Lesson Element
Rules of Fractions Investigation
PRODUCT means MULTIPLY
SUM means ADD
Can you perform these operations with fractions?
Multiply these fractions
1)
2)
 3)
 4)
 5)
 6)
 7)
 8)
 9)
 10)
 11)
 12)
 13)
1 3

4 7
7 1

8 2
7 7

3 5
1 3

4 4
7 7

2 5
1 1

3 4
1 5

2 7
9 9

2 7
1 1

12 2
5 2

11 3
8 8

2 3
2 1

9 3
1 3

4 7













Which give the same answer in both columns?
Can you spot 
anything these have in common? 
Use this to create other fraction pairs that work.
April 2015
Add these fractions
1 3

4 7
7 1

8 2
7 7

3 5
1 3

4 4
7 7

2 5
1 1

3 4
1 5

2 7
9 9

2 7
1 1

12 2
5 2

11 3
8 8

2 3
2 1

9 3
1 3

4 7
Answers
Multiply these fractions
1)
2)
 3)
 4)
 5)
 6)
 7)
 8)
 9)
 10)
 11)
 12)
 13)

1 3 3
 =
4 7 28
7 1 7
 =
8 2 16
7 7 49
 =
3 5 15
1 3 3
 =
4 4 16
7 7 49
 =
2 5 10
1 1 1
 =
3 4 12
1 5 5
 =
2 7 14
9 9 81
 =
2 7 14
1 1 1
 =
12 2 24
5 2 10
 =
11 3 33
8 8 64 32
=
 =
3
2 3 6
2 1 2
 =
9 3 27
1 3 3
 =
4 7 28











Add these fractions
1 3 19
 =
4 7 28
7 1 11
 =
8 2 8
7 7 56
 =
3 5 15
1 3
 =1
4 4
7 7 49
 =
2 5 10
1 1 7
 =
3 4 12
1 5 17
 =
2 7 14
9 9 81
 =
2 7 14
1 1 7
 =
12 2 12
5 2 37
 =
11 3 33
8 8 40 20
=
 =
3
2 3 6
2 1 5
 =
9 3 9
1 3 19
 =
4 7 28

Rows 5 and 8 have the same answer in both columns.
The numeratoris the same, and the sum of the 
denominator values equals the numerator value.
Numerical examples:
4 4 4 4
+ = ×
2 2 2 2
11 11 11 11
+
= ×
3 8
3 8
Algebraic example:
a c ad + bc a c ac
+ =
= × =
must have a = c = b + d
b d
bd
b d bd
April 2015