How To Solve A Problem With A Unit Standard

Transcription

1 Use fraction, ratio and proportion to solve problems Name: In this unit standard you will be required to use ratios and fractions to solve problems in the following situations: Compare e.g. At the SPCA there are 16 dogs and 32 cats. What is the ratio of dogs to cats in its simplest form? Share e.g. Lachlan and Phil buy a bag lollies for $8. Lachlan pays $3 and Phil pays $5. How many lollies should each person get if they share them according to the ratio they each paid? Proportion e.g. ¾ of students in a dance class are female. If there are 60 students in the class, how many are male? Increase/Decrease e.g. A recipe for fruit punch is as follows: 1L of water, 2L of fruit juice, 500mL of lemonade. Denise has 6L of fruit juice. How much water and lemonade will she need to make up punch using all the fruit juice? 1

2 RATIOS AND SIMPLIFYING A ratio is very similar to a fraction, but it shows the way things may be shared. e.g. if Barry pays $5 and Kenny pays $18 towards the cost of petrol, Barry and Kenny have paid in a ratio of 5:18. The order of the numbers matter!!! A ratio of 1:5 says that the second number is five times as large as the first. e.g. the ratio of chocolate to flour in my cake is 2:5. This means for every 2 cups of chocolate, add 5 cups of flour SIMPLIFYING RATIOS When we simplify fractions we use the a b/c button on the calculator: e.g. Simplify 40/ a b/c 400 = 1/10 We can use the same process to simplify ratios e.g. Simplify the ratio 30: a b/c `100 = 3:10 NOTE: If the first part is larger than the second part, the values need to be swapped to use the key e.g. Simplify the ratio 12:3 3 a b/c 12 = 1:4 Swap it back = 4:1 2

3 Exercises Simplify the following ratios 1) 20:80 2) 30:90 3) 25:75 4) 45:135 5) 15:60 6) 40:160 7) 300:50 8) 450:150 9) 60:10 10) 12:72 Matching In each of the squares boxes there are 3 ratios that are the same i.e. will simplify to the same ratio. Circle the ones that are the same. 4:10 14:35 3:15 8:25 8:20 9:21 39:91 6:21 12:35 30:70 10:27 14:21 16:27 34:51 18:27 12:14 36:48 18:24 27:32 99:132 3

4 Fill in the gaps below: 1) A ratio is 2) An example of a ratio is 3) A situation where I would see a ratio is 4) I simplify ratios by In the space below complete: Ex 6.1 Pg 54 Numbers 1-4 only Ex 6.1 1a) 1b) 2a) 2b) 3a) 3b) 4a) 4b) 4c) 4d) Checklist 1) Have you marked your work? 2) If you have not got some right, have you worked out why? 3) On the continuum below indicate where you think your ability is in terms of simplifying ratios Struggling OK FINE 4

5 FINDING A RATIO When the total and a part is known, ratios can be used e.g. Of 28 cats at the SPCA, 12 had been fixed. Calculate the number of cats that were not fixed and hence the ratio of fixed cats to non-fixed cats ANSWER: Non fixed cats : = 14 Ratio of fixed cats to non-fixed cats = 12:14 = 6:7 In the space below complete Ex 6.2 Pg 55 Numbers 1-8 1a) 1b) 1c) 2a) 2b) 2c) 3a) 3b) 3c) 4a) 4b) 4c) 5a) 5b) 5c) 6a) 6b) 6c) 7a) 7b) 7c) 8a) 8b) 8c) 5

6 SHARING IN A GIVEN RATIO e.g. Share the $476 winnings of a lotto ticket between Bill and Ben in a ratio of 2:5 STEP 1: Add up the parts of the ratio to see the total number of parts to be shared = 7 Parts STEP 2: Divide the required total by the number of parts 476 / 7 = $68 STEP 3: Each part of the ratio needs to be multiplied by this amount Bill:Ben = 2:5 Bill 2 x 68 = $136 Ben 5 x 68 = $340 STEP 4: Check that your two values add to the total $136 + $340 = $476 e.g. to make up cordial, the ratio of concentrate to water is 3:5. How much concentrate is needed to make 400mL of cordial? STEP 1: = 8parts STEP 2: 400 / 8 = 50mL STEP 3: Water: Concentrate = 3:5 Water 3 x 50 = 150mL Concentrate 5 x 50 = 250mL STEP 4: = 400mL 6

7 EXERCISES 1) Werimu and Daisy work in a ratio of 6:9. If they get paid $277.50, how much should they each get? Step 1: 2) Lucy and Penny won $968 on an instant kiwi. If Lucy paid $3 and Penny paid $8, how much should they each get? Step 1: 3) Billy is baking a cake. The liquid in the recipe uses water and milk in a ratio of 2:3. If Billy uses 175mL of liquid, how much milk is needed? In the space below, write two of your own ratio questions. 1) 2) 7

8 In the space below complete the following Ex 6.4 Pg 57 Numbers ) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) Checklist 1) Have you marked your work? 2) f you have not got some right, have you worked out why? 3) On the continuum below indicate where you think your ability is in terms of sharing a ratio Struggling OK FINE TEACHER CHECK DATE 8

9 INCREASING OR DECREASING IN A GIVEN RATIO When the ratio is known, it can be used by multiplying or dividing both parts by the same number to give larger or smaller quantities. e.g. In a recipe for porridge for four people, the ingredients are: 1 cup oats ½ teaspoon salt ½ cup cold water 4 cups boiling water If the recipe is to be used to make porridge for 12 people, how much of each ingredient is needed? STEP1: Find out what each ingredient needs to be multiplied by. In this case porridge four people needs to be made for 12 people 4 x 3 = 12 STEP 2: Multiply the parts by this value Therefore every ingredient needs to be multiplied by 3 Oats: Cold water: Salt: Boiling water: 1 cup x 3 = 3 cups ½ cup x 3 = 1 ½ cups ½ tsp x 3 = 1 ½ tsp 4 cups x 3 = 12 cups 9

10 In the space below complete the following Ex 6.5 Ex 6.6 Pg 58 pg 60 Numbers 1-9 Puzzle code 1a) 1b) 1c) 2a) 2b) 2c) 3a) 3b) 3c) 3d) 4a) 4b) 4c) 5a) 5c) 6a) 6b) 6c) 7a) 7b) 7c) 7d) 8a) 8b) 8c) 9a) 9b) 9c) 5b) 10

11 COMPARING USING A RATIO Ratios are often useful when comparing prices in a supermarket. e.g. Which is the best buy for money? Brand A 500mL for $4.70 Brand B 300mL for $2.70 STEP 1: Find a useful unit to be able to compare the same amount of each With 500mL and 300mL, it is easy to find the price of 100mL STEP2: Find the price of Brand A for this amount There are 5 lots of 100mL in 500mL so to find the price of 100mL, divide the price by 5 $4.70 / 5 = $0.94 STEP 3: Find the price of Brand B for this amount There are 3 lots of 100mL in 300mL, so to find the price of 100mL, divide the price by 3 $2.70 / 3 = $0.90 STEP 4: Compare the rate and state which is the better price Brand B is the best buy 11

12 In the space below complete the following Ex 6.7 Pg 61 Numbers ) Step 1: 2) Step 1: 3) Step 1: 4) Step 1: 5) Step 1: 6) Step 1: 7) Step 1: 8) Step 1: 9) Step 1: 10) Step 1: 11) Step 1: 12) Step 1: 12

13 REVISION In the space below complete the following Ex 6.8 Ex 6.9 Pg 61 Pg 63 Numbers 1-6 Numbers 1-12 Ex 6.8 1a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) q) r) s) 2a) b) c) d) e) 3a) b) c) d) e) f) g) h) i) 4a) b) c) d) 13

14 e) f) g) h) i) 5a) b) c) d) 6a) b) c) Ex 6.9 1) 2a) b) c) d) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Checklist 1) Have you marked your work? 2) If you have not got some right, have you worked out why? 3) On the continuum below indicate where you think your ability is in terms of increasing and decreasing by a ratio Struggling OK FINE TEACHER CHECK DATE 14

15 PRACTICE ASSESSMENT 1) In a class of 32 students, 12 are boys. What is the ratio of boys to girls? 2) In a dog kennel there are 70 dogs and cats. If there are 27 cats, what is the ratio of cats to dogs? 3) In a nut and raisin mix the ratio of nuts to raisins is 5:8. If there are 200 nuts, how many raisins are there? 4) Fertilizer is mixed with water in a ratio of 3:5. If Wendy measures out 40mL of fertilizer, how much water will she need? 5) Doctors measure drugs out with saline in a ratio of 2:7. If a doctor has measured out 50mL of a drug, how much saline is needed? 6) Gerald mixes blue and white paint in a ratio of 2:3. If he has 1200mL of white paint, how much blue paint does he need? 7) At Central Perk, three-fifths of customers order a coffee. a) On Wednesday they have 200 customers. How many ordered a coffee? b) On Thursday there were 390 customers. How many didn t order coffee? 15

16 8) Two out of six cats at a cattery are mongrel cats. If there were 90 cats at the cattery, how many were mongrels? 9) Kenny and Andrew bought an instant kiwi for $7. Kenny paid $3 and Andrew paid $4. They win a prize of $750. How much prize money should each person get if the money is to be shared according to the ratio they each paid? 10) Sunny and Jolly buy a lotto ticket for $12. Sunny paid $7 and Jolly paid $5. They win $22,000. How much prize money should each person get if the money is to be shared according to the ratio they each paid? 11) Donna is making a strawberry milkshakes. She uses: 200g Strawberries 500mL Milk 400g Ice Cream For each milkshake. She has to make 6 milkshakes. How much of each ingredient will she need? 12) Lucia is making cheese sauce. The recipe is as follows 2 tablespoons flour 2 tablespoons butter ½ cup of milk 1 cup of cheese 1 cup of water Lucia only has ½ a cup of cheese. How much of the rest of the ingredients should she use to make the sauce now? 16