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Bell Ringer

Bell Ringer. Two boys decided to share a pizza. Johnny ate ½ of the original pizza. Jimmy ate ½ of what was left. How much of the pizza remains? (Hint: Draw a picture.). Jimmy. Johnny. ¼ Remains. Mixed Numbers and Rational Numbers. Rational Numbers.

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Bell Ringer

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  1. Bell Ringer • Two boys decided to share a pizza. Johnny ate ½ of the original pizza. Jimmy ate ½ of what was left. How much of the pizza remains? (Hint: Draw a picture.) Jimmy Johnny ¼ Remains

  2. Mixed Numbersand Rational Numbers

  3. Rational Numbers • The term, Rational Numbers, refers to any number that can be written as a fraction. • This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers. • An integer, like 4, can be written as a fraction by putting the number 1 under it. 4 4 = 1

  4. Rational Numbers Types of Rational Numbers • Reduced Fractions: • Not Reduced Fractions: • Mixed Numbers: • Improper Fractions: • Integers and Whole Numbers: -5, 12, 5 2 3 6 8 1 3 2 15 8

  5. Improper Fractions • To convert an improper fraction to a mixed number: • Divide the denominator into the numerator. Put the remainder over the denominator. 15 4 3 3 4 =

  6. Mixed Numbers • Converting Improper Fractions to Mixed Numbers: • Multiply the denominator by the whole number. • Add the numerator. 4 4 5 24 5 3 22 7 1 7 = =

  7. Multiplying and Dividing Fractions

  8. Multiplying Fractions • When multiplying fractions, they do NOT need to have a common denominator. • To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator. • If the answer can be simplified, then simplify it. 4 5 1 = 7 8 1 =

  9. 1 1 Simplifying Diagonally • When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end. • From the last slide: • An alternative: 4 5 1 = You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end.

  10. 1 1 Mixed Numbers • To multiply mixed numbers, convert them to improper fractions first. 1 4 4 =

  11. Integer Rules • Remember, when multiplying integers... Positive * Positive = Positive. Negative * Negative = Positive. Positive * Negative = Negative. 1 _ 3 20 = 4 1 1 20 = 2

  12. Try These: Multiply Multiply the following fractions and mixed numbers:

  13. Reciprocal • The reciprocal is the “multiplicative inverse” • This means to flip the fraction over, so… 2 3 3 2 The reciprocal of is !

  14. What is my reciprocal? 1 5 10 3 7 8 4 9 1 2 2 3 4 5 2 3 -1 4

  15. Change Operation. Flip 2nd Fraction. Dividing Fractions • When dividing fractions, they do NOT need to have a common denominator. • To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change.

  16. Dividing Fractions • Finish the problem by following the rules for multiplying fractions.

  17. Try These: Divide • Divide the following fractions & mixed numbers:

  18. More than Two Fractions!!! • You can cancel any number from the top with any number from the bottom as long as they have a common factor. 1 1 1 3 8 4 5 5 9 1 6 • • = 1 2 3

  19. Try This One!!!!! 5 7 2 3 3 10 7 8 -4 1 2 _ • = • • •

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