Download Math 8 notes 3.5 key

Math 8 Unit 3: Operations with Fractions.
Name:_________________
Date:________________
Block:__________
Lesson Notes: 3.5: Dividing whole numbers and Fractions. (With Models)
The Dividing procedure is a mathematical process to split thing up equally,
and the logic behind dividing integers is very much the same as dividing
fractions.
a) Use a number line to find each quotient. (How many equal shares of _____ in ____?)
1) 2 ÷
3) 3 ÷
1
3
1
3
5) 4 ÷ 2
5
7)
7
5
÷2
2) 2 ÷
2
3
4) 3 ÷
2
3
6)
8)
4
5
÷4
7
÷4
5
b) Use fraction circles to illustrate the quotient.
1)
3)
4÷
4÷
1
3
2
3
2)
3÷
3
5
4) 5 ÷
3
4
Before we start our next method, we need to review some of the concepts which
are true to integers as well as to fractions.
Concept 1) dividing and multiplying to its reciprocal.
Example 1)
If a number, say 10 is divided by 2, it means 10 is split into two equal halves.
Did you notice that divided by 2 and split into two halves give you the
same result.
10 ÷ 2
Example 2)
If 21 is divided by 7, it means 21 is split into seven equal parts.
Did you notice that divided by 7 and split into 7 equal parts give you the same
result.
21 ÷ 7
Remember that
Practice:
Find the reciprocal of the following numbers.
Concept 2) Divided by itself.
Example 3) If 4 is divided by 4, you get _______.
Example 4) If 137 is divided by 137, answer is ______.
Ok, we got the idea of a whole number divided by itself, but how about using
fractions to divide itself?
Example 5)
Example 6)
Example 7)
***** Conclusion:
When dividing fractions, it is easier to multiply by the
reciprocal of the divisor.
1)
2)
In-class Practice.
Now we are ready for the division between a whole number and a fraction.
1)
Let us use the number line to find out.
Answer: __________
___________________________
2)
Let us use the circle model to find the answer.
Answer:_______
3)
It means how much would you get from dividing a half into 3 equal parts?
Let us use the bar model to find out.
Answer:__________________