ratio

What is ratio? Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another. For example: Use 1 measure screen wash to 10 measures water Use 1 shovel of cement to 3 shovels of sand Use 3 parts blue paint to 1 part white Ratio is the number of parts to a mix. The paint mix is 4 parts, with 3 parts blue and 1 part white. The order in which a ratio is stated is important. For example, the ratio of screenwash to water is 1:10. This means for every 1 measure of screenwash there are 10 measures of water. Mixing paint in the ratio 3:1 (3 parts blue paint to 1 part white paint) means 3 + 1 = 4 parts in all. 3 parts blue paint to 1 part white paint = is ¾ blue paint to ¼ white paint. If the mix is in the right proportions, we can say that it is in the correct ratio. Understanding direct proportion 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. 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. The amount of blue and white paint we need increase in direct proportion to each other. Look at the table to see how as you use more blue paint you need more white paint: Pots of blue paint 3 6 9 12 Pots of white paint 1 2 3 4  Have a look at this graph: Two quantities which are in direct proportion will always produce a graph where all the points can be joined to form a straight line. Using direct proportion 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: 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 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! Pizza base - to serve 2 people:           100 g flour    60 ml water          4 g yeast    20 ml milk          pinch of salt 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. 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 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 The pinch of salt is up to you! Simplifying ratios 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. Example: In a club the ratio of female to male members is 12:18 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. To make the ratio simpler again, we can divide both 6 and 9 by 3      6 ÷ 3 = 2      9 ÷ 3 = 3 So a simplest way of saying 12:18 is 2:3. 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! Key words for ratio and proportion Ratio is a way in which quantities can be divided or shared. Example: Share £20 between two people in a ratio of 3:1.A ratio of 3 + 1 = 4 parts, the money needs to be divided into 4 parts.      20 ÷ 4 = £5.If one person is getting three parts they will have 3 x 5 = £15 The other person will have one part, £5. Simplest form. Ratios can be simplfied by finding common factors. Direct proportion. Ratios are in direct proportion when they increase or decrease in the same ratio. Equivalent ratios. When both sides of a ratio can be multiplied or divided by the same number to give an equivalent ratio. Example: In a group there are 15 males and 12 females. What is the ratio of males to females? Give your example in its simplest form.So the ratio of males to females is 15:12. However, both sides of the ratio can be divided by 3. Dividing 15 and 12 by 3 gives 5:4.      5:4 is the ratio in its simplest form.      5:4 and 15:12 are equivalent ratios. Factor The factors of a number are those numbers which divide into it exactly. Example:       1 x 12 = 12      2 x 6 = 12      3 x 4 = 12So the factors of 12 are 1, 2, 3, 4, 6 and 12. 4