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# Departamento de matemáticas regla de 3

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• It may not be 24 prawns in a quarter kilo, but less.
• ### Departamento de matemáticas regla de 3

1. 1. Maths & Cooking
2. 2. Paella recipe for six people: 200 grammes of squid 300 grammes of prawns ½ kilo of clams
3. 3. ¼ kilo of crabs ¼ kilo of mussels 600 grammes of rice 2 ½ cups of water
4. 4. 2 ripe tomatoes 2 cloves of garlic 1 small onion Parsley
5. 5. 1 green pepper Saffron 800 grammes of chicken Salt
6. 6. 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 = 2 SPREADSHEET
7. 7. 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 = 1.5 SPREADSHEET
8. 8. Other examples of direct proportionalityOther examples of direct proportionality  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.
9. 9. THE RULE OF THREE (Direct)THE RULE OF THREE (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 TAPSINVERSE
10. 10. People Sweets 24 2 12 4 6 8 Number of sweets in the bag= 48 Inverse ProportionalityInverse Proportionality
11. 11. 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
12. 12. 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)
13. 13. THE RULE OF THREE (Inverse)THE RULE OF THREE (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
14. 14. A summertime problemA summertime problem Now it’s noon. It’s boiling. The pool is empty! So, we want to fill it.
15. 15. At the poolAt the pool Two taps Tap A fills the pool in 3 hours 3 hours Tap B fills the pool in 6 hours 6 hours
16. 16. At the pool (and after, theAt 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.