http teachable netres asp r766 Contents Calculator questions

http: //teachable. net/res. asp? r=766

Contents : Calculator questions Best buy questions Long multiplication Long division Simple fractions questions Negative numbers Rounding Estimating Percentages Types of number Products of primes HCF and LCM Indices Simplifying roots Standard Form Ratio Fractions with the four rules Recurring decimals as fractions Units Distance, Speed, Time questions Density, Mass, Volume questions

Calculator questions Which buttons would you press to do these on a calculator ? 2. 5 + 4. 1 3. 5 1. 7 + 2. 8 2. 3 – 0. 2 1. 56 8. 5 x 103 3. 4 x 10 -1 4 1000 1. 72 + 5. 22 6. 31 9. 2 6. 1 – 7. 5 8 3 2. 5 1 1 – 3. 6 2. 3

Best buy questions 87 p Always divide by the price to see how much 1 pence will buy you Beans Large 400 87 = 4. 598 g/p Small 150 34 = 4. 412 g/p Large is better value (more grams for every penny spent) 32 p 0. 95 L 78 p OR 2. 1 L 34 p OR Milk Large 2. 1 78 = 0. 0269 L/p Small 0. 95 32 = 0. 0297 L/p Small is better value OR (looking at it differently) {Large 78 2. 1 = 37. 14 p/L Small 32 0. 95 = 33. 68 p/L}

Long multiplication Use the method that gives you the correct answer !! Question : 78 x 59 70 50 9 Total = 8 3500 400 630 72 3500 + 400 + 630 + 72 Answer : 4602 Now try 84 x 46 and 137 x 23 and check on your calculator !!

Again use the method that gives you the correct answer !! Long division Question : 2987 23 12 9 23 times table 23 46 69 92 115 138 161 184 207 230 29 68 23 6 22 20 2987 Answer : 129 r 20 227 Now try 1254 17 and check on your calculator – Why is the remainder different?

Simple fractions questions Equivalent fractions 1. 3 = 12 ? 20 2. 5 = ? 6 24 3. 9. = ? 12 ? 4. ? = 5. ? 25 Fractions into decimals Divide top by bottom 9. = 9 12 = 0. 75 12 1. 4. 4 5 2. 6 7 3. 5 9 Put the following fractions in order of size, smallest to largest: 3 2 5 4 4 3 8 7 Fractions of amounts 1. 1 of £ 30 2 2. 1 of £ 30 6 3. 5 of £ 30 6 4. 5 of $72 9 Divide by the bottom then times by the top

Negative numbers Put these in order - smallest first - 4 , - 3. 6 , - 0. 4 , - 0. 36 , - 1 , 0 , 2 , - 1. 4 Up and down the scale 1. 2. 3. 4. 5. -3+5= Two signs next to each other -7+2= 1. -3+ -1=-3 -1= -2 -4= 2. -4 - -2= -4+2= 5 - 12 = 3. - 9 - - 11 = -6+4= 4. 5+ -7= Multiplication and Division Signs same +ve answer Signs different -ve answer 3. - 8 - 4 = 2= 1. -4 3= 2. -5 - 4. 20 - 5 = 5. -4 4= 6. (- 7)2 =

Rounding 4715. 692803 cm Round this number off to : (a) 1 decimal place (b) 1 significant figure (c) 2 decimal places (d) 2 significant figures (e) the nearest centimetre (f) the nearest metre (g) 3 decimal places (h) 3 significant figures (a) 4715. 7 cm (b) 5000 cm (c) 4715. 69 cm (d) 4700 cm (e) 4716 cm (f) 47 m (g) 4715. 692 cm (h) 4720 cm 14. 9999 But there is always a trickier one Round this number off to : (a) the nearest whole number (a) 15 (b) 3 significant figures (b) 15. 0 (c) 2 decimal places (c) 15. 00

Estimating If you are asked to estimate an answer to a calculation – Round all the numbers off to 1 s. f. and do the calculation in your head. DO NOT USE A CALCULATOR !! e. g. Estimate the answer to 4. 12 x 5. 98 4 x 6 = 24 Always remember to write down the numbers you have rounded off Estimate the answer to these calculations 1. 58 x 21 2. 399 x 31 3. 4. 5. 7. 12 x 39. 2 0. 87 8. 4. 89 x 6. 01 1. 92 47 x 22 6. 377 19 9. 360 x 87 4899 46 7. 1906 44 10. 58 x 21

Percentages Increase: 13. 17% of Percentage increase and decrease A woman’s wage increases by 13. 7% from £ 240 a week. What does she now earn ? New amount: £ 240 + 31. 608 = 271. 608 13. 17 100 x Her new wage is £ 271. 61 a week 240 = 31. 608 10% = Percentages of amounts (Do these without a calculator) 30% = 75% = 1% = 25% = £ 600 45% = 85% = 20% = 50% = 2% =

Percentages Fractions, decimals and percentages 50% 56% Dec Frac 0. 17 1 2 0. 5 Copy and complete: % 83% 0. 04 9 50 28% 4 25 0. 92 19 20

Reverse % e. g. A woman’s wage increases by 5% to £ 660 a week. What was her original wage to the nearest penny? Original amount x 1. 05 £ 660 Original amount ÷ 1. 05 £ 660 Original amount = 660 ÷ 1. 05 = £ 628. 57 e. g. A hippo loses 17% of its weight during a diet. She now weighs 6 tonnes. What was her former weight to 3 sig. figs. ? Original weight x 0. 83 6 ton. Original weight = 6 ÷ 0. 83 = 7. 23 tonnes ÷ 0. 83 6 ton.

Repeated % e. g. A building society gives 6. 5% interest p. a. on all money invested there. If John pays in £ 12000, how much will he have in his account This is not the correct method: at the end of 5 years. £ 12000 x 0. 065 = 780 x 5 x=1. 065 3900 x 1. 065 12000 + 3900 = £ 15900 x 1. 065 ? He will have = 12000 x (1. 065)5 = £ 16441. 04 e. g. A car loses value at a rate of approximately 23% each year. Estimate how much a $40000 car be worth in four years ? This is not the correct method: 40000 = 9200 x 0. 77 £ 40000 x 0. 77 x 0. 23 x 0. 77 ? 9200 x 4 = 36800 40000 – 36800 = $3200 The car’s new value = 40000 x (0. 77)4 = $14061 (nearest $)

Types of number From this set of numbers list the: • Odd numbers • Even numbers • Multiples of 8 • Factors of 12 • Prime numbers • Square numbers • Cube numbers 100 13 7 2 16 25 3 20 1 27 9 11 6 12 Some useful words to know the meaning of: ü Sum = add together ü Product = multiply together ü Difference = subtract one number from another ü Reciprocal of a number = 1 divided by the number (e. g. Reciprocal of 4 = ¼ or 0. 25)

40 Products of primes Express 40 as a product of primes 2 20 2 40 = 2 x 2 x 5 (or 23 x 5) Express 630 as a product of primes 10 2 630 2 Now do the same for 100 , 30 , 29 , 144 5 315 3 105 3 630 = 2 x 3 x 5 x 7 (or 2 x 32 x 5 x 7) 35 5 7

Finding the HCF and LCM of a pair of numbers HCF stands for the Highest Common Factor (the biggest number that will go into both numbers) LCM stands for Lowest Common Multiple (the first number to appear in both numbers times table) e. g. Find the HCF and LCM of the two numbers 140 and 112 Write both numbers as a product of primes 140 = 2 x 5 x 7 and 112 = 2 x 2 x 7 For the HCF write out all the primes that appear in both answers HCF = 2 x 7 = 28 For the LCM write out the largest number of each prime that exists in either number LCM = 2 x 2 x 5 x 7 = 560

Indices 2 3 1 9 9 3 2 2 10 0 19 3 4 2 5 4 10 5 7 6 2 3 5 1 17 3 7 5 2

Simplifying roots Tip: Always look for square numbered factors (4, 9, 16, 25, 36 etc) e. g. Simplify the following into the form a b 12 4 x 3 2 3 8 4 x 2 2 2 45 9 x 5 3 5 72 36 x 2 700 100 x 7 6 2 10 7

Standard form Write in Standard Form 9. 6 0. 0001 3 600 0. 041 23 600 0. 2 8 900 000 0. 003 Do 3 46. 7 Write as an ordinary number 4. 7 x 109 1 x 102 8 x 10 -3 5. 1 x 104 7 x 10 -2 8. 6 x 10 -1 9. 2 x 103 6 x 106 3. 5 x 10 -3 2 x 100 x 104 x 7 x 105 with and without a calculator

Ratio Equivalent Ratios ? : 10 ? : 6 14 : ? 1 : ? 7: 2 49 : ? ? : 1 £ 600 is split between Anne, Bill and Claire in the ratio 2: 7: 3. How much does each receive? ? : 12 21 : ? 0. 5 : ? Splitting in a given ratio ? : 12 2100 : ? Total parts = 12 Anne gets 2 of 600 = £ 100 12 Basil gets 7 of 600 = £ 350 12 Claire gets 3 of 600 = £ 150 12

Fractions with the four rules +–×÷ Learn these steps to complete all fractions questions: • Always convert mixed fractions into top heavy fractions before you start • When adding or subtracting the “bottoms” need to be made the same • When multiplying two fractions, multiply the “tops” together and the “bottoms” together to get your final fraction • When dividing one fraction by another, turn the second fraction on its head and then treat it as a multiplication

Fractions with the four rules 4⅔ 1½ 4⅔ + 1½ = = 14 3 28 6 37 6 6 + + 3 2 9 6 = = = 1 6 = 14 3 28 9 3 1 9 3 2 2 3

Recurring decimals as fractions Learn this technique which changes recurring decimals into fractions: Express 0. 7777…. . as a fraction. Let n = 0. 7777…. . so 10 n = 7. 7777…. . so 9 n = 7 so n = 7/9 Express 2. 3434…. . as a fraction. Let n= 2. 3434…. . so 100 n = 234. 3434…. . so 99 n = 232 so n = 232/99 Express 0. 13213213…. . as a fraction. Let n= 0. 132132132…. . so 1000 n = 132132132…. . so 999 n = 132 so n = 132/999 n = 44/333

Units Learn these rough conversions between imperial and metric units 1 inch 2. 5 cm 1 yard 0. 9 m 5 miles 8 km 2. 2 lbs 1 kg 1 gallon 4. 5 litres Learn this pattern for converting between the various metric units Metriclength weightconversions capacity conversions Metric x 1000 km kg kl ÷ 1000 x 100 m gl x 10 cm cg cl ÷ 100 mm mg ml ÷ 10

Speed, Distance, Time questions Speed, Distance and Time are linked by this formula S = To complete questions check that all units are compatible, substitute your values in and rearrange if necessary. 1. Speed = 45 m/s Time = 2 minutes Distance = ? 45 m/s and 120 secs S= D T 45 = D. 120 45 x 120 = D D = 5400 m 2. Distance = 17 miles Time = 25 minutes Speed = ? 17 miles and 0. 417 hours S= D T S= 17. 0. 417 S = 40. 8 mph 3. D T Speed = 65 km/h Distance = 600 km Time = ? S= D T 65 = 600. T T = 600. 65 T = 9. 23 hours

Density, Mass, Volume questions Density, Mass and Volume are linked by this formula M D = V To complete questions check that all units are compatible, substitute your values in and rearrange if necessary. 1. Density = 8 g/cm 3 Volume = 6 litres Mass = ? 8 g/cm 3 and 6000 cm 3 D= M V 8= M. 6000 8 x 6000 = M M = 48000 g ( or M = 48 kg) 2. Mass = 5 tonnes Volume = 800 m 3 Density = ? 800 m 3 and 5000 kg D= M V D = 5000. 800 D = 6. 25 kg/m 3 3. Density = 12 kg/m 3 Mass = 564 kg Volume = ? D= M V 12 = 564. V V = 564. 12 V = 47 m 3