7th math sub lesson 2

7th math sub lesson 2

by Mrs. McKinney

​Today, we will learn...

​ Know that the sign rules for division are the same as those for multiplication.

• Understand that division by zero is not allowed.

• Use quotients of integers to solve real-world problems.

• Write problems to model quotients of rational numbers.

• Use the associative property as a strategy to multiply and divide rational numbers.

• Use the commutative property as a strategy to multiply and divide rational numbers.

• Use the distributive property to multiply and divide rational numbers.

• Use multiple properties as strategies to multiply and divide four or more rational numbers.

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• ​

• ​These are from lesson 4.2 and 4.3 ,

• but don't worry if you are not there yet.

​review the youtube videos (search on youtube)

​PBS math club indie family

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MC Santi quotient product signs

Multiple Choice

5.8 * 4.3 =

• 24.94

• 480

• 1.35

• 2494

Multiple Choice

Now, we need to use both sets of rules:

multiply decimals and

multiply negatives

-5.8 * 4.3 =

• -24.94

• 480

• -1.35

• -1.5

Multiple Choice

-4/5 * -7/8 =

Now, use the rules to multiply fractions and to multiply negatives

• -28/40 = -14/20 = -7/10

• 28/40 = 14/20 = 7/10

• 0.914

• This problem is impossible since fractions cannot be negative.

Dividing negatives

​

​

​The rules are the same

​ as for multiplying negatives!

​

​same signs positive

​

​different signs negative

Multiple Choice

Remember, fractions are division problems

What is  5/5 ?

Any number divided by itself is...

• 1

• 5

• 1.5

• -5

Multiple Choice

These are the same signs, so...

-5 / -5 =

• 1

• -1

• 5

• -1.5

Multiple Choice

These all equal

-17 / -17

9/9

-42/-42

• -1

• 42, the meaning of life

• 1

• They all have different answers...tricky, tricky

​negative signs and fractions

​since a fraction is division,

​ the negative sign can go

​

​in front - 1/2

​

​on top -1 / 2

​

​or on bottom 1/ -2

​

​and they are the same

Since a negative divided by a negative is a positive,

​

​-1/-2 is +1/2 ... not the same !

Multiple Choice

Which one is different?

• -3/4

• 3/-4

• -3/-4

• - 3/4

Multiple Choice

Which one is different?

• -5/-6

• 5/6

• +5/6

• -5/6

​You can not divide by 0

​you can have zero as the first or top number

​ but not as the bottom second number

​

​0/5 is okay

​

​5/0 is NOT okay

​

​The reason is that you cannot put 5 things into zero groups...they are already sitting there in one group!

Multiple Choice

Which one is NOT okay?

It is undefined and will give you an error message if you try to put it into a calculator.

• 0/18

• 18/0

• 18+0

• 0/-18

​Now, back to some regular signed division

​same signs have a positive answer

​

​different signs have a negative

answer

​

​then, just divide normally

​

​-10 different signs

​

​ same signs ... 10 divided by 2 is always 5

Multiple Choice

-12  $$\div$$  3

• -4

• 4

• 9

• -9

Multiple Choice

-12 $$\div$$   -6

• -2

• -18

• 2

• -6

​properties

​Multiplication is repeated addition,

​so if a property works for addition it will work for multiplication

​

​commutative means switch the order

​

​associative means change the parentheses

​dividing fractions

​Remember to divide fractions

​ we Keep, Change, Flip

​

​in this example,

​ we keep the 1/2

​

​ change divide to multiply

​

​ and flip 1/4 to make 4/1

​

​Then, we multiply across !

Multiple Choice

$$\frac{1}{2\ }\div\ \frac{1}{4}$$  

• 4/2 = 2

• 2/4 = 1/2

• 1/8

• 2/6 = 1/3

Multiple Choice

$$-\frac{1}{2}\ \div\ \frac{1}{4}$$  

Now, we divide fractions normally then apply the dividing negatives rules to get

• -4/-2 = 2

• -1/6

• -4/2 = -2

• -2/6 = -1/3

Multiple Choice

$$-\frac{1}{3\ }\div\ -\ \frac{4}{5}$$  

• -5/12

• 5/12

• 4/15

• -4/-15