Fraction Demonstrations. 2 ÷ 3 1 2 Divide Each of these by 3.
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Transcript of Fraction Demonstrations. 2 ÷ 3 1 2 Divide Each of these by 3.
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