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Simplifying Fractions

Simplifying Fractions. Fraction Simplification and Equality. Some Fractions are Created Equal. Fractions represent a part of a whole number They are made of numerators and denominators Sometimes fractions with different numerators and denominators can be equal to one another. Numerator.

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Simplifying Fractions

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  1. Simplifying Fractions Fraction Simplification and Equality

  2. Some Fractions are Created Equal • Fractions represent a part of a whole number • They are made of numerators and denominators • Sometimes fractions with different numerators and denominators can be equal to one another. Numerator Denominator

  3. Equal Fractions • These two rectangles are the same size, but they are divided into a different number of pieces • If we shade one piece on the first rectangle, it is the same as shading two pieces on the second rectangle. Thus, the fractions 1/4 and 2/8 are EQUAL! • 1/4 2/8

  4. Equal Fractions • You can see examples of this in real life every day! • Check out these pizzas! They are all the same size but are divided into different numbers of equally sized pieces 1/4 of a pizza = 2/8 of a pizza = 3/12 of a pizza THESE FRACTIONS ARE ALL EQUAL

  5. Simplify or Reduce? . . .That is the question. • We have seen that 1/4 = 2/8 = 3/12 • When we are given a fraction containing larger numbers (3/12) and we are asked to simplify or ‘reduce’, which is the correct terminology? . . . • We already said that 3/12 = 1/4, did we reduce or simplify this number? . . .

  6. Simplify or Reduce? . . .That is the question. (ctd.) • We SIMPLIFIED it! Although the numbers in the numerator and denominator are smaller than they were before, these numbers alone don’t make up the overall number. • The RATIO between the two stayed the same and therefore the number cannot be ‘reduced’. It is SIMPLIFIED.

  7. Simplifying Fractions • Usually, fractions are easiest to understand in their simplest form. • To get to the simplest form you must SIMPLIFY them, if necessary. • Example: What is the simplified form of:

  8. Simplifying Fractions • To simplify a fraction you must be able to divide both the numerator and the denominator by the SAME number. • Can you think of a number by which both 36 and 27 are divisible? • How about 3? • Divide 27 by 3 and get 9 • Divide 36 by 3 and get 12 =

  9. Simplifying Fractions • So now we have , but is this number in the simplest form yet? • Are there any numbers that go into both 9 and 12? • How about 3? • Divide 9 by 3 and get 3 = • Divide 12 by 3 and get 4 • Thus, we have: • = = OR = ¾ is the simplest form of this fraction!

  10. Prime Factorization • Another way to think about simplifying fractions is through Prime Factorization: • In prime factorization, you reduce the numerator and the denominator into their lowest factors. Then you can cancel out pairs of numbers appearing in both the numerator AND the denominator. • Check out these fractions that we have simplified using Prime Factorization: = = = = = = =

  11. Challenge Problem! • Simplify this fraction:

  12. Challenge Problem! • Simplify this fraction: = = = OR = = = =

  13. Great Job! Keep practicing!

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