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Fractions

Fractions. Addition and Subtraction. A tutorial by Mr. Michael Braverman Haverford Middle School. What are Fractions?. Pieces of whole numbers Such as ½ of a pizza ¾ of an hour Ratios (ways to compare two numbers) Parts of a whole/parts available: Ex: 2 wins out of 5 games (2/5)

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Fractions

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  1. Fractions Addition and Subtraction A tutorial by Mr. Michael Braverman Haverford Middle School

  2. What are Fractions? • Pieces of whole numbers • Such as ½ of a pizza • ¾ of an hour • Ratios (ways to compare two numbers) • Parts of a whole/parts available: • Ex: 2 wins out of 5 games (2/5) • 4/5 dentists surveyed recommend a certain brand of gum.

  3. What are Fractions 1 1 1 1 1 1 1 Graphically: Assume each gray box is one whole unit. 3 3 3 4 4 4 4

  4. + What are Fractions 1 1 1 3 2 1 1 1 1 Suppose you had the following addition problem: 4 3 3 3 3 4 4 4 4

  5. + 1 1 1 3 1 2 1 Suppose you had the following addition problem: 3 3 4 4 3 4 4 You cannot add these together directly because they are different sizes. Instead, you need to make each box the same size: Instead, you need to make each box the same size:

  6. + 1 1 1 1 1 3 2 Suppose you had the following addition problem: 3 3 4 4 4 4 3 So…divide the thirds into four pieces each and the fourths into three pieces each to get twelfths.

  7. + 8 12 9 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 + 1 1 3 2 1 2 1 1 3 4 3 3 4 4 4 4 3 3 So…divide the thirds into four pieces each and the fourths into three pieces each to get twelfths. Suppose you had the following addition problem:

  8. + + 8 12 9 12 5 12 17 12 1 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 + 3 3 2 2 3 2 4 4 4 3 3 3 Suppose you had the following addition problem:

  9. + Note that: 8 4 2 12 4 3 9 3 3 12 3 4 5 12 17 12 1 8 12 9 12 3 2 4 3

  10. + Note that: This sets up a Super Shortcut 8 4 2 12 4 3 9 3 3 12 3 4 17 12 5 12 1 8 12 9 12 3 2 4 3

  11. + 3=9 3 4 2=8 3 2 + 4 3 5 12 17 12 1 3  4=12 8 12 9 12 3 2 4 3 3 2 4 4 3 3

  12. + 3=9 3 4 2=8 3 2 + 4 3 17 12 5 12 1 3  4=12 8 12 9 12 3 2 4 3 9 8 8 + 9 12 3 2 + 4 4 3 3 12

  13. Try These:

  14. Try These:

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