Whole Number Multiplication of Fractions Multiplying by a whole number. To multiply a fraction by a...

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Whole NumberMultiplication of Fractions
Multiplying by a whole number.To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
34
5 x =Example 1:
154
3=34
To see why this works consider the diagrams below.
Multiplication of Fractions
Multiplying by a whole number.
34
5 x =Example 1:
154
3=34
To see why this works consider the diagrams below.
1
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
34
5 x =Example 1:
154
3=34
To see why this works consider the diagrams below.
1 2
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
154
3=34
1 2 3 = 3 34
34
To see why this works consider the diagrams below.
34
5 x =Example 1:
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
1
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
1 2
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
1 2 3
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
1 2 3 4
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Multiplication of Fractions
Multiplying by a whole number.
23
8 x =Example 2:
163
5=13
To see why this works consider the diagrams below.
1 2 3 = 5 13
134 5
To multiply a fraction by a whole number simply multiply the numerator by the number then simplify the resulting fraction if necessary.
Questions1
34
3 x =23
2 x =35
5 x =
Answer the following questions:
56
4 x =45
6 x =17
8 x =
310
9 x =45
12 x =23
15 x =
142 1
31 3
4 54
171
7102 3
59 10
263
13= 3
a b c
d e f
g h i
Unit FractionMultiplication of FractionsMultiplying by a unit
fraction.Before considering multiplication of fractions it is important for you to understand that in mathematics of and x (multiplication) mean the same thing.To see why this is the case consider the set of 6 discs shown below:
2 x
If you had this set of discs 2 times you would have a total of 12 discs.
= 12
Or to rephrase this if you had 2 of these sets of discs you would have 12 discs
2 of = 12
Multiplication of Fractions
Multiplying by a unit fraction.To multiply a fraction by a unit fraction simply multiply out the numerators and denominators then simplify the resulting fraction if necessary
= 220
=1
1025
Example 1:
14
x
To see why this is using a diagram consider the following:
25
Taking a ¼ of 2/5 by dividing it by 4
220
110
Multiplication of Fractions
Multiplying by a unit fraction.
To multiply a fraction by a unit fraction simply multiply out the numerators and denominators then simplify the resulting fraction if necessary
= 524
58
Example 2:
13
x
To see why this is using a diagram consider the following:
58
Taking a 1/3 of 5/8 by dividing it
by 3
524
Questions2
Answer the following questions:
16
12
=13
x 23
=14
x 57
=12
x
34
=15
of 16
=16
x 14
=12
of
45
=14
x 38
=18
of 23
=110
x
212
=16
514
320
136
18
420
=15
364
230
=1
15
a b c
d e f
g h i
General FractionMultiplication of Fractions
Multiplying by a general fraction.
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary
= 612
=12
34
Example 1:
23
x
It is often more efficient to cancel highest common factors “top and bottom” and then “multiply out” to arrive at the answer directly.
12
=34
23
x1
21
1
Multiplication of Fractions
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary
= 612
=12
34
Example 1:
23
x
To see why this works consider the diagram below.
Taking 2/3 of 3/4 by dividing it into thirds
34
{34
23
of = 612
=12
Multiplying by a general fraction.
Multiplication of Fractions
To multiply any two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary
= 40180
=29
815
Example 2:
512
x
Using the method of cancelling highest common factors is very useful in this more awkward case.
29
1
33
28
155
12x =
Multiplying by a general fraction.
3 FractionsMultiplication of Fractions
To multiply more than two fractions simply multiply out the numerators and denominators then simplify the resulting fraction if necessary. Cancelling common factors “top and bottom” is advisable.
1
2
1
2
Multiplying more than two fractions.
49
310
Example 1:
58
x x1
3
112
=
89
712
Example 2:
35
of of1445
=1
3
2
3
Questions3
Answer the following questions: (cancelling is strongly advisable!)
49
56
23
x 45
x 49
58
x 310
x
56
34
of 89
of 320
78
x 56
x
78
67
x 89
x 56
1415
of 928
of
112
59
764
23
14
a b
c d
e f
Mixed NumbersMultiplication of Fractions
To multiply fractions involving mixed numbers, rewrite the mixed numbers as improper fractions and proceed as usual.
Multiplying mixed numbers.
Example 1:
58
x2 67
=218
x 67
= 94
14
2=1
3 3
4
Example 2:
=203
x 92 30=
1
10 3
1
23
x6 12
4
Question4
Answer the following questions:
a b
c d
e f
23
x 38
2 3 12
x 14
1 2
9
16
x 15
4 3 34
of 23
6
35
of 518
9 5 110
x 29
8 1
13
13 12
4
910
9
38
3
23
50
Worksheet 1
34
3 x =23
2 x =35
5 x =
Answer the following questions:
56
4 x =45
6 x =17
8 x =
310
9 x =45
12 x =23
15 x =
a b c
d e f
g h i
Worksheet 2
Answer the following questions:
12
=13
x 23
=14
x 57
=12
x
34
=15
of 16
=16
x 14
=12
of
45
=14
x 38
=18
of 23
=110
x
a b c
d e f
g h i
Worksheet 3
Answer the following questions: (cancelling is strongly advisable!)
56
23
x 45
x 49
58
x 310
x
56
34
of 89
of 320
78
x 56
x
78
67
x 89
x 56
1415
of 928
of
a b
c d
e f
Worksheet 4
Answer the following questions:
a b
c d
e f
23
x 38
2 3 12
x 14
1 2
16
x 15
4 3 34
of 23
6
35
of 518
9 5 110
x 29
8 1