|
 The
fact that numbers can be broken into lesser numbers for calculating:
ex. 24 can be "broken" into 20
+ 4 for this problem
ex.(24 x 5)
= (20 + 4) x 5 = (20 x 5) + (4 x 5) |
|
The
Distributive Property of multiplication over addition means that
multiplying a sum by a number will give the same answer as
multiplying each addend by the number and then adding the products
together.
e.g. 2
x(5 + 6) = (2 x 5) + (2 x 6)
2 x 11 = 10 + 12
22 = 22
same
results |
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So how does one relate with the other numbers? |
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How does the Distributive Property help to multiply Mixed Numbers? |
Let's look at
an example: (8 x 3½)
|
First get
ready to use the Distributive Property by "breaking down" the 3½
into
3 + ½ |
(8 x 3½) = 8 x (3
+ ½) |
|
Then
distribute (give) the 8 to both the 3 and the ½ |
8 x (3 +
½) = (8 x 3) + (8 x ½) |
|
Then find the
product inside both parentheses and add those products. |
(8 x 3)
+ (8 x ½) =
24
+ 4 =
28 |
Let's look at
another example: (6 x
4¾)
|
Break down the 4¾ to 4
+ ¾ |
(6 x 4¾) = 6 x (4
+ ¾) |
|
Distribute (give) the 6 to both |
6 x (4 +
¾) = (6 x 4) + (6 x ¾) |
|
Find the product inside
both parentheses and add. |
(6 x 4) +
(6 x ¾)=
24 +
18/4 =
24
+
4 2/4 =
24 +
4 ½ =
28½ |
To
summarize: sometimes using the distributive property makes multiplying
easier. Remember the following steps:
- Break down one of the
factors
- Then distribute
The Distributive Property to find the products.
- Then add the two
products together.
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