Equivalent Fractions and Simplifying Fractions

1. Equivalent Fractions and Simplifying Fractions NS2

2. Equivalent Fractions • …name the same amount but have different numerators and denominators. 1 2 1 1 = 4 2 4 2 1 4

3. Equivalent Fraction Models 1 2 3 = = 2 4 6

4. Equivalent Fraction Models 1 4 = 5 = 2 8 10

5. When a number is multiplied by one, what happens? When a number is multiplied by 1, the value of the number does not change. 4 x 1 = ? 238 x 1 = ? 17 x 1 = ?

6. Identity Property of Multiplication! This is a fancy name for what you already know . . . Any number (a) x 1 = any number (a)! a x 1 = a

7. We use this property to find equivalent fractions! We multiply a number by different names for 1. We call this guy . . . As in, “What Mr. 1 did you use?” Mr. 1

8. Fractions Equal to 1

9. On your slate write a fraction equal to 1 with a denominator of 9.

10. We can find fractions equivalent to By multiplying it by by and by

11. On your slate find the equivalent fraction for by multiplying by a different Mr. 1 . . . = ?

12. You should have written . . .

13. You can find more fractions equivalent to . . . . . . by multiplying by any Mr. 1.

14. Example 1 What Mr. 1 should be multiplied to make ? Think: 3 x ? = 6 And: 4 x ? = 8

15. Example 1 What Mr. 1 should be multiplied to make ? Mr. 1 is

16. Example 2 What Mr. 1 do you need? (Think: 3 x ? = 12)

17. Example 2 So Mr. 1 is Now figure out the equivalent fraction.

19. What Mr. 1 do you use to make the equivalent fraction? c. a. b. d. 3

20. What Mr. 1 do you use to make the equivalent fraction? c. a. b. d. 3

21. Find the numerator that completes the equivalent fraction:

22. Simplifying or Reducing Fractions Sometimes you need to simplify or reduce a fraction. These are also equivalent fractions, but instead of multiplying by Mr. 1, you divide by Mr. 1.

23. What Mr. 1 do you use? • You need to think of the largest number both 6 and 8 be divided by. What is that number? • Now use 2 to make Mr. 1. • Now divide! 2

24. Reducing or Simplifying

25. To Simplify Fractions • Divide the numerator and the denominator by the same number. 4 4 1 ÷ = 12 4 3

26. Lowest Terms When reducing, always try to divide by the largest number you can find to make Mr. 1. You can reduce by using 2 to make Mr. 1, but your answer will not be in lowest terms. What bigger number can you use to make Mr. 1?

27. Lowest Terms The bigger number can you use to make Mr. 1 is 4!

28. Another example. . . not lowest terms lowest terms

29. What Mr. 1 do you use to simplify to lowest terms?

30. Reduce to lowest terms.

31. Which Mr. 1 do you use to simplify 14 to lowest terms? 21 a. 2 2 b. 3 3 c. 7 7 d. 14 14

32. Which fraction is equivalent to ⅖? • 5 20 b. 6 15 c. 15 35 d. 12 25

33. Which number makes this sentence true? 1 3 9 • 3 • 4 • 5 • 6 =

34. The Toothless Wonder Last night when I was sound asleep, My little brother Keith Tiptoed into my bedroom And pulled out all my teeth. You’d think that I would be upset And jump and spit and swear. You’d think that I would tackle Keith And pull out all his hair.

35. But no! I’m glad he did it. So what if people stare. Now, thanks to the Tooth Fairy, I’ll be a millionaire! by Phil Bosta

36. The end!