1.  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.) Johnny Jimmy ¼ Remains

3. 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. 3 4 1 4 =

4. Types of Rational Numbers Reduced Fractions: Not Reduced Fractions: Mixed Numbers: Improper Fractions: Integers and Whole Numbers: -5, 12, 5 4 2323 15 8 1313 2 6868

5.  To convert an improper fraction to a mixed number:  Divide the denominator into the numerator. Put the remainder over the denominator. 3 = 15 4 3434

6.  Converting Improper Fractions to Mixed Numbers:  Multiply the denominator by the whole number.  Add the numerator. 4 4545 = 24 5 3 1717 22 7 =

8. 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. = 4545 1 = 1 7878

9. 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: 1 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. 4545 = 1

10. To multiply mixed numbers, convert them to improper fractions first. 1 1 1414 4 =

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

12. Multiply the following fractions and mixed numbers:

13.  The reciprocal is the “multiplicative inverse”  This means to flip the fraction over, so… 2323 The reciprocal of is 3232 !

14. 1515 1212 4 4949 7878 2323 10 3 4545 23

15. 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. Change Operation. Flip 2nd Fraction.

16. Finish the problem by following the rules for multiplying fractions.

17. Divide the following fractions & mixed numbers:

18.  You can cancel any number from the top with any number from the bottom as long as they have a common factor. 3838 5 9 4545 = 11 1 1 23 1 6

19. 5757 2323 -4 7878 3 10 1212 = _