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Monday , Nov. 18, 2013

Directions : Please come in and get your journal. On your next blank page, write today’s date on the top line. Title this page ~ Adding and Subtracting Fractions . Below the date, write the Challenge Question . .

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Monday , Nov. 18, 2013

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  1. Directions: Please come in and get your journal. On your next blank page, write today’s date on the top line. Title this page ~ Adding and Subtracting Fractions. Below the date, write the Challenge Question. Challenge Question: How does knowing part-to-whole relationships help you add and subtract fractions? Monday, Nov. 18, 2013 Warm-up (independent, level 0 noise): Please complete this in your journal below the CQ Add or Subtract the following Fractions: + - 1 -

  2. Definition: A fraction is an ordered pair of whole numbers, the 1st one is usually written on top of the other, such as ½ or ¾ . numerator denominator The denominator tells us how many congruent pieces the whole is divided into, thus this number cannot be 0. The numerator tells us how many such pieces are being considered.

  3. & dding ubtracting ractions

  4. We need a common denominator to add these fractions. +

  5. We need a common denominator to add these fractions. + Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7's 7, 14, 21, 28, 35…

  6. Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7's 7, 14, 21, 28, 35… The first number IN COMMON that appears on both lists becomes the common denominator

  7. x 5 15 Make equivalent fractions. = X 5 x 7 7 + Add the numerators = x 7 15 + 7 = 22 22

  8. We need a common denominator to add these fractions. + Count by 7's 7, 14, 21, 28, 35, 42, 49, 56, 63 Count by 8's 8, 16, 24, 32, 40, 48, 56, 64, 72

  9. 32 x 8 Make equivalent fractions. = x 8 21 Add the numerators x 7 + 32 + 21 = 53 = x 7 53

  10. Try These A B D C

  11. 17 27 10 9 19 20 13 12 Try These C A D B

  12. Subtracting Fractions

  13. Subtraction • Subtracting fractions begins exactly the same way as adding fractions. • The first thing you have to do is figure out if you CAN subtract them as they are. • If not, you will need to convert a denominator so you can.

  14. Let’s do one together • 1 ½ - ¼ • You can see that one of them needs to be converted so you can subtract them. • What will the common denominator be? • ANSWER: 4

  15. Identify the common denominator. 1 ½ - ¼ ANSWER: 4 Since ¼ already has a denominator of 4 you don’t need to change it. But ½ needs to be converted to 4’ths. Step #1 Step #2

  16. Step #2 (continued) • How do you convert ½ into 4ths? • (what number) x 2 = 4? • ANSWER: 2 • Now, multiply both the numerator (top number) and the denominator (bottom number) by 2. • 1 x 2 = 2 2 x 2 = 4

  17. Step #3 • So now ½ has been converted to 2/4. • Now we have: 1 2/4 – ¼ • Go ahead and subtract ONLY the numerators. What did you get? • ANSWER: 1 ¼

  18. BORROWING!!! • Generally, borrowing is the most difficult thing to do in subtracting fractions. • There are 4 simple steps to follow and it works for ANY fraction in ANY problem. • Don’t worry, it’s easy once you learn the steps.

  19. Here is the problem • Let’s say that you got a problem like this: • 3 ¼ - 15/16 • First step: They can’t be subtracted as they are. • Second step: What is the common denominator? ANSWER: 16 • Third step: Convert a fraction.

  20. Let’s go through it • With a common denominator of 4 we need to figure out: (what number) x 4=16? • ANSWER: 4 • SO: 4 x 1 = 4 4 x 4 = 16

  21. The problem now reads like this: 3 4/16 – 15/16 Normally you would now subtract. The problem is that 4 – 15 would be a negative number. We can’t have that! THUS, BORROWING IS NEEDED! Oops! What’s this?

  22. Borrowing • In this problem: 3 4/16 – 15/16 • Borrowing is having to increase the value or amount of 4/16 so that it’s bigger than 15/16. • In other words, we need to make 4/16 bigger so that we CAN subtract.

  23. Here’s how to do it • 3 4/16 needs to be changed somehow. • We’re going to take 1 whole number from the 3 and add it to 4/16. • Would you agree that: 2 + 1 4/16 = 3 4/16? • NOW COMES THE TRICKY PART.

  24. 2 + 1 4/16 needs to be changed a bit before we can subtract from it. Lets take 1 4/16 and “fix” it. Because 16 is the common denominator we need to write 1 in 16ths. We can write 1 as: 2/2 = 1 3/3 = 1 4/4 = 1 And so forth up to: 16\16 = 1 SO NOW: 16 + 4 = 20 16 16 16 The tricky part

  25. Try These A B C

  26. 1 4 7 8 5 12 Try These B A C 1

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