Dividing Signed Numbers © Math As A Second Language All Rights Reserved next #9 Taking the Fear out of Math + 6 ÷ - 2

If we use our “unmultiplying” model for division, the division of signed numbers almost becomes an anecdotal footnote to our discussion of multiplication of signed numbers. next © Math As A Second Language All Rights Reserved For example, consider a problem such as - 12 ÷ - 3. It means that we want to find the number which when multiplied by - 4 yields - 12 as the answer.

In terms of a “fill in the blank” question, we are saying that the question… next © Math As A Second Language All Rights Reserved - 12 ÷ - 4 = ____ next … is equivalent to the problem… - 4 ×____ = - 12

Recalling that when we multiply two signed numbers, we multiply the magnitudes to get the magnitude of the product and we multiply the signs to get the sign of the product, we see that we have to multiply 4 by 3 to obtain 12 and we have to multiply negative by positive to obtain negative. next © Math As A Second Language All Rights Reserved Hence, we conclude that we must multiply - 4 by + 3 to obtain - 12 as the product. next

Since - 4 ×____ = - 12 is a simply a restatement of - 12 ÷ - 4 = ____ we see that… © Math As A Second Language All Rights Reserved - 12 ÷ - 4 = + 3 next The fact that we were dealing with the specific numbers - 12 and - 4 is just a special case of what happens when we divide one negative number by another.

Specifically, if we concentrate just on the signs, the fact that… © Math As A Second Language All Rights Reserved positive × negative = negative next …means in terms of “unmultiplying” that… positive = negative ÷ negative

In summary when we divide two negative numbers the sign of the quotient is positive and the magnitude is the quotient of the two magnitudes. next © Math As A Second Language All Rights Reserved

In a similar way the fact that… next © Math As A Second Language All Rights Reserved next means that… negative × negative = positive negative = positive ÷ negative

More concretely… next © Math As A Second Language All Rights Reserved next + 6 ÷ - 2 = ____ means the same thing as… - 2 ×____ = + 6

We have to multiply 2 by 3 to get 6 as the magnitude and we have to multiply negative by negative to get positive. That is… next © Math As A Second Language All Rights Reserved next or… - 2 × - 3 = ÷ - 2 = - 3

next © Math As A Second Language All Rights Reserved Summary Dividing Signed Numbers The magnitude of the quotient is the quotient of the two magnitudes. next For example, the magnitude of + 12 ÷ + 3, + 12 ÷ - 3, - 12 ÷ + 3 and - 12 ÷ - 3 is 4 because in each case the magnitudes of the two numbers are 12 and 3 respectively.

© Math As A Second Language All Rights Reserved In short, notice that the magnitude of the quotient does not depend on the signs of the factors. next The sign of the quotient of two numbers is positive, if they have the same sign. For example… + 12 ÷ + 3 = ÷ - 3 = + 4 next

© Math As A Second Language All Rights Reserved The sign of the quotient of two numbers is negative, if they have the different signs. For example… + 12 ÷ - 3 = ÷ + 3 = - 4 next

In the next presentation, we will begin a discussion of whole number exponents. © Math As A Second Language All Rights Reserved Whole Number Exponents