Division of Integers

Division of Integers

October 26, 2020

Multiple Select

Review: Check off each multiplication rule that we discussed last week.

• negative x negative = negative

• positive x negative = negative

• negative x negative = positive

• positive x positive = positive

Learning Targets

• I can recognize that division is the reverse process of multiplication and that integers can be divided as long as the divisor is not 0 with 85% mastery.

• I can follow SOAR norms and STAR expectations during virtual learning with 100% mastery.

Open Ended

What is the definition of quotient?

What is the relationship between multiplication and division? What do you notice about the equations below? 

•  $6\times4=24$  
  

•  $4\times6=24$  
  

•  $24\div4=6$  

•  $24\div6=4$  

Review our Multiplication Rules

•  $6\times4=24$  (positive x positive = positive )

•   $6\times\left(-4\right)=-24$  (positive x negative = negative)

•  $-6\times\left(-4\right)=24$  (negative x negative = positive)

Poll

Based on our conversation about the relationship between multiplication and division facts, do you think the rules for multiplication are the same for division?

• Yes, the rules are the same.

• No, the rules are different.

Yes the rules are the same! Dividing Integers Rules

•  $positive\div positive=positive$  

•  $positive\div negative=negative$  

•  $negative\div positive=negative$  

•  $negative\div negative=positive$  

• SAME SIGNS give you a POSITIVE ANSWER!

• DIFFERENT SIGNS give you a NEGATIVE ANSWER!

Dividing Integers Examples

•  $24\div6=4\$   $\left(positive\div positive=positive\right)$  

•  $24\div\left(-6\right)=-4\ \left(positive\div negative=negative\right)$  

•  $-24\div6=-4\ \left(negative\div positive=negative\right)$  

•  $-24\div\left(-6\right)=4\ \left(negative\div negative=positive\right)$  

Multiple Choice

 $35\ \div\ \left(-5\right)\ =$  

• 7

• -7

Multiple Choice

 $-35\div\left(-5\right)=$  

• 7

• -7

Multiple Choice

 $-35\div5=$  

• 7

• -7

Division can lead to a Rational Answer

• Sometimes when we divide two integers, we will end up with a rational number (fraction or decimal) as our answer.

• Fun fact: the / in a fraction is another symbol for division.

•  $For\ example,\ \frac{1}{4\ }\ is\ the\ same\ as\ 1\div4.$  

•  $Another\ example,\ -\frac{1}{2\ }\ is\ the\ same\ as\ -1\div2\ or\ 1\div\left(-2\right)$  

Multiple Choice

 $2\div\left(-3\right)=$  

•  $\frac{2}{3}$  

•  $-\frac{2}{3}$  

Multiple Choice

 $-2\div\left(-3\right)$  

•  $\frac{2}{3}$  

•  $-\frac{2}{3}$  

Multiple Choice

 $-2\div3$  

•  $\frac{2}{3}$  

•  $-\frac{2}{3}$