EQUIVALENT FRACTIONS

1
EQUIVALENT FRACTIONS

• The more we change, the more we stay the same.

2
Equivalent fractions are fractions that might
look different but are really equal in their value
3
Lets begin with the most famous fraction of all.
½
4
½ of this square is shaded.
5
No matter how many additional lines we add to
this square, ½ is still shaded.
6
No matter how many additional lines we add to
this square, ½ is still shaded.
2 1 4 2

7
No matter how many additional lines we add to
this square, ½ is still shaded.
4 1 8 2

8
No matter how many additional lines we add to
this square, ½ is still shaded.
8 1 16 2

9
No matter how many additional lines we add to
this square, ½ is still shaded.
16 1 32 2

10
No matter how many additional lines we add to
this square, ½ is still shaded.
32 1 64 2

11
No matter how many additional lines we add to
this square, ½ is still shaded.
64 1 128 2

12
Even though the square has been further divided,
½ of the square is still shaded.
64 1 128 2

13
½ is said to be in LOWEST TERMS because this is
the simplest way to describe the fraction.
1 2
14
This is also the simplest way to show that ½ of
the square is shaded.
1 2
15
2 3 4 5 6 7 8







2 4 6 8 10 12 14 16
16

• 2 3 4 5 6 7 8

2 4 6 8 10 12 14 16
You can check to see that all of these fractions
are EQUAL by converting to decimals.
17

• 2 3 4 5 6 7 8

2 4 6 8 10 12 14 16
1 ? 2 .5 5 ? 10 .5 2 ? 4 .5 6 ? 12 .5 3
? 6 .5 7 ? 14 .5 4 ? 8 .5 8 ? 16 .5
18
Equivalent fractions have some unique properties.
19
If the numerators and denominators differ by the
same FACTOR, the two fractions are equal.
3 4
9 12

20
If the numerators and denominators differ by the
same FACTOR, the two fractions are equal.
x 3
3 4
9 12

x 3
21
If the numerators and denominators differ by the
same FACTOR, the two fractions are equal.
3 ?
3 4
9 12

3 ?
22
Another unique property of equivalent fractions
has to do with their cross products.
3 4
9 12

23
Another unique property of equivalent fractions
has to do with their cross products.
12 x 3 36
4 x 9 36
3 4
9 12

24
If the cross products are equal, then the
fractions are equal.
12 x 5 60
6 x 10 60
5 6
10 12

25
This property is true for any pair of equivalent
fractions.
21 x 2 42
7 x 6 42
2 7
6 21

26
Find the missing number.
3 4
? 24

27
x 6
3 4
18 24

x 6
28
Find the missing number.
2 3
? 24

29
x 8
2 3
16 24

x 8
30
Find the missing number.
20 24
? 6

31
?? 4
20 24
5 6

?? 4
32
Find the missing number.
36 45
? 5

33
?? 9
36 45
4 5

?? 9
34
Simplify this fraction to lowest terms.
20 30
35
Since both the numerator denominator end in
zero, both numbers are divisible by 10.
20 30
36
Since both the numerator denominator end in
zero, both numbers are divisible by 10.
? 10
20 30
2 3

? 10
37
Simplify this fraction to lowest terms.
25 35
38
Since both the numerator denominator end in
five, both numbers are divisible by 5.
25 35
39
Since both the numerator denominator end in
five, both numbers are divisible by 5.
? 5
25 35
5 7

? 5
40
Simplify this fraction to lowest terms.
14 22
41
Since the numerator denominator are both even
numbers, both numbers are divisible by 2.
14 22
42
Since the numerator denominator are both even
numbers, both numbers are divisible by 2.
? 2
14 22
7 11

? 2
43
Simplify this fraction to lowest terms.
12 21
44
At first glance, this fraction might appear
simplified already.
12 21
45
Always check to see if both numbers are divisible
by 3.
12 21
46
Always check to see if both numbers are divisible
by 3.
? 3
12 21
4 7

? 3
47
When simplifying fractions, check to see if the
numerator denominator 1) both end in 0 (?
10) 2) both end in 5 or 0 (? 5) 3) both are
even (? 2) 4) are divisible by 3 (? 3) 5)
are divisible by 7 (? 7)
48
THE END.