# Compare by ewghwehws

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```									 Lesson 4.7

Double Operators
Compare

12 + [5] = 17 with                12 + [5 + 3] = 20
Increase of 5                     The increase of 5 has
been increased by 3.

When an increase is increased,
17  20              the effect is an increase.

“If you receive more, you will have more.”

+ (+ a) = + a
Compare

12 + [5] = 17 with                12 + [5 – 3] = 14
Increase of 5                     The increase of 5 has
been decreased by 3.

When an increase is decreased,
17  14              the effect is a decrease.

“If you receive less, you will have less.”
+ (– a) = – a
Compare

12 – [5] = 7         with         12 – [5 + 3] = 4
Decrease of 5                     The decrease of 5 has
been increased by 3.

When a decrease is increased,
7  4                the effect is a decrease.

“If you give more away, you will have less left.”
– (+ a) = – a
Compare

12 – [5] = 7         with         12 – [5 – 3] = 10
Decrease of 5                     The decrease of 5 has
been decreased by 3.

When a decrease is decreased,
7  10              the effect is an increase.

“If you give less away, you will have more left.”
– (– a) = + a
Summary of the Sign Operators

+ ( ) changes a number into an increase: + (b) = + b
– ( ) changes a number into a decrease: – (b) = – b

+ ( ) leaves an increase or a decrease the same.
+ ( + b ) = + b and       +(–b) = –b
– ( ) changes an increase into a decrease and a decrease into an
increase.
– ( + b ) = – b and – ( – b ) = + b
Recall:   – ( ) is called the opposite operator.

What happens when a sign operator is applied to an expansion or a
contraction?
When a sign operator is applied to an expansion or a contraction, we
get a double operator.

First      Second      Double
Operator   Operator    Operator

5( )        +( )        + 5( )        an increase of 5 times something

5( )        –( )        – 5( )        a decrease of 5 times something

( )                      ( )
+( )        +             an increase something divided by 2
2                        2
( )                        ( )
–( )        –             a decrease something divided by 2
2                          2

The + ( ) and the – ( ) determine the kind of change,
( )
while the 5( ) and the         effect the size of the change.
2
The sign operators distribute over sums and differences.

28 + (6 – 4) = 28 + 6 – 4

28 – (6 – 4) = 28 – 6 + 4

28 – (6 + 4) = 28 – 6 – 4

Double operators also distribute over sums and differences.

28 + 3(6 – 4) = 28 + 18 – 12

28 – 3(6 – 4) = 28 – 18 + 12

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