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California Standards NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. Also covered: NS2.4
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VOCABULARY CARD Rational Number
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7 9 2 9 Which is greater, or ? To compare fractions with the same denominator, just compare the numerators. 7 9 = 7 9 2 9 > because 7 > 2. 2 9 =
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One way to compare fractions with unlike denominators is to use models
One way to compare fractions with unlike denominators is to use models. For example, the models show that < . 3 8 1 2 3 8 = 1 2 = Another way to compare fractions with unlike denominators is to first write equivalent fractions with common denominators. Then compare the fractions.
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Teacher Example 1A: Comparing Fractions
Compare the fractions. Write < or >. 7 9 5 8 The LCM of the denominators 9 and 8 is 72. 7 9 7 8 9 8 56 72 = Write equivalent fractions with 72 as the denominator. = 5 8 5 9 8 9 45 72 = = Compare the numerators. 56 72 > 45 , and so 7 9 > 5 8
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Teacher Example 1B: Comparing Fractions
Compare the fractions. Write < or >. 2 5 3 7 – – Both fractions can be written with a denominator of 35. 2 5 –2 7 5 7 –14 35 Write equivalent fractions with 35 as the denominator. Put the negative signs in the numerators. – = = 3 7 –3 5 7 5 –15 35 – = = 14 35 15 35 2 5 3 7 – > – , and so – > –
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A fraction less than 0, such as - , can be
written as - , , or . Helpful Hint! 2 5 -2 5
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Student Practice 1A: Compare the fractions. Write < or >. 5 6 7 8 The LCM of the denominators 6 and 8 is 48. 5 6 40 48 Write equivalent fractions with 48 as the denominator. 5 8 6 8 = = 7 8 7 6 8 6 42 48 = = Compare the numerators. 40 48 < 42 , and so 5 6 < 7 8
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Student Practice 1B: Compare the fractions. Write < or >. 6 8 5 7 – – Both fractions can be written with a denominator of 56. 6 8 –6 7 8 7 –42 56 Write equivalent fractions with 56 as the denominator. Put the negative signs in the numerators. – = = 5 7 –5 8 7 8 –40 56 – = = 42 56 40 56 6 8 5 7 – < – , and so – < –
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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.
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Teacher Example 2A: Comparing Decimals
Compare the decimals. Write < or >. 0.427 0.425 0.427 7 Line up the decimal points. The tenths and hundredths are the same. 0.425 5 Compare the thousandths: 7 > 5. Since > 0.005, >
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Compare the decimals. Write < or >.
Teacher Example 2B: Compare the decimals. Write < or >. 0.73 0.734 0.73 = _ 0.733… 3 0.73 is a repeating decimal. Line up the decimal points. 0.734 4 The tenths and hundredths are the same. Compare the thousandths: 3 < 4. Since is < 0.004, 0.73 <
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Student Practice 2A: Compare the decimals. Write < or >. 0.535 0.538 0.535 5 Line up the decimal points. The tenths and hundredths are the same. 0.538 8 Compare the thousandths: 5 < 8. Since < 0.008, <
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Student Practice 2B: Compare the decimals. Write < or >. 0.3 0.334 0.3 = 0.3333… 3 0.3 is a repeating decimal. Line up the decimal points. The tenths and hundredths are the same. 0.334 4 Compare the thousandths: 3 < 4. Since is < 0.004, 0.3 <
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A rational number is a number that can be written as a fraction or quotient of integers with a nonzero denominator. When rational numbers are written in a variety of forms, you can compare the numbers by writing them all in the same form.
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The values on a number line increase as you move from left to right.
Remember!
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Teacher Example 3: Ordering Fractions and Decimals
4 5 Order , 0.93, and 0.9 from least to greatest. Write as decimals with the same number of places. 4 5 = 0.80 0.93 = 0.93 0.9 = 0.90 Graph the numbers on a number line. 0.93 0.80 < 0.90 < 0.93 Compare the decimals. 4 5 From least to greatest, the numbers are , 0.9, 0.93.
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Order , 0.84, and 0.7 from least to greatest.
Student Practice 3: 3 5 Order , 0.84, and 0.7 from least to greatest. Write as decimals with the same number of places. 3 5 = 0.60 0.84 = 0.84 0.7 = 0.70 Graph the numbers on a number line. 0.84 0.60 < 0.70 < 0.84 Compare the decimals. 3 5 From least to greatest, the numbers are , 0.7, 0.84.
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Compare the fractions. Write > or <. 1. 2.
Lesson Quiz Compare the fractions. Write > or <. Compare the decimals. Write < or >. and 0.312 3 7 4 10 5 8 2 3 and > < and > 5 6 4. Order , 0.8, from least to greatest. Graph the numbers on a number line. 0.8, 0.826, 5 6 56 0.8 0.826
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