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The Wonder Number Lessons

  1. Basic Counting
  2. Comparison
  3. Addition – Single Digit
  4. Addition – Double Digit
  5. Subtraction – Single Digit
  6. Subtraction – Double Digit
  7. Patterning
  8. Multiples and Factors
  9. Multiplication
  10. Primes and Composites
  11. Squares
  12. Division – No Remainder
  13. Division – With Remainder
  14. Simplifying Fractions
  15. Least Common Denominator
  16. Goldbach’s Conjecture

Lesson No. 14:  Simplifying Fractions

Finding lowest terms for fractions can be a complicated operation for students.  The Wonder Number Board’s use of color-coded factors for each block makes it significantly easier for students to find the greatest common factor. By finding the greatest common factor, the student will be able to simplify the fraction in one step.  If the student uses a common factor instead of the Greatest Common Factor, the fraction will take more then one step to simplify.

The first fraction to be simplified is 18/23.  Place a viewer on both 18 and 23 (see fig 73).  Look in both blocks for the greatest common factor of both numbers.  Since there are no common factors for these numbers, 18/23 is at its lowest terms.  (The only common factor is 1)

The second fraction to be simplified is 16/19.  Place a viewer on both 16 and 19 (see fig 74).  Look in both blocks for the greatest common factor of both numbers.  Since there are no common factors for these numbers, 16/19 is at its lowest terms.  (The only common factor is 1)

The third fraction to be simplified is 10/15.  Place a viewer on both 10 and 15 (see fig 75).  Look in each block to find the greatest common factor of both numbers.  Both blocks contain a green 5 as a factor, so 10/15 can be simplified.  To do so, divide the numerator 10 by the greatest common factor 5.  The answer is 2.  Then divide the denominator 15 by the greatest common factor 5. The answer is 3.  The simplified fraction is 2/3 and is at its lowest terms.

 The fourth fraction to be simplified to its lowest terms is 42/48.  Place a viewer on both 42 and 48 (see fig 76).  Look in both blocks to find the greatest common factor of both numbers, and that greatest common factor is 6.  Sometimes students do not see the greatest common factor and instead use another common factor to simplify, in this case 2.  Both numbers have a Blue 2 as a factor so 42/48 can be simplified.  The students divide the numerator 42 by 2 to get 21, and divide the denominator 48 by 2 to get 24.  The new numerator is 21 and the new denominator is 24 which can be expressed as 21/24. This fraction is not at its lowest terms. The student must   now place a viewer on both 21 and 24, look in both blocks for the greatest common factor, which in this case is 3 (see fig 77).  Divide 21 by 3 to get 7, and divide 24 by 3 to get 8.  The simplified fraction is 7/8 and is at its lowest terms. The fraction 42/48 could have been simplified in one step if the student would have used the greatest common factor of 6.

© 2007 The Wonder Number Learning System, Patent No. 3975051 Dated 1976