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Understanding Fractions: Exploring Fractions of Whole Numbers

Learn about fractions by understanding how to find fractions of whole numbers and mixed numbers. Discover how the numerator and denominator work together to represent parts of a whole.

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Understanding Fractions: Exploring Fractions of Whole Numbers

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  1. Fractions: What are they? We’ll learn about: • Fractions of whole numbers • Mixed Numbers Mr. Madden

  2. Let’s understand a fraction The top number (numerator) tells HOW MANY parts of the whole object we have 1 ¾ 2 3 The bottom number (denominator) tells HOW MANY parts the whole object is divided into. Mr. Madden

  3. Let’s check this out Pretend you are at a party and you get to have 5/6 of a tasty pizza. Which picture shows how many parts it should be divided into? 5 6 Mr. Madden

  4. HOT STUFF !!! 5 6 Yes, the bottom number (denominator) tells us it Is divided into 6 parts. Mr. Madden

  5. HOT STUFF !!! Now, how many parts do you get? Click on the arrow. 5 6 ? ? Mr. Madden

  6. HOT Pepperonis !!! The top number (numerator) tells us how many we get. 5 6 5 On to Bigger and Better Mr. Madden

  7. Oh mushrooms, no, try again !!! The top number (numerator) tells us how many parts we get. 5 6 5 NO! Try again Mr. Madden

  8. Whoops, darn, shucks… 5 6 The bottom number (denominator) tells us it is divided into 6 parts. Hint: Divided and Denominator both start with D, and so does the word Down, like Down under. Try Again Mr. Madden

  9. Try this one 7 10 Mr. Madden

  10. Finding fractions of whole numbers To find a fraction of a whole number, first divide the number into equal parts. • A class predicts that ¾ of 88 piano keys are ivory. First divide the 88 keys into how many equal parts? 3 12 4 Mr. Madden

  11. Nope, try again! Go again Mr. Madden

  12. Bingo! 4 is correct! Okay! Let’s move on. Mr. Madden

  13. Now that you’ve got 88 keys divided into 4 equal groups, you need to find how many keys will belong to each group. Will there be: 22 92 40 Mr. Madden

  14. Yep, because 88 divided four equal ways is 22. Don’t stop now! Mr. Madden

  15. Okay, now we know that if we take the 88 keys and break them up into 4 equal groups, we’ll have 4 groups of 22 keys. But if we want to find ¾ of 88 keys, how many groups do we consider? 3 12 4 Mr. Madden

  16. Nicely done! 3 equal parts Now what? Mr. Madden

  17. The answer to “What is ¾ of 88?” is the total number of keys in the 3 groups of 22. What’s the total? 66 6 6.6 Mr. Madden

  18. Absolutely right, because 22 multiplied by 3 is 66. Good work! What about Mixed Numbers? Mr. Madden

  19. Mixed Numbers • When a part is more than a whole, you can describe it two ways: • Fraction If the pizza is divided into six equal pieces, then each piece is 1/6 of the pizza, right? Right! Check it out! Mr. Madden

  20. Well, what if you ordered 7 slices, or pieces? How many pizzas would you have now? 7/6 and 1 1/6 2 6/6, or one whole 1/6, or one-sixth Mr. Madden

  21. Improper Fractions Nicely done! Yes, if you have a total of seven pieces of pizza, and each is 1/6 of the whole, then you have 7/6 pizzas! But doesn’t it look strange, or improper, to have the numerator (7) larger than the denominator (6)? So what do we do? Mr. Madden

  22. Mixed Numbers Well, we have a whole pizza (1) and a fraction of another pizza (1/6). Let’s put them together. Now we have one and one-sixth pizzas. We write this 1 1/6. Try this! Mr. Madden

  23. How many red squares are shown? 3 3 1/4 4 Mr. Madden

  24. You got it square on the target! Since three whole squares (3), and one-fourth (1/4) of another square are red, then there are 3 + 1/4 red squares, but we don’t use the “+” sign. Just write “3 1/4.” Give it a shot Mr. Madden

  25. Your big cousin, Ernie, and you have a pizzafest. You buy 7 pizzas, and eat for hours. Below is what you didn’t eat. How much pizza is left? 17/6 2 5/6 6/17 Mr. Madden

  26. I’m surprised you can move! Yep! You and Ernie still have 17/6, or 2 5/6 pizzas left to chow on. (Maybe you should save them for breakfast.) Good job!! Mr. Madden

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