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 CARD Rational Number

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 =

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.

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

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 – > . –

A fraction less than 0, such as - , can be written as - , , or . Helpful Hint! 2 5 -2 5 2 -5

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

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 – < . –

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.

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 0.007 > 0.005, 0.427 > 0.425.

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 0.003 is < 0.004, 0.73 < 0.734.

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 0.005 < 0.008, 0.535 < 0.538.

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 0.003 is < 0.004, 0.3 < 0.334.

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.

The values on a number line increase as you move from left to right. Remember!

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 0.2 0.4 0.6 0.8 1 0.80 < 0.90 < 0.93 Compare the decimals. 4 5 From least to greatest, the numbers are , 0.9, 0.93.

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 0.2 0.4 0.6 0.8 1 0.60 < 0.70 < 0.84 Compare the decimals. 3 5 From least to greatest, the numbers are , 0.7, 0.84.

Compare the fractions. Write > or <. 1. 2. Lesson Quiz Compare the fractions. Write > or <. 1. 2. Compare the decimals. Write < or >. 3. 0.32 and 0.312 3 7 4 10 5 8 2 3 and > < and > 5 6 4. Order , 0.8, 0.826 from least to greatest. Graph the numbers on a number line. 0.8, 0.826, 5 6 56 0.8 0.826 0.80 0.81 0.82 0.83 0.84 0.85