 __ 14 4 __ –3.4   –4 –3 –2 –1 0 1 2 3 4 5 6 __ 14 4 Additional Example 3: Social Studies Application 6.0  –2.5 

  17. 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. Place the numbers on a number line and read them from left to right. 7 2 __ 7 2 __ –3.9   –5 –4 –3 –2 –1 0 1 2 3 4 5 The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and . 7 2 Check It Out! Example 3 3.0  –2.2 

  18. 9 11 7 8 6 7 2 9 1 4 8 9 < Lesson Quiz Compare. Write <, >, or =. 1 3 1. > 2. – –0.29 > 3. –2 –2 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? second jump

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