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Learn how to compare and order positive and negative fractions, decimals, and mixed numbers using number lines, models, and equivalent fractions. Understand the concept of rational numbers and practice comparing fractions and decimals.
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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
Vocabulary rational number A number that can be written as a fraction with integers for its numerator and denominator.
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 =
3 8 = 1 2 = One way to compare fractions with unlike denominators is to use models. For example, the models show that < . 1 2 3 8 Another way to compare fractions with unlike denominators is to first write equivalent fractions with common denominators. Then compare the fractions.
7 9 7 9 7 9 5 8 5 8 5 8 56 72 7 8 9 8 45 72 5 9 8 9 56 72 45 72 , and so . > > Example 1A: Comparing Fractions Compare the fractions. Write < or >. The LCM of the denominators 9 and 8 is 72. Write equivalent fractions with 72 as the denominator. = = = = Compare the numerators.
2 5 2 5 2 5 3 7 3 7 Example 1B: Comparing Fractions Compare the fractions. Write < or >. – – Both fractions can be written with a denominator of 35. Write equivalent fractions with 35 as the denominator. Put the negative signs in the numerators. –14 35 –2 7 5 7 = – = –15 35 –3 5 7 5 = – = 3 7 14 35 15 35 – – > , and so – > . –
25 Helpful Hint! 25 -25 2 -5 A fraction less than 0, such as - , can be written as - , , or .
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.
Example 2A: Comparing Decimals Compare the decimals. Write < or >. 0.427 0.425 Line up the decimal points. 0.427 7 The tenths and hundredths are the same. 0.425 5 Compare the thousandths: 7 > 5. Since 0.007 > 0.005, 0.427 > 0.425.
0.73 is a repeating decimal. _ 0.73 = Since 0.003 is < 0.004, 0.73 < 0.734. Example 2B: Comparing Decimals Compare the decimals. Write < or >. 0.73 0.734 0.733… 3 Line up the decimal points. The tenths and hundredths are the same. 0.734 4 Compare the thousandths: 3 < 4.
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.
Remember! The values on a number line increase as you move from left to right.
0 0.2 0.4 0.6 0.8 1 Example 3: Ordering Fractions and Decimals 4 5 , 0.93, and 0.9 from least to greatest. Order 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.
5 6 5 6 5 6 7 8 7 8 7 8 40 48 5 8 6 8 42 48 7 6 8 6 40 48 42 48 , and so . < < Check It Out! Example 1A Compare the fractions. Write < or >. The LCM of the denominators 6 and 8 is 48. Write equivalent fractions with 48 as the denominator. = = = = Compare the numerators.
Check It Out! Example 2A Compare the decimals. Write < or >. 0.535 0.538 Line up the decimal points. 0.535 5 The tenths and hundredths are the same. 0.538 8 Compare the thousandths: 5 < 8. Since 0.005 < 0.008, 0.535 < 0.538.
0 0.2 0.4 0.6 0.8 1 Check It Out! Example 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.
