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Ratio

Ratio. Worksheet 3. 1. On a farm, the ratio of the number of ducks to the number of goats is 2:3. If there are a total of 192 legs, find the number of goats on the farm. . Lets’ put the ratio in a model. 2 legs. 2 legs. Ducks Goats. 192 legs. 4 legs. 4 legs. 4 legs.

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Ratio

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  1. Ratio Worksheet 3

  2. 1. On a farm, the ratio of the number of ducks to the number of goats is 2:3. If there are a total of 192 legs, find the number of goats on the farm. Lets’ put the ratio in a model 2 legs 2 legs Ducks Goats 192 legs 4 legs 4 legs 4 legs Since ducks have 2 legs and goats have four legs each, let’s put them in the model. Now that the units are represented correctly, 4 units of ducks’ legs + 12 units of goats’ legs = 192 Can you calculate the number of legs per unit? Calculate the total number of legs for the ducks. Can you find how many ducks there are? Calculate the total number of legs for the goats. Can you find how many goats there are?

  3. 2. The ratio of the number of guavas to the number of papayas in Basket A and B are 2:3 and 4:5 respectively. Both baskets have the same number of guavas. When 40 papayas are transferred from Basket B to Basket A, the ratio of the number of guavas to the number of papayas becomes 2:5. What is the total number of fruits in the two baskets? Basket A Basket B = Guavas Papayas

  4. 2. The ratio of the number of guavas to the number of papayas in Basket A and B are 2:3 and 4:5 respectively. Both baskets have the same number of guavas. When 40 papayas are transferred from Basket B to Basket A, the ratio of the number of guavas to the number of papayas becomes 2:5. What is the total number of fruits in the two baskets? Basket A Basket B = Guavas Papayas Let’s so the same for the units of papayas in Basket A Let’s make the units of guavas in Basket A be the same as the number of units in Basket B

  5. 2. The ratio of the number of guavas to the number of papayas in Basket A and B are 2:3 and 4:5 respectively. Both baskets have the same number of guavas. When 40 papayas are transferred from Basket B to Basket A, the ratio of the number of guavas to the number of papayas becomes 2:5. What is the total number of fruits in the two baskets? Basket A Basket B Guavas Papayas Guavas Papayas After 40 papayas were moved from Basket B to A, the ratio of Guavas to Papayas in A is 2:5 or 4:10

  6. 2. The ratio of the number of guavas to the number of papayas in Basket A and B are 2:3 and 4:5 respectively. Both baskets have the same number of guavas. When 40 papayas are transferred from Basket B to Basket A, the ratio of the number of guavas to the number of papayas becomes 2:5. What is the total number of fruits in the two baskets? Basket A Basket B Guavas Papayas Guavas Papayas Can you find how many units represents the 40 papayas that were moved? Find the value of 1 unit. What is the total number of units? Can you solve the sum?

  7. 3. A box contained 50¢ coins and 20¢ coins in the ratio 2:3. When I took out four 50¢ coins, exchanged them for 20¢ coins, and then put the money into the box, the ratio became 2:7. Find the sum of money in the box. 50 ¢ 20 ¢ When we change 4-50¢ coins to 20¢ coins, how many coins would that be? 50 ¢ 20 ¢ Less 4 coins Add 10 coins

  8. 3. A box contained 50¢ coins and 20¢ coins in the ratio 2:3. When I took out four 50¢ coins, exchanged them for 20¢ coins, and then put the money into the box, the ratio became 2:7. Find the sum of money in the box. Less 4 coins Add 10 coins Let’s make the ratio of the 50¢ coins before and after have a difference of 4, and the same goes for the 20¢ coins Notice, the difference of the units is also the same as the number of coins? Notice, the difference of the units is also the same as the number of coins. Can you find out the amount? 50 ¢ 20 ¢ Before 2 : 3 = 12 : 18 After 2 : 7 = 8 : 28 Difference 4 10

  9. Square A Square C Square B 4. The figure consists of 3 over-lapping squares, A,B and C. The ratio of the area of A to that of B to that of C is 1:2:3. If 40% of B is shaded, what percentage of the figure is not shaded? Let’s make things simpler. Let’s change the ratio into multiples of 50, or make B the base of 100. 1 : 2 : 3 = 50 : 100 : 150 So what do we have? A : B : C = 50 : 100 : 150 Is 40% of B equivalent to 40 units? How many units of A , B and C are not shaded? Put the unit values in the diagram. Notice B’s value is in C? Do you use B’s value when you total the unshaded parts?

  10. A P Q R S B Y X Z C 5. In the figure, not drawn to scale, ∆ABC is divided into 4 parts. BX = XC. The ratios of the areas of the parts are such that P:Q = 1:2 and R:S = 5:4. What is the ratio of the areas of P + Q to R + S? If it costs $240 to paint part Q, how much will it cost to paint part S? If the base of ∆ABX and ∆AXC are equal, and both have the same height, would the areas be equal? If they have the same areas, shouldn’t their total units be the same too? Can you find the number of units for Q that cost $240? Solve the sum. P Q Q R R R R R S S S S

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