Algebra2go®
Multiplying Fractions
Objective 1
Perform Multiplication with Fractions
Recall that multiplication represents
repeated addition of the same quantity.
1⋅ = 1+1+1+1+1+1 =
2 6 2 2 2 2 2 2
3
We can also write the 6 as an improper
6
fraction 1 and multiply. We will reduce by
dividing out a common factor of 2.
3
1 ⋅ 6 = 1 ⋅ 6 = 1 ⋅6 = 6 = 6 = 3 =
1
2 1 2 1 2⋅1 2 2
1
3
Notice how we multiply 21 to 61 . We multiply
straight across the numerators and straight
across the denominators.
Whenever we are multiplying fractions
together we can use a technique called “crosscancelling”, but it is very important that you
remember that this technique can only be used
when multiplying fractions together!
3
Page 1 of 3
1 ⋅6 = 1 ⋅6 = 3 =
2 1 21 1 1
3
Here it is understood that you are
dividing out a common factor of 2
before multiplying.
Algebra2go®
Dividing out common factors before
multiplying fractions together is very useful,
especially when you are working with large
numbers. Sometimes you will have to divide
out factors multiple times. Notice how the
following challenging problem is worked.
8
1
2
5
12
2
72 ⋅ 55 ⋅ 14 = 72 ⋅ 55 ⋅ 14 = 8 ⋅ 1 ⋅ 2 =
35 108 110 35 108 110 5 ⋅ 12 ⋅ 2
2
1
8=
⋅1⋅2
⋅1⋅1 2
2=
5 ⋅ 12 ⋅ 2 5 ⋅ 3 ⋅ 1 15
3
1
There are different ways of approaching the
problem above. But no matter how many steps
it takes you, we should all end up with the
same answer!
Answer the following homework questions.
In Exercises 1 – 9, multiply by first dividing out common factors.
8
1) ⋅ 3
6
2) ⋅ 8
3)
Page 2 of 3
1
2
4
3
40
3
⋅ 109
4)
5)
6)
⋅
7)
⋅
8)
24 9
6 8
15 5
10 30
16 x 20
5 12 y
⋅
9)
⋅
6 x 2 21a
7 a 2 12 x
x y
y x
ab c c
c a b
⋅
⋅ ⋅
Algebra2go®
Recall that exponents are used to represent
repeated multiplications.
Example 1: Simplify each expression.
a)
 1
− 
 2
2
−9
 1  1  1 
 −  −  −  −
 2  2  2 
−
1
8
−
1
 
3
2
b)
9 3  3 
1
1
 
2
2
 1  1 
  
 2  2 
1
9⋅ 9
1
1
4
⋅8
+  2 
3
2
⋅9
⋅8 +  23  23 ⋅9
⋅8
+
1
9
⋅9
Answer the following homework questions.
In Exercises 10 – 15, simplify each expression.
1
10)  
2
11)
Page 3 of 3
2
⋅8
2 7 
−  
3 6
12)
3
 
2
3
⋅
5
13) 16  
4
2
8
9
⋅
7
25
14)
3⋅
15)
1
− 
2
7
 
3
2
2
⋅ 215
⋅ 65 ⋅ 16