Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
3. Real Numbers and the Number Line
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Exercise 33 Page 20

Can the fraction reduced?

Rational numbers

Practice makes perfect

Before we consider the given number, let's recall the various types of numbers.

  • Rational Number: A number is a rational number if it can be written in the form ab, where a and b are both integers and b≠ 0.
  • Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, a1.
  • Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.
    • Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.
    • Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.
    Now, let's try to categorize the given number using these definitions. 17/4573 This is a fraction with integers in the numerator and denominator, so we can immediately identify it as a rational number. Let's reduce this fraction to see if it can fall into any other category.
    17/4573
    1/269
    After reducing the fraction, it is still in the form ab. Therefore, this number cannot be classified as anything other than a rational number.