1. 6.4 Introduction to representations of multiplying and dividing fractions

2. Introduction Boxes can be split into all kinds of sections
Introduction Boxes can be split into all kinds of sections. Can you tell what fraction is shaded in each box?

3. To multiply, put together like this
To multiply, put together like this! Vertical is first, Horizontal is last! Order does not matter with multiplication, but it sure does with division! So we are going to always do it like this.
2/3 x 1/2
Tada!
The product
is 2/6 or 1/3!
The denominator is
all the sections
and the numerator is
the overlap!
Now Watch!

4. We can check this! ¼ x 3/5 is 1 x 3= 3 4 x 5= 20 The product is 3/20
Try these! ¼ x 3/5
We can check this!
¼ x 3/5 is 1 x 3= 3
4 x 5= 20
The product is 3/20

5. Do you think you can? 5/6 x 1/4
5 x 1 = 5
6 x 4 = 24
The product is 5/24

6. Try another? 5/8 x 7/12
Check!
5 x 7 = 35
8 x 12 = 96
The product is 35/96

7. Try another? 1/4 x 1/2
Check!
1 x 1 = 1
4 x 2 = 8
The product is 1/8

8. Now
for
DIVISION!

9. When using division models, order matters.
The first bar is the dividend and the second bar is the divisor.
This means how many will fit into
2 5
11 12
11 12
2 5
÷ Same Change Flip x = =2 7 24
2 5

10. Now it’s time to set up our notebook and practice!
6.4
The student will demonstrate multiple representations of multiplication and division of fractions

11. 6.4 Directions Multiplication
Pg 13
6.4 Directions Multiplication
First fraction square is vertical. Overlap the second fraction square horizontally.
Multiplication-
count all the sections once squares are overlapped. This is the denominator.
Count the sections where the colors or patterns combine. This is the numerator.
Example ½ x ¼
1 section overlaps
8 sections total
Product is 1/8
Check- ½ x ¼ =1/8
Vocabulary pg. 14
mixed number
SOL 6.4/6.6
A numerical value that combines a whole number and a fraction EX- 2 ¾
addition
The act or process of combining numerical values, so as to find their sum
simplest form
A fraction is in simplest form when the greatest common factor of the numerator and denominator is 1.
sum
An amount obtained as a result of adding numbers EX 2+2=4 4 is the sum
simplify
To reduce the numerator and the denominator in a fraction to the smallest form possible. To divide the numerator and denominator by the GCF is simplifying a fraction.
subtraction
The arithmetic operation of finding the difference between two quantities or numbers
LCD
difference
The least common multiple of the denominators of two or more fractions. Example: 6 is the least common denominator of 2/3 and 1/6.
An amount obtained as a result of subtracting numbers EX 5-3= is the difference
reciprocal
estimate
Any two numbers whose product is 1.
To make an approximate or rough calculation, often based on rounding
Example: ½ and 2 are reciprocals because ½ X 2 = 1product
An amount obtained as a result of multiplying numbers
division
The operation of determining how many times one quantity is contained in another; the inverse of multiplication.
quotient
An amount obtained as a result of dividing numbers EX-12 ÷ 2= six is the quotient
numerator
The expression written above the line in a fraction EX- ½ One is the numerator
denominator
The expression written below the line in a fraction that indicates the number of parts into which one whole is divided. EX- ½ is the denominator
improper fraction
A fraction in which the numerator is larger than or equal to the denominator. The value of an improper fraction is greater than or equal to one. EX- 14/5

12. Dividend- first fraction bar Divisor- second fraction bar
Pg __
6.4 Directions for division .
Example ½ ÷ ¼
same change flip
x = = 2
Dividend- first fraction bar
Divisor- second fraction bar
Quotient- the answer
FLIP is the reciprocal
Pg __ Practice Multiplication
Draw a box. When you shade use stripes.
Split vertically into 3 sections. Shade 1 section.
Split horizontally into 2 sections. Shade one.
This is 1/3 x ½ = 1/6
Practice Division
___ ÷ ___
___ x ___ = ___