1. Mrs. Ennis Equivalent Fractions Lesson Twenty
Math Grade 4
Mrs. Ennis
Equivalent Fractions
Lesson Twenty

2. D = 4310
826 – 415 =
5 x B = 20
L x 8 = 72
36 ÷ 6 =
6. How many obtuse angles in this figure?

3. cm = _________m
How many dimes in $1.65?
The concession stand at the ballpark sells hot dogs for $1.00 each. Their cost per hot dog is $ If they sold 20 hotdogs, what was their profit?

4. 10. The grocer places a case of canned tomatoes in a 3-shelf display
10. The grocer places a case of canned tomatoes in a 3-shelf display. He puts 7 cans on each shelf and had 3 cans left over. How many cans in the case?

6. Fraction Notation The number above the bar is the numerator.
The number below the bar is the denominator.
The fraction one-third
is written like this:
Numerator 1 3
Denominator

7. Equivalent Fractions

8. A fraction can have many different names.
6/12
3/6
5/10
2/4
4/8

9. In the picture we have ½ of a cake because a whole cake is divided into two congruent parts and we have only one of those parts.
But if we cut the cake into smaller congruent pieces, we can see that =
Or we can cut the original cake into 6 congruent pieces,

10. Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same.
Therefore, = =
If you don’t like this, we can cut the original cake into 8 congruent pieces,

11. Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same.
Therefore, =
We can generalize this to: =
whenever n is not 0

12. We can generalize this to=
(whenever n is not 0) =

13. Vocabulary
Equivalent fractions are fractions that name the same amount. 2 4 = 8 4

14. What do you get when you multiply a number by 1? You get that number!
7 x 1 = 7
5 x 1 = 5
37 x 1 = 37
23 x 1 = 23
17 x 1 = 17

15. All these fractions = 1 7 2 33 4 5 When the numerator &
denominator of a
fraction are the same,
the fraction
equals 1. 2 33 4 5

16. AN EQUIVALENT FRACTION
What do you get when you multiply a fraction by 1?
You get
AN EQUIVALENT FRACTION
(This makes adding & subtracting fractions possible.)

17. Whole Halves Thirds Fourths Fifths Sixths Eighths Ninths Tenths
Equivalent Fractions
Whole
Halves
Thirds
Fourths
Fifths
Sixths
Eighths
Ninths
Tenths
Twelfths

18. To Make Equivalent Fractions
Multiply the numerator and denominator by the same number.
You will get a new fraction with the same value as the original fraction.
We are not changing the value of the fraction, because we are simply multiplying by a fraction that is equivalent to ONE.

19. These fractions represent the same amount.3 5 4 12 20 x =
This fraction equals 1.
These fractions represent the same amount.

20. These fractions represent the same amount.2 3 3 6 9 x =
This fraction equals 1.
These fractions represent the same amount.

21. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
denominator by ... 2 3 6
x 3 = 3 9
x 3

22. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
denominator by ... 4 9 16
x 4 = 4 36
x 4

23. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
denominator by ... 5 8 45
x 9 = 9 72
x 9

24. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
denominator by ... 2 7 6
x 3 = 3 21
x 3

25. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
denominator by ... 6 7 24
x 4 = 4 28
x 4

26. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 3 7 12
x 4 = 4 28
x 4

27. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 7 8 21
x 3 = 3 24
x 3

28. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 1 3 5
x 5 = 5 15
x 5

29. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 2 4 10
x 5 = 5 20
x 5

30. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 4 5 24
x 6 = 6 30
x 6

31. Make An Equivalent Fraction Find the Missing Numerator!
We multiplied the
numerator by ... 4 5 8
x 2 = 2 10
x 2

32. If you have larger numbers, you can make equivalent fractions using division. Divide by a common factor.
In this example, we can divide both numbers by 7. 4 28
÷ 7 = 5 35
÷ 7
28/35 is equivalent to 4/5.
7/7 is equal to 1.

33. If you have larger numbers, you can make equivalent fractions using division. Divide by a common factor.
In this example, we can divide both numbers by 3. 7 21
÷ 3 = 10 30
÷ 3
28/35 is equivalent to 7/10.
3/3 is equal to 1.

34. If you have larger numbers, you can make equivalent fractions using division. Divide by a common factor.
In this example, we can divide both numbers by 5. 3 15
÷ 5 = 5 25
÷ 5
15/25 is equivalent to 3/5.
5/5 is equal to 1.

35. Make An Equivalent Fraction Find the Missing Denominator!
We divided the
numerator by ... 24 30 12
÷ 2 = 2 15 ÷2

36. Make An Equivalent Fraction Find the Missing Denominator!
We divided the
numerator by ... 18 24 6
÷ 3 = 3 8 ÷3

37. Make An Equivalent Fraction Find the Missing Denominator!
We divided the
numerator by ... 20 25 4
÷ 5 = 5 4 ÷5

38. Make An Equivalent Fraction Find the Missing Numerator!
We divided the
denominator by ... 9 15 3
÷ 3 = 3 5 ÷3

39. Make An Equivalent Fraction Find the Missing Numerator!
We divided the
denominator by ... 12 24 1
÷ 12 = 12 2
÷12

40. Make An Equivalent Fraction Find the Missing Numerator!
We divided the
denominator by ... 36 40 9
÷ 4 = 4 10 ÷4

41. Fractions in Simplest Form (This is also known as “reducing.”)
Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1.
Examples of fractions that are in simplest form: 4 5 1 2 3 8

42. Writing Fractions in Simplest Form.
Find the greatest common factor (GCF) of the numerator and denominator.
Divide both numbers by the GCF.

43. 5 20 ÷ 4 = 7 28 ÷ 4 20 28 Example: GCF: 4 Simplest Form
20: 1, 2, 4, 5, 10, 20 20 28
28: 1, 2, 4, 7, 14, 28
1 x 20
2 x 10
4 x 5
1 x 28
2 x 14
4 x 7
Common Factors: 1, 2, 4
GCF: 4
We will divide by 4.

44. 3 27 ÷ 9 = 5 45 ÷ 9 27 45 Example: GCF: 9 Simplest Form
20: 1, 3, 9, 27 27 45
28: 1, 3, 5, 9, 15, 45
1 x 27
3 x 9
1 x 45
3 x 15
5 x 9
Common Factors: 1, 3, 9
GCF: 9
We will divide by 9.

45. 5 15 ÷ 3 = 6 18 ÷ 3 15 18 Example: GCF: 3 Simplest Form
15: 1, 3, 5, 15 15 18
18: 1, 2, 3, 6, 9, 18
1 x 15
3 x 5
1 x 18
2 x 9
3 x 6
Common Factors: 1, 3
GCF: 3
We will divide by 3.

46. 2 8 ÷ 4 = 3 12 ÷ 4 8 12 Example: GCF: 4 Simplest Form 8: 1, 2, 4, 8
8: 1, 2, 4, 8 8 12
12: 1, 2, 3, 4, 6, 12
1 x 8
2 x 4
1 x 12
2 x 6
3 x 4
Common Factors: 1, 2, 4
GCF: 4
We will divide by 4.

47. Online Practice Flash Cards
Flash Cards

48. Math Fun:
Fiona went to the produce market. She spent $1.20 for a bag of squash, which sold for $0.60 per pound. Her bag of 6 equally-sized apples weighed the same as their bag of 2 identical squash. Her 8 peaches, all about the same size, weighed as much as 3 apples and 1 squash. She also purchased a small pumpkin that weighed the same as 12 peaches.
How much did the pumpkin weigh?

49. Answer:
The pumpkin weighed 3 pounds. Fiona bought 2 squash. Since she spent $1.20, with squash priced at $0.60 per pound, the 2 squash must have weighed 2 pounds. This means that 6 apples also weigh 2 pounds, and 3 apples weigh 1 pound. You also know that 8 peaches weigh 2 pounds, so 4 peaches weigh 1 pound and 12 peaches must weigh = 3 pounds, which is also the weight of the pumpkin.

50. Resources:
star.spsk12.net/math/5/equivalent_fractions.ppt