Rewriting addition problems

There are some important properties with whole numbers that you may have been using for a while, but maybe you never knew it.

 

Commutative Property

$a+b=b+a$a+b=b+a

The commutative property for addition states that if you take an additive expression like $12+7$12+7 that this is equivalent to $7+12$7+12.  We know that this makes sense as on a number line we can see that $12+7$12+7  and $7+12$7+12 result in the same answer.

 

Associative Property

$a+b+c=a+b+c$a+b+c=a+b+c

The associative property states that it doesn't matter how we group terms when we add them. For example, $2+3+4$2+3+4 is equivalent to $2+3+4$2+3+4. Again, we know this make sense because, when we plot them on a number line, we get the same answer.

 

Distributive Property

$a\times\left(b+c\right)=a\times b+a\times c$a×(b+c)=a×b+a×c

The distributive property is one that deals with groups.  We can say that $3$3 groups of $4$4 is the same as $3$3 groups of $3$3 and $3$3 groups of $1$1.

We can write this mathematically, remembering that groups of, is another way of representing multiplication.

$3\times4=3\times3+3\times1$3×4=3×3+3×1

With one more rearrangement, we can see that 

Mathematically we write this as

$3\times3+3\times1=3\times\left(3+1\right)$3×3+3×1=3×(3+1) $=$= $3\left(3+1\right)$3(3+1)

 

Let's run through some more examples now.

Examples

Question 1

 

Question 2

 

Question 3