Fraction Demonstrations

2 ÷ 3

1 2

Divide Each of these by 3

2 ÷ 3

TAKEA

THIRDOF

WHATHAS

BEENSLICED

2 ÷ 3

2 ÷ 3=2/3

PUT THESE

TOGETHER

Number Line Model of 23

2/3 equals 8/12

=

3 x 1/3

ONE

TWO

3 =1

7 x 1/5COUNT THE GREEN

FIFTHS!

=1 2/5

2/3 x 4ONE

TWO

THREE

FOUR8/3

1/3 x 1/2 Overlap is 1 of 6 rectangles

=1/6

2/3 x 4/5 Overlap is 8 of 15 rectangles

=8/15

=(3 + 1/3) x (4 + 1/7) 3 x 4=12

3 x 1/7=3/71/3 x 4=4/3

1/3 x 1/7=1/21

3 1/3 x 4 1/7

We can keep track of total down here!

3 1/3 x 4 1/7 =12 + 4/3 + 3/7 + 1/21

5 68 9

10 11 1213 14 15

16 17 18

19 20 21

A third is 7 small rectangles so 4/3 is 1

whole and 7 rectangles

A seventh is 3 small rectangles so we need 9

WE WILL MAGNIFY A BLUE

SQUARE IN ORDER TO COMBINE

FRACTIONAL PARTS

3rds by 7ths gives 21sts!

2 3147

=13 17/21

3 1/3 x 4 1/7 =13 17/21

4 1/7 ONCETWICETHRICEA 3rd More

I have 2 feet of board but I only need ¼ foot. What fraction of the board am I using?

2 FEET OF BOARD

¼ foot

I have 2 feet of board but I only need ¼ foot. What fraction of the board am I using?

1 2 3 4 5 6 87

So you are only using an 8th of the board!

¼ ÷ 2 =1/8

I want to divide 1/4th of a Pie among two people. How much does each person get?

1/8th 1/8th

I get a Piece!

ME TOO!

¼ ÷ 2 =1/8

21/2 ÷ 1/4

4 4 2

=10

Context for

A tank leaks gallons of water every 15 minutes. What is the rate of leakage in gallons per hour?

Are ratios just like Fractions?

Combining Ratios

• Bob Mows of a lawn in 15 minutes• Sam Mows of a lawn in 45 minutes IF they only have one lawn mower and each needs to rest after their stint, what is their rate per hour?

Combining Ratios

THIS IS 1 LAWN per HOURYOU CAN’T DO THAT WITH

FRACTIONS!

Combining Ratios

• Bob Mows of a lawn in 15 minutes• Sam Mows of a lawn in 45 minutes IF they each have one lawn mower and they can mow at this rate all day long then how do we see their combined rate?

+ = = 2 Lawns Per Hour

2/3 ÷ 2/6

1

= 2

1

Demo 3/4 ÷ 2/3

1 Unit 3/4 Unit 2/3 Unit We will stuff the yellow into the blue!

Method of Gupta /Lamberg

Stuffed in already!

Waiting to stuff

Extra Capacity Unused

Stuff complete Goes One time i.e. 8 green

Rectangles!

=1 1/8=9/8

Unused Capacity

1 left over

This is 8GREEN

rectangles

5/4 ÷ 4/5

1 Unit 5/4 4/5

How many times does yellow go into the 5/4 Blue Unit?

Goes 1 time which takes 16

rectangles

The result isOnce and 9 more squares

Method of Gupta /Lamberg

1234

5 6 7 8 9