1.9 Properties of real numbers  (Page 3/10)

Notice that in each case, the missing number was the reciprocal    of the number!

We call $\frac{1}{a}$ the multiplicative inverse    of a . The reciprocal of $a$ number is its multiplicative inverse. A number and its reciprocal multiply to one, which is the multiplicative identity. This leads to the Inverse Property of Multiplication that states that for any real number $a,a\ne 0,a·\frac{1}{a}=1.$

We’ll formally state the inverse properties here:

Use the properties of zero

The identity property of addition says that when we add 0 to any number, the result is that same number. What happens when we multiply a number by 0? Multiplying by 0 makes the product equal zero.

What about division involving zero? What is $0÷3?$ Think about a real example: If there are no cookies in the cookie jar and 3 people are to share them, how many cookies does each person get? There are no cookies to share, so each person gets 0 cookies. So,

We can check division with the related multiplication fact.

So we know $0÷3=0$ because $0·3=0.$

Now think about dividing by zero. What is the result of dividing 4 by 0? Think about the related multiplication fact: $4÷0=?$ means $?·0=4.$ Is there a number that multiplied by 0 gives 4? Since any real number multiplied by 0 gives 0, there is no real number that can be multiplied by 0 to obtain 4.