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Chapter 2

Chapter 2. Rational Numbers. Rational Numbers. Numbers that can be written as a fraction. Rational Numbers include: Whole numbers Zero Positive and negative integers Positive and negative fractions Positive and negative decimals. Comparing Fractions. Compare ¾ and 5/8

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Chapter 2

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  1. Chapter 2 Rational Numbers

  2. Rational Numbers • Numbers that can be written as a fraction. • Rational Numbers include: • Whole numbers • Zero • Positive and negative integers • Positive and negative fractions • Positive and negative decimals

  3. Comparing Fractions • Compare ¾ and 5/8 • Step 1: Find the lowest common denominator (the smallest number that both denominators will divide into evenly.) The lowest common denominator is 8. • Step 2: Change fourths to eighths by multiplying three fourths by two halves: • Step 3: Since the denominators are the same, the fraction with the larger number is greater.

  4. Comparing the mixed numbers • Compare 1 3/5 and 1 2/3 • Step 1: Change the mixed numbers to improper fractions. • Step 2: Find the lowest common denominator for the improper fractions. The lowest common denominator is 15. • Step 3: Change fifths to fifteenths and thirds to fifteenths.

  5. Comparing Decimals • A decimal is the point after a whole number. • A decimal is commonly used in monetary notations, such as $12.54. • A decimal is also used to express a whole number and a fractions, such as one and a quarter pies expressed as 1.25 pies.

  6. Comparing Decimals • Decimals preceded by zeros represent numbers less than one, such as a quarter of a pie, 0.25pies. • BE SURE TO INCLUDE A LEADING ZERO TO THE LEFT OF THE DECIMAL FOR NUMBERS LESS THAN ONE. • A decimal can be read as ‘point’; 1.25 is read as ‘one point two five’ • It can also be read as ‘one and twenty-five hundredths’

  7. Comparing Decimals

  8. Comparing Decimals • Compare 4.1 and 4.11 • Step 1: Arrange numbers with decimal points directly under each other. 4.1 4.11 • Step 2:Fill in with zeros so they all have the same number of digits after the decimal point. Read the numbers as if the decimal points were not there. 4.10 4.11 4.1< 4.11

  9. Comparing Decimals • Compare: • 7.2 and 7.02 • 8.55 and 8.555 • 97.08 and 97.18 • 0.21 and 0.211 • 17.1001 and 17.1011

  10. Changing Fractions to Decimals • Change • To change a fraction to a decimal, divide the top number by the bottom number . 8 √1 • Add a decimal point and a 0 after the 1 and divide. • Continue adding 0s and dividing until there is no remainder. • 0.125 to a decimal.

  11. Change the following fractions to decimals. • 4/5 • 5/8 • 5/11 • 8/9

  12. Changing decimals to fractions. • Change 0.25 to a fraction. • Copy the decimal without the point. This will be the top number of the fraction 25. • The bottom number is a 1 with as many 0s after it as there are digits in the top number Two digits Two 0’s You need to simplify the fraction.

  13. Change the following decimals to fractions. • 0.55 • 0.75 • 0.71 • 0.35

  14. Change the following decimals to mixed numbers. • 7.125 • 99.5 • 2.13 • 16.95

  15. Graphing Rational Numbers • Where would 4/3 fall on the number line? • Convert the improper fraction to a mixed number. • That is 1/3 of the distance between the numbers 1 and 2. Estimate the distance by dividing the distances between points 1 and 3 into thirds.

  16. Graphing Rational Numbers • Plot the value of -1.75 on the number line. • Convert the value of -1.75 to a mixed number. • That is ¾ of the distance between the numbers -1 and -2. Estimate this distance by dividing the distance between -1 and -2 into fourths.

  17. Plot and label the following values on your number line! • A. 5/4 • B. 12/5 • C. 2/3 • D. =3/2

  18. Plot and label the following values on your number line! • 0.25 • 0.9 • 1.9 • 2.6

  19. Comparing Rational Numbers • When comparing numbers, use the greater than (>), less than (<), or equal to (=0 signs. • The simplest way to compare numbers that are in different notations, like percent, decimals, and fractions, is to change all of them to one notation. • Decimals are the easiest to compare!!

  20. Which is larger? • Or 1.3 • Change to a decimal. 1.25, which is smaller than 1.3. Which is smaller?: 0.6 or 2/3? Change 2/3 to a decimal – 0.666… 0.6 is smaller than- 0.666… so 0.6 < 2/3

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