Introduction To Simplifying Fractions

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Introduction To Simplifying Fractions

  1. 1. Equivalent Fractions One Whole 1
  2. 2. Equivalent Fractions Shown is one half on the left and one half on the right . 1 2 NUMERATOR How many pieces we have! DENOMINATOR How many pieces the whole one is split into!
  3. 3. Equivalent Fractions I cut my shape again I still have 1 2 On the left and one half on the right , but each half is in two pieces now (quarters).
  4. 4. Equivalent Fractions So we have also split each half into… 2 4 So we can see how 2 quarters is equal - or equivalent to 1 half.
  5. 5. Equivalent Fractions One half is EQUIVALENT TO 2 quarters 1 2 2 4
  6. 6. Equivalent Fractions 1 2 2 4 This symbol looks like an equals sign with a third line. It is the mathematical sign for EQUIVALENT TO - which means “is worth the same as”.
  7. 7. Equivalent Fractions We can find equivalent fractions to make our numbers easier to handle by finding the lowest equivalent fraction possible. To do this, we just have to divide the numerator and denominator by a number that both can be divided by with no remainder. 160 200 16 20 4 5 ÷ 10 ÷ 10 ÷ 4 ÷ 4 A number that you can divide both the numerator and the denominator by with no remainder is called a COMMON FACTOR
  8. 8. Equivalent Fractions This fraction is as simple as we can make it, because there is nothing that we can divide both the numerator and denominator by without a remainder! 160 200 4 5 We can use different language for making the fraction as small as possible. Watch out for this language in the future. Finding smaller fractions is often called “simplifying” or “cancelling down” or sometimes even “expressing a fraction in its lowest terms.” Lowest terms Simplified Cancelled down
  9. 9. Equivalent Fractions 15 45 60 80 The trick is to look for numbers that both the NUMERATOR and the DENOMINATOR can be divided by. We want numbers bigger than 1, since any number divided by 1 gives you the same answer! We call these COMMON FACTORS
  10. 10. Equivalent Fractions 15 45 ÷ 3 ÷ 3 60 80 ÷ 10 ÷ 10 These numbers have 3 as a common factor. This means they can both be divided by 3 with no remainder. A common factor in this example is 10, because both 60 and 80 can be divided by 10 exactly!
  11. 11. Equivalent Fractions 15 45 5 15 ÷ 3 ÷ 3 60 80 6 8 ÷ 10 ÷ 10
  12. 12. Equivalent Fractions 15 45 5 15 ÷ 3 ÷ 3 ÷ 5 ÷ 5 60 80 6 8 ÷ 10 ÷ 10 ÷ 2 ÷ 2
  13. 13. Equivalent Fractions 15 45 5 15 1 3 ÷ 3 ÷ 3 ÷ 5 ÷ 5 60 80 6 8 3 4 ÷ 10 ÷ 10 ÷ 2 ÷ 2
  14. 14. Equivalent Fractions 15 45 1 3 60 80 3 4 If the top number is a 1, we know we can stop! If the top and bottom number are not DIVISIBLE by the same number, we stop.
  15. 15. Equivalent Fractions 15 45 1 3 60 80 3 4 They have no FACTORS in common other than 1 They have no FACTORS in common other than 1

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