When adding real numbers with the same sign the sum will have the
same sign as the numbers added.
When adding real numbers with different signs you subtract the
lesser absolute value from greater one. The sum will then have the
same sign as the number with the greater absolute value.
There are a couple of properties of addition:
The additive commutative property tells us that the
order in which you add the numbers does not change the sum.
And the additive associative property tells us that it
also that the order in which we group three or more numbers does
not affect the sum.
The additive identity property tells us that the sum of
a number and 0 is always the number.
And the additive inverse property tells us that if you
add a number with its opposite you will always get 0
You know by now that
This means that subtracting 2 from 10 is the same as adding
negative 2 to 10. This is called the subtraction rule.
If you remember from pre-algebra the product of two real numbers
with the same sign is always positive
This also holds true if you multiply more than two numbers. If
you multiply with an odd number of negative numbers the product
will be negative
Whereas if you multiply with an even number of negative numbers
the product will be positive
As with addition there are a couple of properties of
multiplication as well
The multiplicative commutative property tells us the
same things as its additive counterpart. The product is not
affected by order in which you multiply the numbers
The same goes for the multiplicative associative
property. The product is not affected by how you group three
or more numbers.
The multiplicative identity property tells us that if
we multiply a number with 1 the product is always the number
The multiplicative identity of 0 tells us that the
product is always 0 when you multiply a number with 0
The last property of multiplication is the multiplicative
property of -1 and this property tells us that a product of a
number and -1 is the opposite of the number
Reciprocals are numbers that when multiplied have the product
These are also called multiplicative inverses. Zero does not
have a multiplicative inverse since everything multiplied with 0 is
0 as we could see above.
The inverse property of multiplication can be written
It can also be written as
The division rule tells us that to divide a number a
with a number b is the same as multiplying a with the
multiplicative inverse of b
Since we can express a division as a multiplication the sign
rules of multiplication holds true for division as well.
The quotient of two numbers with the same sign is positive
Whereas the quotient of two numbers with different signs is
The quotient of 0 and any nonzero real number is always 0
Since 0 does not have a multiplicative inverse you cannot divide
a number by 0.
Videolesson: Simplify the expression