Download Properties: Homework Guide When you write your properties I want

Properties: Homework Guide
When you write your properties I want you to explain how you knew the answer.
Here are examples of how I would describe some properties and at the end there is
an explanation about the term reciprocal.
1) x + 2 = 2 + x
You write: This is the commutative property of addition because we are changing
the order that we add the terms x and 2 in. We are allowed to do this because the
result will be the same either way.
2) 3y=y×3
You write: This is the commutative property of multiplication because we are
changing the order that we multiply the factors 3 and y in. We are allowed to do this
because the result will be the same either way.
3) 3 + (d + 8) = (3 + d) + 8
You write: This is the associative property of addition because the order of the
terms we are adding stays the same but the grouping symbols move. We are allowed
to do this because the result will be the same either way.
4) (u×5)×r=u(5×r)
You write: This is the associative property of multiplication because the order of the
factors stays the same but the grouping symbols move. We are allowed to do this
because the result will be the same either way.
5) 7(3 + 6) = 21 + 42
You write: This is the distributive property because seven is being distributed
(multiplied) over 3 + 6 resulting in 21 + 42.
6) w + (5 – 5) = w
You write: w + 0 = w
Because 5 – 5 = 0, we know that this is the identity property of addition. If
we add zero to any number the result is the same number.
c
7) 8( )=8
c
You write: 8(1) = 8
c
Because ( ) equals 1, we know that this is the identity property of
c

multiplication. Any number times one equals the same number.
8) 8 + (-8) = 0

You write: This is the inverse property of addition because we are adding opposite
numbers and the result is zero.
1
=1
6
You write: This is the inverse property of multiplication because we are multiplying
1
a number(6) and its reciprocal( ) and the result is one.
6
9) 6 ×

Reciprocal: The reciprocal of a whole number is always one over that number. For
1
example the reciprocalof 12 is .
12
The reciprocal of a fraction has the numerator and the denominator
m
4
switched. For example the reciprocal of
is .
4
m

These are both examples of reciprocals because when you multiply them they both
result in one.
1 12 1 12  1 12 


1
12 ×
= 
12 1 12 1  12 12


m
4
m4 m4 m 4

  11 1
and
×
=
4
m 4m m4 m 4

Multiplying reciprocals with a result of one is the inverse property of multiplication.

 
Try to write sentences about these properties!
1) x + (-x) = 0
2) c + (2– 2) = c
3) (e × 3) × 2=e(3 × 2)
1
4) 7 × = 1
7
5) 3 + 2 = 2 + 3
6) 1 + (2 + 3) = (1 + 2) + 3
7) 4 × 5 = 5 × 4

x
8) 9( )=9
x
9) 4(3 + w) = 12 + 4w
