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Preview Warm Up California Standards Lesson Presentation

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

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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

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Vocabulary least common denominator (LCD)

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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.

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**Multiply 6 and 10 to find a common denominator.**

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 5 10 = 5 6 10 10 50 60 Write the fractions with a common denominator. 7 6 = 7 10 6 6 42 60 50 60 5 6 > 42 60 ,so 7 10 Compare the fractions.

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Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.

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**List multiples of 3 and 5. The LCM is 15.**

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 2 5 3 5 = 2 3 5 5 10 15 Write the fractions with a common denominator. 4 3 = 4 5 3 3 12 15 10 15 2 3 < 12 15 ,so 4 5 Compare the fractions.

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**Multiply 2 and 5 to find a common denominator.**

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 1 5 2 5 = 1 2 5 5 5 10 Write the fractions with a common denominator. 2 2 = 2 5 2 2 4 10 5 10 1 2 > 4 10 ,so 2 5 Compare the fractions.

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**List multiples of 3 and 4. The LCM is 12.**

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

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**Additional Example 2: Comparing by Using Decimals**

Compare. Write <, >, or =. 2 9 _ 2 7 _ A < 5 = 5.2 and 5 = … 2 9 _ 2 7 Write the fractions as decimals. 5.2 < …, so 5 < 5 _ 2 9 2 7 Compare the decimals.

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**Additional Example 2: Comparing by Using Decimals**

Compare. Write <, >, or =. 2 5 _ B. – – < – = –0.4 2 5 _ Write - as decimal. 2 5 _ –0.44 < –0.4, so –0.44 < – 2 5 _ Compare the decimals. 1 9 _ C > 1 9 _ = 0.1 Write as decimal. 1 9 _ 0.1 > 0.1, so > 0.1 1 9 _ Compare the decimals.

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**_ _ _ _ Write the fractions as decimals. Compare the decimals.**

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

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**_ _ _ _ _ _ _ _ Write – as decimal. Compare the decimals.**

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

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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.

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**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. __ Place the numbers on a number line and read them from left to right. 14 4 __ –3.4 6.0 –2.5 –4 –3 –2 – 14 4 The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. __

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**__ Check It Out! Example 3 7 2 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 __ –3.9 3.0 –2.2 –5 –4 –3 –2 – The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and .

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**< > > Lesson Quiz Compare. Write <, >, or =. 1 4 1 3 1.**

2 9 > 2. – –0.29 6 7 7 8 3. – –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 m. Which jump was the longest? 8 9 9 11 second jump

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