3 Number: Ratios and proportion
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1 Number: Ratios and proportion. Ratio HOMEWORK A Express each of the following ratios in their simplest form. a :9 b : c : d 0 : 0 e :9 f : 0 g : 0 h 0 : i : j : 0 Express each of the following ratios of quantities in their simplest form. (Remember to change to a common unit where necessary.) a to 8 b to c g to 00 g d miles : miles e 0 cm : 0 cm f 80p :.0 g kg : 00g h 0 seconds : minutes i 9 hours : day j mm: cm 0 is shared out between Bob and Kathryn in the ratio :. a What fraction of the 0 does Bob receive? b What fraction of the 0 does Kathryn receive? In a class of students, the ratio of boys to girls is :. a What fraction of the class is boys? b What fraction of the class is girls? E FM AU PS 7 FM 8 Pewter is an alloy containing lead and tin in the ratio : 9. a What fraction of pewter is lead? b What fraction of pewter is tin? Roy wins two-thirds of his snooker matches. He loses the rest. What is his ratio of wins to losses? In the 009 Ashes cricket series, the numbers of wickets taken by Steve Harmison and Monty Panesar were in the ratio :. The ratio of the number of wickets taken by Graham Onions to those taken by Steve Harmison was :. What fraction of the wickets taken by these three bowlers was by Monty Panesar? In a motor sales business, the ratio of the area allocated to selling new cars to the area for selling used cars is :. Half the area for selling new cars is changed to used cars. What is the ratio of the areas now? Give your answer in its simplest form. HOMEWORK B ivide each of the following amounts in the given ratios. a 0 in the ratio : b in the ratio : c 0 in the ratio : d 0 g in the ratio : e 0 hours in the ratio : 9 FM Functional Maths AU (AO) Assessing Understanding PS (AO) Problem Solving
2 HAPTER : Number: Ratios and proportion AU PS 0 PS FM FM AU The ratio of female to male members of a sports centre is :. The total number of members of the centre is 00. a How many members are female? b How many members are male? A 0 m length of cloth is cut into two pieces in the ratio : 9. How long is each piece? ivide each of the following amounts in the given ratios. a kg in the ratio : b 0 days in the ratio : c 70 m in the ratio : d in the ratio : 7 e day in the ratio : James collects beer mats and the ratio of British mats to foreign mats in his collection is :. He has 00 beer mats. How many foreign beer mats does he have? Patrick and Jane share out a box of sweets in the ratio of their ages. Patrick is 9 years old and Jane is years old. If there are 00 sweets in the box, how many does Patrick get? For her birthday Reena is given 0. She decides to spend four times as much as she saves. How much does she save? Mrs Megson calculates that her quarterly electric and gas bills are in the ratio :. The total she pays for both bills is. How much is each bill? You can simplify a ratio by changing it into the form : n. For example, : 7 can be rewritten as : 7 = :. by dividing each side of the ratio by. Rewrite each of the following ratios in the form : n. a : b : c : d :8 e 0 : The amount of petrol and diesel sold at a garage is in the ratio :. One-tenth of the diesel sold is bio-diesel. What fraction of all the fuel sold is bio-diesel? At a buffet, there are twice as many men as women. The organiser takes 00 altogether. There are 0 men at the buffet. How much does each person pay for the buffet? The cost of show tickets for adults and children are in the ratio :. 0 adults and 0 children visit the show. hildren s tickets cost.0. How much money will the show take altogether? HOMEWORK FM Peter and Margaret s ages are in the ratio :. If Peter is years old, how old is Margaret? ans of lemonade and packets of crisps were bought for the school disco in the ratio :. The organiser bought 0 cans of lemonade. How many packets of crisps did she buy? In his restaurant, Manuel is making fruit punch, a drink made from fruit juice and iced soda water, mixed in the ratio :. Manuel uses 0 litres of fruit juice. a How many litres of soda water does he use? b How many litres of fruit punch does he make? upro-nickel coins are minted by mixing copper and nickel in the ratio :. a How much copper is needed to mix with 0 kg of nickel? b How much nickel is needed to mix with 0 kg of copper?
3 HAPTER : Number: Ratios and proportion AU 7 PS 8 9 AU 0 The ratio of male to female spectators at a school inter-form football match is :. If 0 boys watched the game, how many spectators were there in total? Marmalade is made from sugar and oranges in the ratio :. A jar of Savilles marmalade contains 0 g of sugar. a How many grams of oranges are in the jar? b How many grams of marmalade are in the jar? Each year Abbey School holds a sponsored walk for charity. The money raised is shared between a local charity and a national charity in the ratio :. Last year the school gave 000 to the local charity. a How much did the school give to the national charity? b How much did the school raise in total? Fred s blackcurrant juice is made from parts blackcurrant and part water. Jodie s blackcurrant juice is made from blackcurrant and water in the ratio 7 :. Which juice contains the greater proportion of blackcurrant? Show how you work out your answer. Sand and cement is mixed in the ratio :. ement is sold in kg bags. Sand is sold in 87 kg sacks. How many sacks of sand would be needed to mix with 0 bags of cement? The ratio of tins of white paint to coloured paint in a shop storeroom is :. There is enough room on the shelves for 0 tins of paint. How many tins of white paint can be put on the shelf if the ratio of the tins of white paint to coloured paint is also :?. Speed, time and distance HOMEWORK A cyclist travels a distance of 0 miles in hours. What was her average speed? How far along a motorway will you travel if you drive at an average speed of 0 mph for hours? Mr Baylis drives on a business trip from Manchester to London in hours. The distance he travels is 07 miles. What is his average speed? The distance from Leeds to Birmingham is miles. The train I catch travels at an average speed of 0 mph. If I catch the.0 am train from Leeds, at what time would I expect to be in Birmingham? opy and complete the following table. a b c d e f istance travelled 0 miles 0 km 00 miles 90 km Time taken 8 hours hours hours hours Average speed mph 0 km/h 00 mph km/h
4 HAPTER : Number: Ratios and proportion 7 8 PS 9 FM 0 AU A coach travels at an average speed of 0 km/h for hours on a motorway and then slows down in a town centre to do the last 0 minutes of a journey at an average speed of 0 km/h. a What is the total distance of this journey? b What is the average speed of the coach over the whole journey? Hilary cycles to work each day. She cycles the first miles at an average speed of mph and then cycles the last mile in 0 minutes. a How long does it take Hilary to get to work? b What is her average speed for the whole journey? Martha drives home from work in hour minutes. She drives home at an average speed of mph. a hange hour minutes to decimal time in hours. b How far is it from Martha s work to her home? A tram route takes minutes at an average speed of mph. The same journey by car is two miles longer. How fast would a car need to travel to arrive in the same time? A taxi travelled for 0 minutes. The fare was. If the fare was charged at.0 per mile, what was the average speed of the taxi? Two cars are 0 miles apart but travelling towards each other. The average speed of one car is twice as fast as the other car. The slower car is averaging 0 mph. How long is it before they meet up?. irect proportion problems HOMEWORK E FM 7 If four video tapes cost.0, what would 0 video tapes cost? Five oranges cost 90p. Find the cost of oranges. ylan earns 8.0 in hours. How much will he earn in 8 hours? Barbara bought postcards for euros when she was on holiday in Tenerife. a How many euros would she have paid if she had only bought 9 postcards? b How many postcards could she have bought with a euro note? Five ay-rover bus tickets cost 8.0. a What is the cost of tickets? b Pat has 0. She wants to buy tickets. an she afford them? Show your working of how you decide. A car uses 8 litres of petrol on a trip of 7 miles. a How much would be used on a trip of miles? b How far would the car go on a full tank of litres? It takes a photocopier 8 seconds to produce copies. How long will it take to produce copies?
5 HAPTER : Number: Ratios and proportion 8 Val has a recipe for making flapjacks. 00 g margarine tablespoons golden syrup 80 g granulated sugar 00 g rolled oats FM PS a b What is the recipe for: i flapjacks ii flapjacks iii 0 flapjacks? What is the maximum number of flapjacks she can make if she has kg of each ingredient? AU 9 FM 0 PS Greg the baker sells bread rolls in pack of for. om the baker sells bread rolls in packs of for.9. I have to spend on bread rolls. How many more can I buy from Greg than from om? To make white coffee, one-quarter of a cup is filled with milk. A cup holds 00 ml of white coffee altogether. How many cups of coffee can be made if you have litre of milk? A nurse can examine 0 patients each hour. There are 70 patients visiting a three-hour clinic. How many nurses are needed?. Best buys HOMEWORK F FM ompare the prices of the following pairs of products and state which, if any, is the better buy. a Mouthwash:.99 for a twin pack, or.9 each with a for offer. b usters: 79p for a pack of with a buy one pack and get one pack free offer, or.0 for a pack of 0. ompare the following pairs of products and state which is the better buy and why. a Tomato ketchup: a medium bottle which is 00 g for p or a large bottle which is 0 g for 87p. b Milk chocolate: a g bar at 77p or a 00 g bar at 9p. c offee: a 70 g tin at.9 or a 00 g tin at 7.8. d Honey: a large jar which is 900 g for. or a small jar which is g for p. Boxes of Wetherels teabags are sold in three different sizes. Small Medium Large 80 teabags. 0 teabags.0 00 teabags. Which size box of teabags gives the best value for money? 7
6 HAPTER : Number: Ratios and proportion AU Bottles of ola are sold in different sizes. opy and complete the table. Size of bottle Price ost per litre litre p litres 99p litres.0 litres.9 Which size of bottle gives the best value for money? The following special offers were being promoted by a supermarket. Only.99 each Buy for the price of ornflakes 70 g.99 ornflakes 00 g.9 Which offer is the better value for money? Explain why. PS Hannah scored 7 out of 0 in a test. John scored 0 out of 0 in a test of the same standard. Who got the better mark?. ensity HOMEWORK G B 7 PS 8 9 AU 0 Find the density of a piece of wood weighing g and having a volume of 0 cm. alculate the density of a metal if 0 cm of it weighs 00 g. alculate the weight of a piece of plastic, cm in volume, if its density is. g/cm. alculate the volume of a piece of wood that weighs 0 g and has a density of 0.7 g/cm. Find the weight of a statue, 0 cm in volume, if the density of marble is. g/cm. alculate the volume of a liquid weighing kg and having a density of. g/cm. Find the density of a stone which weighs g and has a volume of cm. It is estimated that a huge rock balanced on the top of a mountain has a volume of 0 m. The density of the rock is 8. g/cm. What is the estimated weight of the rock? A kg bag of flour has a volume of about 900 cm. What is the density of flour in g/cm? m = cm A storage area has 0 tonnes of sandstone. The density of some sandstone is. g/cm a What is the volume of sandstone in the storage area? Give your answer in m. b The density of granite is.7 g/cm. The same volume of granite is stored as the volume of sandstone. How much heavier is the granite? 8
7 HAPTER : Number: Ratios and proportion AU FM The density of a piece of oak is 0 kg/m. The density of a piece of mahogany is 0 kg/m. Two identical carvings are made, one from oak and the other from mahogany. The oak carving has a mass of grams. What is the mass of the mahogany carving? Two identical-looking metal objects are side by side. They have different masses. How does this tell you that they are probably made from different metals? Functional Maths Activity B Metal objects You run a charity shop and the items listed in the table below have been donated. You have estimated their volume in cubic centimetres. Now you need to price them. The second table provides data about the density of metal and the cost per gram. Use the information to work out the value of each item. How much would you price each item at and why? Item Volume (cm³) andlestick (brass) Statue (cast iron) Ring (gold) 0. Tankard (Stainless steel) Jug (silver) Plate (opper) 7 Metal ensity (g/cm³) ost per gram Brass 8. 9p opper 8.9 p Gold 9..8 Silver 0. 80p Stainless steel 7. p ast iron 7. 8p 9
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