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Probability,[object Object],How to express Probability.,[object Object]
How to Express it...,[object Object],There are two main methods of expressing probability:,[object Object],Probabilities are most commonly shown as fractions:,[object Object],The probability of getting 'tails' when you toss a coin is a 1 in 2 chance, or1/2,[object Object],The probability of getting a 3 when you roll a dice is a 1 in 6 chance, or 1/6,[object Object],Probabilities can also be shown as decimals or percentages:,[object Object],A probability of 1/2 can also be shown as 0.5 or 50%,[object Object],A probability of 3/4 can also be shown as 0.75 or 75%,[object Object],The results of an experiment can give different probabilities to those you expect. If you throw a dice 6 times, you would expect to get one six as the probability of throwing a six is 1 in 6. But in fact you might get more than one six or no sixes at all!,[object Object]
Scales...,[object Object],Probability scales,[object Object],Probabilities can be shown on a scale between 0 (impossible) and 1 (certain).,[object Object],For example, imagine a shopping bag contains three bananas and nothing else:,[object Object],The probability of reaching into the bag and pulling out a banana is 1 (certain), as there is nothing else in the bag.,[object Object],The probability of reaching into the bag and pulling out an apple is 0 (impossible), as there are no apples in the bag.,[object Object]
Working it all out...,[object Object],Working out probability,[object Object],Work out the probability of throwing an even number on a dice.,[object Object],Count up the total number of possible results.When throwing a dice, for example, there are 6 possible numbers the dice can land on (1, 2 ,3 ,4, 5, 6).,[object Object],Then count up the number of results you are interested in.In this example, you are only interested in throwing a 2, 4 or 6 (all the even numbers on a dice). So you are interested in 3 numbers.,[object Object],The probability of getting an even number on a dice is 3 chances out of 6 chances which you write as 3/6.3/6 is the same as 1/2 which can also be expressed as 'half', 0.5 or 50%.,[object Object]
Formulae and equations.,[object Object],Function Machines and More.,[object Object]
Function Machines...,[object Object],Function machines have three parts. You may have questions which ask you to find the numbers coming in and out of the machine, or even the missing function. ,[object Object],If you are asked which number goes into the machine, you will need to know the inverse function:,[object Object],The opposite of adding is subtracting,,[object Object], The opposite of multiplying is dividing et cetera.,[object Object],Some functions may have more than one operation. Just put a number in and carry out the operations in order: For example: ,[object Object],     (6x2)-3=9.,[object Object],Top Tip!,[object Object]
Formulae and Equations...,[object Object],You need to work out what the symbol or letter stands for every time. ,[object Object],Use numbers to help you, and say it as a sentence: “What added to 2 makes 6?” etc.,[object Object],If you are finding it difficult to work out the value of a letters write it out again using a box instead of a letter. You can them try different numbers un the box to see if the equation works.,[object Object],Eg. 3t-1=14,[object Object],Add the one, (do the opposite.),[object Object], Divide the number by three, to get what one ‘t’ equals.,[object Object],A number before a letter or a symbol indicates how many of them are there. If just one is there, no numbers will appear.,[object Object],Remember!,[object Object]
Tricky Equations...,[object Object],If it is a complicated equation, you may need to work it out step my step.,[object Object],4y+3=15,[object Object],Do the opposite! Minus the three from the fifteen.,[object Object], You now have twelve, what do you do now?,[object Object], Divide this by 4 to find one y- SIMPLE!,[object Object],Simples!,[object Object]
RATIO AND PROPORTION.,[object Object],Simplifying, Doubling- fantastic!,[object Object],1:27= 1/27.,[object Object]
Direct Proportion...,[object Object],Understanding direct proportion,[object Object],Two quantities are in direct proportion when they increase or decrease in the same ratio. For example you could increase something by doubling it or decrease it by halving.If we look at the example of mixing paint the ratio is 3 pots blue to 1 pot white, or 3:1.,[object Object],But this amount of paint will only decorate two walls of a room. What if you wanted to decorate the whole room, four walls? You have to double the amount of paint and increase it in the same ratio.If we double the amount of blue paint we need 6 pots.If we double the amount of white paint we need 2 pots.,[object Object],Look at this graph:,[object Object],Two quantities which are in direct proportion will always produce a graph where all the points can be joined to form a straight line.,[object Object]
Using it...,[object Object],Using direct proportion,[object Object],Understanding proportion can help in making all kinds of calculations. It helps you work out the value or amount of quantities either bigger or smaller than the one about which you have information. Here are some examples:,[object Object],Example 1: If you know the cost of 3 packets of batteries is £6.00, can you work out the cost of 5 packets?To solve this problem we need to know the cost of 1 packet.If three packets cost £6.00, then you divide £6.00 by 3 to find the price of 1 packet.            (6 ÷ 3 = 2)Now you know that they cost £2.00 each, to work out the cost of 5 packets you multiply £2.00 by 5.            (2 x 5 = 10)So, 5 packets of batteries cost £10.00 ,[object Object],Example 2: You've invited friends round for a pizza supper. You already have the toppings, so just need to make the pizza base. Looking in the recipe book you notice that the quantities given in the recipe are for 2 people and you need to cook for 5!,[object Object],Pizza base - to serve 2 people:           100 g flour    60 ml water          4 g yeast    20 ml milk          pinch of salt,[object Object],The trick here is to divide all the amounts by 2 to give you the quantities for 1 serving. Then multiply the amounts by the number stated in the question, 5.,[object Object],For 1 serving, divide by 2:          100 g ÷ 2 = 50 g    60 ml ÷ 2 = 30 ml          4 g ÷ 2 = 2 g    20 ml ÷ 2 = 10 ml,[object Object],For 5 servings, multiply by 5:           50 g x 5 = 250 g    30 ml x 5 = 150 ml          2 g x 5 = 10 g    10 ml x 5 = 50 ml,[object Object]
Simplifying Ratios...,[object Object],Simplifying ratios,[object Object],We can often make the numbers in ratios smaller so that they are easier to compare. You do this by dividing each side of the ratio by the same number, the highest common factor. This is called simplifying.,[object Object],Example: In a club the ratio of female to male members is 12:18,[object Object],Both 12 and 18 can be divided by 2.      12 ÷ 2 = 6      18 ÷ 2 = 9So a simpler way of saying 12:18 is 6:9.,[object Object],To make the ratio simpler again, we can divide both 6 and 9 by 3      6 ÷ 3 = 2      9 ÷ 3 = 3,[object Object],So a simplest way of saying 12:18 is 2:3.,[object Object],These are all equivalent ratios, they are in the same proportion. All these ratios mean that for every 2 female members in the club there are 3 males:      12:18         6:9         2:32:3 is easier to understand than 12:18!,[object Object]
Quick Tips!,[object Object],Tips for ratio and proportion sums,[object Object],Ratio can be used to solve many different problems, for example recipes, scale drawing and map work.,[object Object],Changing a ratio A common test question will ask you to change a ratio - the reverse of cancelling down.,[object Object],Example: A map scale is 1 : 25 000. On the map the distance between two shopping centres is 4 cm. What is the actual distance between the shopping centres? Give your answer in km.,[object Object],A scale of 1 : 25 000 means that everything in real life is 25 000 times bigger than on the map.So 4 cm on the map is the same as 4 x 25 000 = 100 000 cm in real life.(Reminder 1 m = 100 cm and 1 km = 1 000 m)Now change the real life distance of 100 000 cm to metres100 000 ÷ 100 = 1 000 mAnd 1 000 m is the same as 1 km.So the shopping centres are 1 km apart.,[object Object]
Quick Tips!,[object Object],Keeping things in order When working with ratios keep both the words and the numbers in the same order as they are given in the question.,[object Object],Example: Share a prize of £20.00 between Dave and Adam in the ratio 3:2.,[object Object],The trick with this type of question is to add together the numbers in the ratio to find how many parts there are, divide by the number of parts to find the value of 1 part, then multiply by the number of parts you want to calculate.,[object Object],First add together the number of parts in the ratio: 3 + 2 = 5,[object Object],Divide to find out how much 1 part will be: £20.00 ÷ 5 = £4.00,[object Object],To find Dave's share multiply £4.00 x 3 = £12.00,[object Object],Adam's share is £4.00 x 2 = £8.00,[object Object],Dave's £12.00 is  of £20.00 (3 of 5 parts). Adam's £8.00 is  of £20.00 (2 of 5 parts).,[object Object],You can check that you have worked out the ratio correctly by adding the shares together. In this sum Dave's and Adam's shares should equal £20.00Let's check: £12.00 + £8.00= £20.00 Correct!,[object Object]
Quick Tips!,[object Object],Use the same units Always check that the things you are comparing are measured in the same units. ,[object Object],Example: Jenna has 75 pence. Hayley has £1.50 What is the ratio of Jenna's money to Hayley's?.,[object Object],In this problem one amount is in pence, the other in pounds. Before you calculate the ratio you have to make sure they are the same units. We have to convert Hayley's amount into pence first.    There are 100 pence to a pound    Hayley's £1.50 = 150 pence    So the ratio is 75 : 150You can simplify this ratio as both numbers are divisible by 75. The ratio is 1:2.,[object Object]
Film time!,[object Object],Watch a short video on percentages.,[object Object]
Fractions of quantities,[object Object],Learn how to find complex fractions of a number.,[object Object]
Finding Fraction Parts...,[object Object],What if four people want to share a box of 24 chocolates? ,[object Object],A practical way would be for each person to take it in turns to choose a chocolate, until all the sweets have gone. They would have six chocolates each. ,[object Object],You could also find the answer by working out a quarter of the total number of chocolates.,[object Object],       of 24 is easy to do, just divide 24 by 4.,[object Object],      24  ÷  4  =  6.,[object Object],So the answer is six chocolates.,[object Object],Similarly if three people wanted to share 24 chocolates you could find the answer by working out a third. In this case you would divide by 3.,[object Object],      24  ÷  3  =  8,[object Object],So the answer is eight chocolates.,[object Object],Example  £50 has been won in a pub quiz. Five people were in the team. How much does each person get?,[object Object],      Find a  of £50 by dividing by 5.,[object Object],      50  ÷  5  =  10,[object Object],So each person gets £10.,[object Object]
Fraction Problems...,[object Object],You can use unit fractions to help you solve harder problems:Find  of a box of 24 chocolates.,[object Object],It is easy to do this if you think of the sum as 3 lots of  of the chocolates.,[object Object],      First find  of 24:                                         24  ÷  4  =  6       Then multiply the answer by 3:                     3  x  6  =  18,[object Object],So the answer is 18 chocolates.,[object Object], Find  of a box of 24 chocolates.,[object Object],Think of this as 2 lots of the chocolates.,[object Object],      First find  of 24:                                            24  ÷  3  =  8,[object Object],      Then multiply the answer by 2:                       2  x  8  =  16,[object Object],So the answer is 16 chocolates.,[object Object],These questions look easy, as long as you can see what numbers to divide and multiply by. You do this by looking at the fraction you want. The bottom number (denominator) is the dividing number and the top number (numerator) is the multiplying number.,[object Object]
Percentages of quantities,[object Object],Learn how to find complex percentages of a number.,[object Object]
You can use the fraction method!,[object Object],Remember that percentages are always out of one hundred. So 50& is the same as 50/100, and 27% is the same as 27/100- they’re all the same! If you wanted to find out 27% of 250, you’d do this:,[object Object],Divide 250 by 100, to find one percent, or 1/100. (2.5),[object Object],Multiply this by 27, to find the percentage you want. (67.5),[object Object],It’s that easy!,[object Object]
GAMES,[object Object],Test your knowledge by playing these challenging games.,[object Object],Probability.,[object Object],Ratio and Proportion.,[object Object],Percentages.,[object Object],Fractions.,[object Object]

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Preparing for KS3- Probability, Formulae and Equations, Ratio and Proportion, Percentages of Quantities and Fractions of Quantities.

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