Working with Numbers: Working with Numbers 03 July 2011
Objectives: Objectives Use place value to carry out calculations correctly Solve problems using the four operations
Place Value: Place Value T U . H . Th TTh 2 3 6 7 2 4 6 1 2 5 7 6 2 7 3 5 2 1 5 3 Each DIGIT in ANY number has a special value 2 is worth 2000 4 is worth 400 7 is worth 70 3 is worth 30 3 is worth 3
Place Value together ........: Place Value together ........ T U . H . Th TTh 5 4 7 6 4 5 9 0 3 6 7 2 8 0 0 2 7 4 3 2 Each DIGIT in ANY number has a special value 4 is worth 9 is worth 3 is worth 2 is worth 3 is worth 400 90 3000 2 30
Place Values ... Your turn: Place Values ... Your turn T U . H . Th TTh 4 2 9 3 1 5 7 1 4 6 7 1 8 3 2 4 5 3 2 4 4 is worth 3 is worth 4 is worth 4 is worth 3 is worth 400 30000 4000 4 300
Place Values 4 u – value of the underlined: Place Values 4 u – value of the underlined 5 2 4 9 1 7 3 9 2 0 4 16 92 7 3 01 1 5 2 8 02 3 816 2 7 59 180 4 6 271 3 537 726 3 1 4 5087 9 6 331 3 8656 2 6 800
Place Values 4 u – answers: Place Values 4 u – answers Two Forty Ten Nine Twenty Four Hundred Seven Three Hundred Fifty Eight hundred Three Thousand Seven Hundred Four Six thousand Three thousand Thirty Forty Thousand Six Thousand Thirty Thousand Six Thousand
In words: In words 79 81 45 12 96 546 160 851 206 738 2734 9461 5657 1945 6812 4501 7036
In words - answers: In words - answers Seventy-Nine Eighty-One Forty-Five Twelve Ninety-Six Five hundred and forty six One hundred and sixty Eight Hundred and fifty-one Two hundred and six Seven hundred and thirty eight Two thousand seven hundred and thirty four Nine thousand four hundred and sixty-one Five thousand six hundred and fifty seven One thousand nine hundred and forty-five Six thousand eight hundred and twelve Four thousand five hundred and one Seven thousand and thirty six
In Numbers: In Numbers Forty-nine Sixty Eight Fifteen Eighty Seven Two hundred and twenty five Nine hundred and eighteen Seven hundred and forty three Six hundred and thirty four One hundred and two Three hundred and eight Four thousand six hundred and twelve Eight thousand three hundred and twenty four Two thousand four hundred an fifty one Seven thousand four hundred and nineteen Six thousand nine hundred and forty two
In Numbers -answers: In Numbers - answers 49 68 15 87 225 918 743 634 102 308 4612 8320 2451 7419 6942
Addition and Subtraction – whole numbers 1: Addition and Subtraction – whole numbers 1 T U . H . Th TTh 3 4 2 5 T U . H . Th TTh 6 4 3 2 + - 9 5 3 2
Addition and Subtraction – whole numbers 2: Addition and Subtraction – whole numbers 2 T U . H . Th TTh 4 7 5 6 T U . H . Th TTh 8 3 4 7 + - 0 6 3 3 1 1 1 1
Addition and Subtraction- whole numbers – 4 U: Addition and Subtraction- whole numbers – 4 U 23 + 15 = 35 + 14 = 61 + 18 = 76 + 25 = 84 + 48 = 75 + 89 = 231 + 34 = 354 + 45 = 524 + 67 = 777 + 333 = 87 – 23 = 55 – 21 = 77 – 43 = 254 – 32 = 47 – 19 = 63 – 25 = 51 – 37 243 – 38 = 412 – 66 = 354 – 182 =
Addition and Subtraction – whole numbers - answers: Addition and Subtraction – whole numbers - answers 23 + 15 = 38 35 + 14 = 49 61 + 18 = 79 76 + 25 = 101 84 + 48 = 132 75 + 89 = 164 231 + 34 = 265 354 + 45 = 399 524 + 67 = 591 777 + 333 = 1110 87 – 23 = 64 55 – 21 = 34 77 – 43 = 34 254 – 32 = 222 47 – 19 = 32 63 – 25 = 38 51 – 37 = 14 243 – 38 = 205 412 – 66 = 346 354 – 182 = 172
Addition and Subtraction – decimals : Addition and Subtraction – decimals . tths hths U T Hun 3 7 . 4 8 2 6 . 7 5 . . tths hths U T Hun 4 1 . 3 4 1 2 . 5 7 . + - 2 3 4 6 8 2 7 7 1 1 1 1 1 1 1 1 1
Addition and Subtraction- decimals – 4 U: Addition and Subtraction- decimals – 4 U 23. 21 + 15.37 = 35.42 + 14.56 = 61.27 + 18.72 = 76.45 + 25.35 = 84.37 + 48.26 = 75.48 + 89.84 = 231.95 + 34.49 = 354.66 + 45.66 = 524.07 + 67.96 = 777.35 + 333.86 = 87.46 – 23.21 = 55.47 – 21.23 = 77.54 – 43.31 = 254.56 – 32.38 = 47.44 – 19.53 = 63.61 – 25.39 = 51.22 – 37.55 = 243.05 – 38.27 = 412.44 – 66.88 = 354.11 – 182.88 =
Addition and Subtraction- decimals – 4 U - answers: Addition and Subtraction- decimals – 4 U - answers 23. 21 + 15.37 = 38.58 35.42 + 14.56 = 49.98 61.27 + 18.72 = 79.99 76.45 + 25.35 = 101.80 84.37 + 48.26 = 132.63 75.48 + 89.84 = 165.32 231.95 + 34.49 = 266.44 354.66 + 45.66 = 400.32 524.07 + 67.96 = 592.03 777.35 + 333.86 = 1111.21 87.46 – 23.21 = 64.25 55.47 – 21.23 = 34.24 77.54 – 43.31 = 34.23 254.56 – 32.38 = 222.18 47.44 – 19.53 = 27.91 63.61 – 25.39 = 38.22 51.22 – 37.55 = 13.67 243.05 – 38.27 = 204.78 412.44 – 66.88 = 345.56 354.11 – 182.88 = 171.23
Multiplication: Multiplication T U . H . Th TTh 2 3 3 X T U . H . Th TTh 4 5 7 X 9 6 5 3 1 3
Multiplication 4 U: Multiplication 4 U 4 x 7 = 8 x 9 = 5 x 7 = 11 x 8 = 10 x 12 = 5 x 110 = 7 x 120 = 8 x 301 = 9 x 240 = 8 x 231 = 9 x 222 = 7 x 924 = 8 x 333 = 9 x 209 = 6 x 745 = 8 x 352 = 7 x 289 = 11 x 354 =
Multiplication - answers: Multiplication - answers 4 x 7 = 28 8 x 9 = 72 5 x 7 = 35 11 x 8 = 88 10 x 12 = 120 5 x 110 = 550 7 x 120 = 840 8 x 301 = 903 9 x 240 = 2160 8 x 231 = 1848 9 x 222 = 1998 7 x 924 = 6468 8 x 333 = 2664 9 x 209 = 1881 6 x 745 = 4470 8 x 352 = 2816 7 x 289 = 2023 11 x 354 = 3894
Multiplying Integers by powers of 10: Multiplying Integers by powers of 10 23 x 1 00 = 147 x 1 000 = 2 x 1 0000 = 15 x 1 00 = 2003 x 1 00 =
Multiplying Integers by powers of 10: Multiplying Integers by powers of 10 23 x 1 00 = 23. 147 x 1 000 = 147. 2 x 1 0000 = 2. 15 x 1 00 = 15. 2003 x 1 00 = 2003.
Multiplying Integers by powers of 10: Multiplying Integers by powers of 10 23 x 1 00 = 23.00000000 147 x 1 000 = 147.0000000 2 x 1 0000 = 2.0000000 15 x 1 00 = 15.0000000 2003 x 1 00 = 2003.0000000
Multiplying Integers by powers of 10: Multiplying Integers by powers of 10 23 x 1 00 = 23.00000000 = 2300 147 x 1 000 = 147.0000000 = 147000 2 x 1 0000 = 2.0000000 = 20000 15 x 1 00 = 15.0000000 = 1500 2003 x 1 00 = 2003.0000000 = 200300
Your Turn: Your Turn 12 x 1000 = 15 x 1000 = 241 x 1000 = 4 x 1000 = 16 x 100 = 213 x 100 = 12 x 10 = 23 x 1000 = 12 x 20 = 13 x 300 = 22 x 3000 = 102 x 200 =
Your Turn - answers: Your Turn - answers 12 x 1000 = 12000 15 x 1000 = 15000 241 x 1000 = 241000 4 x 1000 = 4000 16 x 100 = 1600 213 x 100 = 21300 12 x 10 = 120 23 x 1000 = 23000 12 x 20 = 240 13 x 300 = 3900 22 x 3000 = 66000 102 x 200 = 20400
Multiplying by moving the decimal point: Multiplying by moving the decimal point T U . tenths hundredths thousandths H . Th TTh 4 7 . 0 0 3 1 . 1 0 2 6 3 2 0 . 5 4 7 2 . 1 0 4 0 . 3 7 0 X X X X X 10 100 10 100 1000
Multiplying by moving the decimal point: Multiplying by moving the decimal point T U . tenths hundredths thousandths H . Th TTh 4 7 0 . 0 3 1 1 0 . 2 6 3 2 0 5 . 4 7 2 1 0 . 4 3 7 0 .
Some Examples: Some Examples T U . tnths hunths thths H . Th TTh 4 2 3 1 2 1 2 3 9 0 2 1 5 4 2 0 1 X X X X X 10 100 10 100 1000 . . . . . 0
Your Turn (5 minutes): Your Turn (5 minutes) 2.3 x 10 = 16.9 x 100 = 521.1 x 100 = 0.37 x 1000 = 4.002 x 100 = 0.003 x 1000 = 2.102 x 100 = 387.1 x 100 = 22.22 x 1000 = 4.004 x 100 =
Your Turn - answers: Your Turn - answers 2.3 x 10 = 23 16.9 x 100 = 1690 521.1 x 100 = 52110 0.37 x 1000 = 370 4.002 x 100 = 400.2 0.003 x 1000 = 3 2.102 x 100 = 210.2 387.1 x 100 = 38710 22.22 x 1000 = 22220 4.004 x 100 = 400.4
Dividing Integers by powers of 10: Dividing Integers by powers of 10 23 ÷ 1 00 = 23. ÷ 100 = 147 ÷ 1 000 = 147. ÷ 1000 = 2 ÷ 1 0000 = 2. ÷ 10000 = 15 ÷ 1 00 = 15. ÷ 100 = 2003 ÷ 1 00 = 2003. ÷ 100 = 0.23 0.147 0.0002 0.15 20.03
Practice: Practice 3.7 x 100 2.15 x 10 9.32 x 1000 17.5 x 100 243.2 x 100 0.302 x 100 0.003 x 10000 7.002 x 100 320 ÷ 10 5400 ÷ 100 27.3 ÷ 10 153 ÷ 100 7.9 ÷ 10 8710 ÷ 100 0.9 ÷ 10 32.1 ÷100
Practice - answers: Practice - answers 3.7 x 100 = 370 2.15 x 10 = 21.5 9.32 x 1000 = 9320 17.5 x 100 = 1750 243.2 x 100 = 24320 0.302 x 100 = 30.2 0.003 x 10000 = 30 7.002 x 100 = 700.2 320 ÷ 10 = 32 5400 ÷ 100 = 54 27.3 ÷ 10 = 2.73 153 ÷ 100 = 1.53 7.9 ÷ 10 = 0.79 8710 ÷ 100 = 87.1 0.9 ÷ 10 = 0.09 32.1 ÷100 = 0.321
Division: Division 195 ÷ 5 88.8 ÷ 6 1 4 2 4 5 does not divide into - so 0 in the answer – and carry the 1 5 divides into 19 3 times so 3 in the answer and carry remainder 4 5 divides into 4 5 9 times so 9 in the answer – and no remainder 6 divides into 8 1 times – so 1 in the answer and carry the remainder 2 6 divides into 28 4 times – so 4 in the answer and carry the remainder 4 6 divides into 46 8 times – so 8 in the answer – and no remainder
Division – 4 U : Division – 4 U 85 ÷ 5 = 115 ÷ 5 = 189 ÷ 7 = 333 ÷ 9 = 492 ÷ 4 = 2448 ÷ 6 = 1053 ÷ 7 = 308 ÷ 11 = 1224 ÷ 12 = 728 ÷ 13 = 12.3 ÷ 3 = 11.5 ÷ 5 = 27.7 ÷ 5 = 25.6 ÷ 8 = 55.2 ÷ 8 = 8.52 ÷ 4 = 15.54 ÷ 7 = 36.63 ÷ 9 = 57.36 ÷ 6 = 72.38 ÷ 11 =
Division – 4 U - answers: Division – 4 U - answers 85 ÷ 5 = 17 115 ÷ 5 = 23 189 ÷ 7 = 27 333 ÷ 9 = 37 492 ÷ 4 = 123 2448 ÷ 6 = 408 1053 ÷ 7 = 149 308 ÷ 11 = 28 1224 ÷ 12 = 102 728 ÷ 13 = 56 12.3 ÷ 3 = 4.1 11.5 ÷ 5 = 2.3 27.7 ÷ 5 = 5.5 25.6 ÷ 8 = 3.2 55.2 ÷ 8 = 6.9 8.52 ÷ 4 = 2.3 15.54 ÷ 7 = 2.22 36.63 ÷ 9 = 4.07 57.36 ÷ 6 = 9.56 72.38 ÷ 11 = 6.58
Problems: Problems John’s training run takes him 20 times around the 400 metre track. How far does he run?
Problems: Problems John’s training run takes him 20 times around the 400 metre track. How far does he run? Possible Solution 1 times around the track = 400 20 times around the track = 20 x 400 = 8000 metres
Problems: Problems The 10000 metres final is run around a 400 metres track. How many times do runners have to run around the track?
Problems: Problems The 10000 metres final is run around a 400 metres track. How many times do runners have to run around the track? Possible Solution Once around the track is 400 metres To cover the 10000 metres runners need to run around the track 10000 ÷ 400 = 25 times
Problems: Problems Gupta buys 200 chocolate bars at 47p each. How much do they cost him?
Problems: Problems Gupta buys 200 chocolate bars at 47p each. How much do they cost him? Possible Solution 1 bar costs 47p So, 200 bars cost 200 x 47p = 9400p = £94.00
Problems: Problems Sean has counted that he walks 1275 steps to school. If we assume that each of his steps is a metre, how far does he walk in kilometres?
Problems: Problems Sean has counted that he walks 1275 steps to school. If we assume that each of his steps is a metre, how far does he walk in kilometres? Possible Solution 1 step = 1 metre 1275 steps = 1275 metres There are1000 metres in a kilometre So Sean walks 1275 ÷ 1000 = 1.275 km
Problems: Problems Rajesh is paid £5.70 per hour. How much does he get for a 40 hour week?
Problems: Problems Rajesh is paid £5.70 per hour. How much does he get for a 40 hour week? Possible Solution 1 hour’s work = 1 x 5.70 = £5.70 40 hour’s work = 40 x 5.70 = £228
Problem: Problem Simon gets paid £220 for a 40 hour week. How much does he get per hour?
Problem: Problem Simon gets paid £220 for a 40 hour week. How much does he get per hour? Possible Solution 220 = 40h (where h is hours Divide both sides by 40, to get 5.50 = 1h So, Simon is paid £5.50 an hour
Problems: Problems Michael gets paid £6 per hour for the first 40 hours and time and a half for each of the next 20 hours. He work 50 hours. How much does he get paid?
Problems: Problems Michael gets paid £6 per hour for the first 40 hours and time and a half for each of the next 20 hours. He work 50 hours. How much does he get paid?
Problems: Problems Michael gets paid £6 per hour for the first 40 hours and time and a half for each of the next 20 hours. He work 50 hours. How much does he get paid? Possible Solution First 40 hours = 40 x 6 = £240 Overtime hours = 50 – 40 = 10 at time an a half (£9 an hour) Gets paid 10 x 90 for the overtime Total pay = £240 + £90 = £330
Problem: Problem A coach has 53 seats. 250 people want to go on a trip. How many coaches will be needed?
Problem: Problem A coach has 53 seats. 250 people want to go on a trip. How many coaches will be needed? Possible Solution 1 x 53 = 53 will go on one coach 2 x 53 = 125 will go on two coaches 3 x 53 = 159 will go on three coaches 4 x 53 = 212 will go on 4 coaches And there will be 38 passengers ‘left over’ – for which you need an extra coach So the number of coaches needed will be 5
Problem: Problem A shop sells eggs in two sizes of box – 6 in a box and 12 in a box. They have 250 eggs. How many of each size can they use? Give reasons for your choice.
Problem: Problem A shop sells eggs in two sizes of box – 6 in a box and 12 in a box. They have 250 eggs. How many of each size can they use? Give reasons for your choice. Possible Solution Imagine boxes looking like this where the smaller box is a 6 egg box and the larger a 12 egg box The shop would need 250 ÷ 18 = 13 of these combination boxes (i.e. 13 of the 12 egg boxes and 13 of the 6 egg boxes) This would account for all the eggs except 16 – and these would fit into one 12 egg box and 1 six egg box So total number of boxes = 13 + 1 = 14 of the 12 egg boxes and 13 + 1 = 14 of the six egg boxes
Problem: Problem Bricks come in packs of 50 and cost £23 per pack. Bob the Builder uses 373 bricks. He has to pay for complete packs; how much doe he have to pay for the bricks? How many will he have left over?
Problem: Problem Bricks come in packs of 50 and cost £23 per pack. Bob the Builder uses 373 bricks. He has to pay for complete packs; how much doe he have to pay for the bricks? How many will he have left over? Possible Solution 373 bricks ÷ 50 = 7 packs and 23 bricks over 7 packs will cost 7 x 23 = £161 PLUS he must pay for an extra pack (even though he is only using 23 of the bricks) So, cost is 161 + 23 = £184
Problem: Problem A newspaper charges £12.50 per single column centimetre for adverts. How much will an advert which is three columns wide and 7 centimetres long cost?
Problem: Problem A newspaper charges £12.50 per single column centimetre for adverts. How much will an advert which is three columns wide and 7 centimetres long cost? Possible Solution The first column will cost £12.50 x 7 = £87.50 There are three columns so: £87.50 x 3 = £262.50
Problem: Problem Chippy Ash the carpenter wants to place an advert regularly in the newspaper. He is told that for 5 adverts he will pay £360, but for 12 adverts he will pay £900. Which offer is the best deal?
Problem: Problem Chippy Ash the carpenter wants to place an advert regularly in the newspaper. He is told that for 5 adverts he will pay £360, but for 12 adverts he will pay £900. Which offer is the best deal? Possible Solution 5 adverts cost £360 – so 1 advert costs 360 ÷ 5 = £72 12 adverts cost £900 – so 1 advert costs 900 ÷ 12 = £75 So the 5 adverts for £360 is the best deal
Problem: Problem Walking burns off 80 calories for each 20 minutes walked. How long would you need to walk to burn off 960 calories?
Problem: Problem Walking burns off 80 calories for each 20 minutes walked. How long would you need to walk to burn off 960 calories? Possible Solution One period of walking uses up 80 calories There are 960 calories to be burned, so Number of periods of walking = 960 ÷ 80 = 12 Each period is 20 minutes So, total time is 12 x 20 = 240 minutes = 4 hours
Paying the Bills: Paying the Bills 03 July 2011 Objectives Calculate the amounts due in a range of bills
Problem: Problem If Siobhan gets paid £5.27 an hour. How much does she receive for 20 hours work?
Problem: Problem If Siobhan gets paid £5.27 an hour. How much does she receive for 20 hours work? Possible Solution For 1 hour get paid 1 x 5.27 = £5.27 For 20 hours get paid 20 x 5.27 = £105.40
Problem: Problem If Ishtak’s wages for a week’s work are £162 for 30 hours work, what was his hourly rate of pay?
Problem: Problem If Ishtak’s wages for a week’s work are £162 for 30 hours work, what was his hourly rate of pay? Possible Solution 30 hours gets 162 pounds Divide BOTH SIDES by 30, to get 1 hour gets 163 ÷ 30 = £5.40
Problem: Problem Peter gets three cans of deodorant for the price of two. If each can originally costs £3, how much does he pay for EACH of the three he buys?
Problem: Problem Peter gets three cans of deodorant for the price of two. If each can originally costs £3, how much does he pay for EACH of the three he buys? Possible Solution Two cans cost £3 each – so total cost is 2 x 3 = £6 But he gets 3 cans for this £6 so each can costs 6 ÷ 3 = £2
The Electricity Bill: The Electricity Bill There are usually two parts to the charges on a bill: The standing charge The rate for each unit of electricity Example The standing charges is £12 per quarter The units rate is 5p per unit If you use 300 units how much will your bill be?
Working out the bill: Working out the bill Standing charge = £12 Electricity used costs 500 x 0.03 = £15 Total Bill £27
problem: problem To hire a car costs a fixed fee of £25 and £15 per day. How much does it cost to hire for a week?
problem: problem To hire a car costs a fixed fee of £25 and £15 per day. How much does it cost to hire for a week? Possible Solution Fixed fee = £25 Cost of hire for a week = 7 x 15 = £105 So, total cost = £105 + £25 = £130
problem: problem A mobile phone costs £15 per month and 3p per minute for calls. How much will it cost for a month with 350 calls?
problem: problem A mobile phone costs £15 per month and 3p per minute for calls. How much will it cost for a month with 350 calls? Possible Solution Fixed fee = £15 Calls cost 350 x 3 = 1050p = £10.50 So total cost for the month = £15 = £10.50 = £25.50
problem: problem An electricity company has two tariffs – A - 7p a unit and B - 12 p a unit. If the standing charge is £13 and Mrs Jones uses 230 A units and 130 B units. How much is her bill?
problem: problem An electricity company has two tariffs – A - 7p a unit and B - 12 p a unit. If the standing charge is £13 and Mrs Jones uses 230 A units and 130 B units. How much is her bill? Possible Solution Tariff A 230 x 7p = 1610p = £16.10 Tariff B 130 x 12 = 1560p = £15.60 Standing charge is £13 So total bill is £16.10 + £15.60 + £13 = £44.70
Problem: Problem A PAYGO phone costs 7p per minute for calls. How much will it cost for 230 minutes?
Problem: Problem A PAYGO phone costs 7p per minute for calls. How much will it cost for 230 minutes? Possible Solution Cost = 230 x 7 = 1610p = £16.10
Problem: Problem A rental deal has a free handset, with £15 per month rental and 4p per minute. How much will it cost for the month in which 130 minutes of calls were made?
Problem: Problem A rental deal has a free handset, with £15 per month rental and 4p per minute. How much will it cost for the month in which 130 minutes of calls were made? Possible Solution Call = 130 x 4 = 520p = £5.20 Rental = £15 So, total monthly cost = £15 + £5.20 = £20.20
Problem: Problem A rental deal has a free handset and £30 per month rental. The first 100 minutes of calls are free. The next 200 cost 5p per minute. How much will the phone cost in the month when 180 minutes of calls were made? Possible Solution Rental = £30 180 – 100 = 80 calls to be paid for at 5p a minute = 80 x 5 = £4 So, total cost of the phone = 30 + 4 = £34
Problem: Problem A rental deal has a free handset and £30 per month rental. The first 100 minutes of calls are free. The next 200 cost 5p per minute. How much will the phone cost in the month when 180 minutes of calls were made?
Summary: Summary You should now be able to: Carry out the four operations of addition, subtraction, multiplication and division – accurately and consistently Solve problems which require you to use these basic skills