departamento de matemáticas regla de 3
TRANSCRIPT
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Maths
&
Cooking
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Paella recipe for six people:
200 grammes of squid
300 grammes of prawns
½ kilo of clams
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¼ kilo of crabs
¼ kilo of mussels
600 grammes of rice
2 ½ cups of water
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2 ripe tomatoes
2 cloves of garlic
1 small onion
Parsley
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1 green pepper
Saffron
800 grammes of chicken
Salt
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Ingredients For six people For twelve people Division
squid 200 grammes 400 grammes 400:200 = 2
prawns 300 grammes 600 grammes 600:300 =2
clams ½ kilo 1 kilo 1 : ½ = 2
crabs ¼ kilo ½ kilo ½ : ¼ =2
mussels ¼ kilo ½ kilo ½ : ¼ =2
rice 600 grammes 1200 grammes 1200:600 = 2
cups of water 2 ½ 5 5 : 2 ½ = 2
12 people : 6 people = 2SPREADSHEET
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Ingredients For six people For nine people
squid 200 grammes 200 *1.5=300grammes
prawns 300 grammes 300*1.5=450 grammes
clams ½ =0.5 0.5*1.5=0.75 =3/4 kilo
crabs ¼ =0.25 0.25*1.5=0.375 =3/8 kilo
mussels ¼ =0.25 0.25*1.5=0.375 =3/8 kilo
rice 600 grammes 600*1.5=900 grammes
cups of water 2 ½=2.5 2.5*1.5=3.75
9 people : 6 people = 1.5SPREADSHEET
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Other examples of direct Other examples of direct proportionalityproportionality If an object travels at a constant speed, then
the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.
On a map drawn to scale, the distance between any two points on the map is proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.
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THE RULE OF THREE THE RULE OF THREE (Direct)(Direct)
First, write the titles of the two magnitudes
Second, place the quantities you know in their correspondent column
Third, write an x for the unknown quantity.
Last, multiply in cross, make equal the terms, and find the x.
6
4 0,5 kilo
x
TAPS
INVERSE
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People Sweets24 2
12 46 8
Number of sweets in the bag= 48
Inverse ProportionalityInverse Proportionality
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Inverse ProportionalityInverse Proportionality
Some examples:
Magnitude A Magnitude B Proportionality constant
speed time spent traveling
distance of the journey
number of people working
number of working days
working days for an only worker
price of sweets number of sweets I can buy
my money
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Inverse ProportionalityInverse Proportionality(24 very small prawns in the paella)(24 very small prawns in the paella)
For four people
For six people
For seven people
Six prawns for each one
Four prawns for each one
Three prawns and a half for each one (aproximately)
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THE RULE OF THREE THE RULE OF THREE (Inverse)(Inverse)
First, write the titles of the two magnitudes
Second, place the quantities you know in their correspondent column
Third, write an x for the unknown quantity.
Last, multiply in line, make equal the terms, and find the x.
4 6
x8
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A summertime problemA summertime problemNow it’s noon. It’s boiling.The pool is empty!
So, we want to fill it.
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At the poolAt the poolTwo taps
Tap A fills the pool in 3 hours
3 hours
Tap B fills the pool in 6 hours
6 hours
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At the pool (and after, the At the pool (and after, the paella)paella)
So, if in an hour, we fill a half of the pool, it’s evident that we will need two hours to fill completly the pool.
Solution: 2 hours later, at 2 P.M.