Skills - Mental Arithmetic



M1 MathsMental Arithmeticknow the + and facts to 9+9 and 99 and the corresponding – and facts develop, choose and use a flexible range of methods for performing arithmetic calculations mentally and on paperhave a sense of the size of numbers; be able to estimate the result of a calculation before performing it and check the reasonableness of an answer after calculating it.Number Facts Mental Arithmetic Techniques Number Sense and EstimationMain Number Facts Practice Number Facts Progress ChartExtra Number Facts PracticeMental Arithmetic PracticeNumber FactsWhy learn the number facts?Knowing the number facts is important because it allows you to concentrate on the bigger calculations you are doing without having to keep stopping to work out the basic facts. For example, suppose you are multiplying 24 by 7 to work out how many hours in a week. You may do 7 20 which is 140 and 7 times 4 which is 28, then add 20 to 140 to get 160, then add the 8 to get 168. If you have to keep stopping to work out 7 2, 7??4, 4 + 2 etc., then you tend to lose track of what you were doing in the bigger calculation. It can be very frustrating to have to keep starting again because you have forgotten where you were up to.How to learn the number factsNumber facts just have to be learnt – sort of parrot fashion. There is no reason why 7 + 6 is 13; it just is and you just have to memorise it so that you can know the answer instantly without having to take time to work it out.There are various ways to learn number facts. One of the best ways is to use a grid like the one on page 6 of this module. You can print copies of this. Pick one operation. Time yourself while filling in the 64 answers. As you go, circle any that you have to stop and think about or can’t do. At the end, write the time you took in minutes and seconds in the space provided under the operation. Then mark your work using the answer sheet on page 7 and circle any that you got wrong if they are not circled already. It is easiest if you print the answer sheet and fold it vertically down the right-hand side of each column of answers, then lay the answer-sheet answers to the left of your answers. Then write your number correct out of 64 in the space provided under the operation.After timing yourself on an operation and marking it, make an effort to memorise the facts that you have circled (both those you had to think about and those you got wrong or didn’t do) by repeating them to yourself often. This is the most important part of the learning process and will ensure that you improve from one attempt to the next. Ideally, you should be able to get all 64 correct on the Practice Sheet in about 1 ? minutes for the addition and multiplication and 2 minutes for subtraction and division. You should practise until you can do this consistently.To add a bit of variety to your practice, there are various different practice sheets on pages 10 to 18.There is a progress chart on page 8 which you can use to track your progress in mastering your number facts. Seeing your progress can be rewarding and motivating. Instructions for using the chart can be found on page 9.Mental Arithmetic TechniquesWe spend a lot of time in Years 1 to 7 learning procedures for adding, subtracting, multiplying and dividing on paper. Most of the arithmetic that people do in day to day life, though, is done mentally – and the written methods you learn aren’t always the easiest ones to use in your head.For example, suppose you were working out the change from $10 if you spend $1.65. The standard written method is very laborious with lots of decomposition. But most of us can do that calculation quite easily, for instance, by taking a dollar from $10 to make $9, then taking 60c to make $8.40, then taking 5c to make $8.35.Likewise, suppose you wanted the price of 18 Freddos at 25c each. The standard method would be difficult in your head because there are lots of things to remember. Try it if you are not convinced. However, you might spot that 4 Freddos cost $1, therefore 16 cost $4 and 18 cost $4.50.No single method is quickest for every problem. Someone who is good at arithmetic has numerous methods they can use depending on what is easiest for that problem. And they also have the ability to make up new ones if they can make the problem easier.There are two main ways to improve your repertoire of methods and to become skilful at using them.Firstly have lots of practice at doing calculations mentally, trying to think of good short cuts where possible. Practice exercises are provided on pages 19 to 28 and the answers are on pages 29 to 33. There are different degrees of difficulty for students working on different levels.These can be used in a number of ways, but generally it is good to do them in batches of 10 questions. You could read the questions from a screen and write the answers on paperYou could print the page you are working on and write the answers on the sheet or on a different sheet.You could get someone to read you the questions and you could write the answers on paper. Your teacher may do this as a whole-class activity to give you regular practice.Secondly, after doing a mental arithmetic calculation, see how other people did the same calculation. Nearly always when a class does a calculation, more than one method will be used. Listen to the methods others used and, if you hadn’t thought of them, try to add them to your own repertoire and practise them.Your teacher will hopefully give you opportunities to do mental arithmetic and share methods so that you can see how other people did the same calculations.We do arithmetic on paper only because there is too much to remember at once if we do it in our heads. Sometimes, when working on paper, all we need to put down is a couple of jottings. Other times we will need to lay out the calculation more fully. Even if you lay it out more fully, there are usually several different methods by which the calculation can be done. You can choose whatever method makes it easiest and most reliable. There is no need to use a ‘standard’ method.Number Sense and Estimation Number sense is the ability to have a feel for how big the answer will be before doing a calculation. For instance, seeing that:72 × 59 is likely to be a 4-digit number, the number of 0.05s that would be needed to make 40 is likely to be quite a bit more than 40. In other words that 40 ÷ 0.05 is quite a bit more than 40, 5/12 is less than 4/7,120332516319500120332510985500135% of $42.40 will be about $50 to $60.Number sense comes from having a good understanding of numbers – what they mean – what fractions mean, what the different places in a decimal mean etc. It also comes from lots of experience with doing calculations with different types of numbers. And, in particular, it comes from estimating the results of calculations before doing them and comparing the estimate with the actual answer afterwards. If you can get into the habit of that when you calculate, it will help your number sense immensely. And good number sense will make you much more competent with anything involving numbers.In a lot of situations in life, you only need an approximate answer for a calculation. Good number sense will allow you to get this without going to the trouble of doing it fully. As mentioned above, good number sense will tell you that 72 × 59 will probably be a 4-digit number. To get a better idea, we could start multiplying by the grid method by doing 70 × 50 = 3500. The answer will be a bit more than 3500 – maybe 4000. Even better would be to notice that 59 is almost 60 and so to work out 70 × 60 as 4200. Because 59 is just below 60 and 72 is just above 70, the errors will sort of cancel each other out a bit, so 4200 should be fairly close. The exact answer is 4248. Finally, good number sense will allow you to see easily if the answer to a calculation is wrong and this can be useful in lots of situations, not least in seeing if any of your answers on a test need re-checking.Main Number Facts Practice Sheet2+55+93+72+94+86+57+95+66+84+29+44+49+67+44+34+72+38+36+63+95+56+29+99+25+72+79+87+78+75+44+66+96+33+38+22+45+23+69+77+58+57+69+52+86+75+82+62+26+48+87+35+34+53+27+83+48+93+58+67+23+88+44+99+3+ Time . . . . . . . . . . . . + Correct . . . . . . . . . . . 12–76–312–48–214–615–911–24–29–714–78–517–810–310–412–88–411–69–69–414–912–916–77–45–39–28–314–511–811–47–514–811–317–910–69–313–516–815–712–36–45–211–910–810–713–710–513–89–511–515–87–313–67–213–46–211–718–910–216–912–512–68–613–915–6? Time . . . . . . . . . . . . ? Correct . . . . . . . . . . . 2×55×93×72×94×86×57×95×66×84×29×44×49×67×44×34×72×38×36×63×95×56×29×99×25×72×79×87×78×75×44×62×26×33×38×22×45×23×69×76×98×57×69×52×86×75×82×67×56×48×87×35×34×53×27×89×38×93×58×67×23×88×44×93×4× Time . . . . . . . . . . . . × Correct . . . . . . . . . . .357243455189102549255568124217844273281821422131837284262842791644863063646481626371265461532046320545912340830518624816882155369147244497639355729625674059348836612224681927332410528742÷ Time . . . . . . . . . . . ÷ Correct . . . . . . . . . . .Main Number Facts Practice Sheet – Answers2+575+9143+7102+9114+8126+5117+9165+6116+8144+269+4134+489+6157+4114+374+7112+358+3116+6123+9125+5106+289+9189+2115+7122+799+8177+7148+7155+494+6106+9156+393+368+2102+465+273+699+7167+5128+5137+6139+5142+8106+7135+8132+682+246+4108+8167+3105+384+593+257+8153+478+9173+588+6147+293+8118+4124+9139+31212–756–3312–488–2614–6815–9611–294–229–7214–778–5317–8910–3710–4612–848–4411–659–639–4514–9512–9316–797–435–329–278–3514–5911–8311–477–5214–8611–3817–9810–649–3613–5816–8815–7812–396–425–2311–9210–8210–7313–7610–5513–859–5411–5615–877–3413–677–2513–496–2411–7418–9910–2816–9712–5712–668–6213–9415–692×5105×9453×7212×9184×8326×5307×9635×6306×8484×289×4364×4169×6547×4284×3124×7282×368×3246×6363×9275×5256×2129×9819×2185×7352×7149×8727×7498×7565×4204×6242×246×3183×398×2162×485×2103×6189×7636×9548×5407×6429×5452×8166×7425×8402×6127×5356×4248×8647×3215×3154×5203×267×8569×3278×9723×5158×6487×2143×8248×4324×9363×4123575243845591892102554962555568712432173842427632841829142721371836728942672847279316444868306536496488162863791262546915352045632205445951234408530561863248316828241553369414722446497763973557729862356784058933488636661226246481992739324810522874422 Number Facts Progress Chart You can use this to plot your progress – Instructions on the next page 32404856 4 3 2 1 02416 8Number CorrectTime 1 23 4 5 10 15 20 25Attempt32404856 4 3 2 1 02416 8Number CorrectTime 1 23 4 5 10 15 20 25AttemptNumber Facts Progress Chart – Instructions for UseSome people like to keep track of their progress in mastering the number facts. You can do this by printing the progress chart on the page 8 and plotting your results for the Main Number Facts Practice Sheet on it. This is how you plot them. Let’s say you attempt the addition facts. If you get less than 64 correct, then plot the number correct on the bottom part of the graph. Use a + symbol (use a – symbol if you did the subtraction facts etc.). Put the symbol on the first vertical dotted line – the one corresponding to Attempt 1. Judge the vertical position by using the scale on the left. Estimate between the graduations. For instance, if you got 38 correct, then you will put the symbol between the horizontal dotted line for 32 and the one for 40, but closer to the 40 (because 38 is closer to 40 than to 32).If you get all 64 correct, then you don’t plot your number correct, but instead, you plot your time on the top half of the graph. Note the scale goes from 4 minutes at the bottom to 0 at the top. If you took 4 minutes or more, then plot your symbol on the 4 minutes line. If you took less than 4 minutes, plot it at the right height according to the scale on the left. Again the symbol goes on the first vertical dotted line.Note that you will only plot one symbol – on either the bottom part or the top part of the graph – not both. When you have your next go at that same operation, you plot your result the same way, but on the second vertical dotted line – the one corresponding to Attempt 2. And so on for up to 25 attempts. Join your symbols with lines to make a line graph.When you have your first go at a different operation, you plot your result using the symbol for that operation. Your first attempt with that operation goes on the first vertical line (Attempt 1), the second on the second and so on. This will mean that you can plot 25 attempts at each of the 4 operations (100 attempts in total) on the one chart. There should eventually be four symbols on each vertical line (+, –, and ). It will make the chart easier to read if you use a different colour for each operation.After timing yourself on an operation and marking it, make an effort to memorise the facts that you have circled by repeating them to yourself often. This is the most important part of the learning process and will ensure that you improve from one attempt to the next. Don’t expect every attempt to be better than the last, but a trend of improvement should show once you have made a few attempts. This will appear as a line heading generally upwards on the chart, even if it has a few wiggles along the way. Learning number facts takes time. You might already know all your number facts. But, if not, you will have to spend time practising them. If you make the effort after each attempt to learn the ones you got wrong, it should take you a lot less than 25 attempts to know them all. Aim for being able to do the + and sets in about 1? minutes each and the – and sets in about 2 minutes each.Extra Number Facts Practice 1: Mixed Operations2+55+93+72+94+86+57+912–76–312–48–214–615–911–22×55×93×72×94×86×57×93572434551891025492556+84+29+44+49+67+44+39–714–78–517–810–310–412–86×84×29×44×49×67×44×3124217844273281821422+38+36+63+95+56+29+911–69–69–414–912–916–77–42×38×36×63×95×56×29×91837284262842791644865+72+79+87+78+75+44+69–28–314–511–811–47–514–85×72×79×87×78×75×44×63646481626371265461536+33+38+22+45+23+69+717–910–69–313–516–815–712–36×33×38×22×45×23×69×7632054591234083051868+57+69+52+86+75+82+65–211–910–810–713–710–513–88×57×69×52×86×75×82×6168821553691472444976+48+87+35+34+53+27+811–515–87–313–67–213–46–26×48×87×35×34×53×27×835572962567405934888+93+58+67+23+88+44+918–910–216–912–512–68–613–98×93×58×67×23×88×44×91222468192733241052875+64+79+26+97+59+33+48–45–311–36–49–511–715–65×64×79×26×97×59×33×4568213306204248639366Extra Number Facts Practice 1: Mixed Operations - Answers71410111211165386869104521183230635892565146138151172739764488361654281233264975111212108185355393624362725128169773481291714159107593726351472495620249889295961067916846888918916810186324545631313141013138322365540424516424012243426710161089515674759424642115206567838836178149111213987762472154814243236649982411111115121274282449302818543527127755376Extra Number Facts Practice 2: Addition and Multiplication PRIVATE 38269475629547382482795633684795 PRIVATE 73952864893647257358228669359447 PRIVATE 37492586267935489468258377593246Extra Number Facts Practice 2: Answers – AdditionPRIVATE 382694756295473825104811697410613981171281116101417121513284117695107101591316111412915111814131612175813711149121061281511101391436115912710839512871061169148121510131181410171312151116471261013811971391614111410159121711151813161451171410912813 PRIVATE 739528648936472571410161291513113111269710585128141071311981617111412151013295117410862101158694781511171310161412614159121013811613915118141210917181215131611143106128511975131481191271091612181411171513412137108116941171396121087151610131114912 PRIVATE 374925862679354891216131811141715461011137981269131015811141281014151711131216259611471085711121481091381115121710131614359101268711710141116912151379131416101211155812914710131191115161812141317361071258119248911576104711813691210681213159111014 Extra Number Facts Practice 2: Answers – MultiplicationPRIVATE 382694756295473826164121881410424836201628123282464164872325640212418108146167215614426328493595418814536632772515401030452035256361254302442184839246182712211531862715122192461848123654244230848167240325624644123282436162820742146335284921569277218548136634553010452520351540 PRIVATE 739528648936472574910163514564228324279181221615535154525104030208647224483256164021461810416128216186128144108562472401664483264854183624421230642185430124836249728127543663184532192715624181254045153020351025963278145187254364323612241611620428123620832241675663214228491412 PRIVATE 374925862679354892763368118457254482428361220163261842245412304836816485672244032642514818410161251030354515252040824563272164064483618212791512247214928631435564271442496321352856515352045102540309185463812745367239211227615241824121418610816412281636820322461236425418302448 Extra Number Facts Practice 3: Subtraction and Division 4–2 =11–8 =10–2 =14–8 =11–9 =12–3 =10–7 =11–6 =18–9 =8–4 =15–7 =5–3 = 6–4 =13–4 =11–7 =15–6 =7–3 =16–8 =5–2 =12–5 =13–8 =8–6 =9–2 =10–5 =16–9 =7–2 =12–6 =13–9 =10–8 =15–8 =11–3 =13–7 =12–7 =6–3 =12–4 =8–2 = 15–9 =9–7 =14–6 =11–2 =9–4 =14–7 =8–5 =17–8 =9–5 =8–3 =14–5 =17–9 =10–6 =16–7 =7–5 =11–5 =9–3 =13–6 =10–3 =12–8 =6–2 =9–6 =10–4 =14–9 =11–4 =13–5 =12–9 =7–4 =205 =82 =729 =246 =213 =147 =426 =162 =459 =155 =62 =819 =248 =164 =546 =186 =305 =639 =105 =244 =306 =93 =567 =273 =369 =204 =405 =324 =497 =488 =287 =366 =357 =243 =455 =189 =102 =549 =255 =142 =124 =217 =728 =183 =123 =182 =486 =279 =364 =63 =168 =355 =42 =427 =284 =328 =84 =648 =153 =408 =122 =568 =637 =126 =8–5 =17–8 =9–5 =8–3 =14–5 =17–9 =9–4 =14–7 =10–6 =16–7 =7–5 =11–5 =9–3 =13–6 =10–3 =12–8 =7–3 =16–8 =5–2 =12–5 =13–8 =8–6 =9–2 =10–5 =16–9 =7–2 =12–6 =13–9 =10–8 =15–8 =11–3 =13–7 =12–7 =6–3 =12–4 =8–2 =15–9 =9–7 =14–6 =11–2 =6–2 =9–6 =10–4 =14–9 =11–4 =13–5 =12–9 =7–4 =4–2 =11–8 =10–2 =14–8 =11–9 =12–3 =10–7 =11–6 =18–9 =8–4 =15–7 =5–3 = 6–4 =13–4 =11–7 =15–6 =287 =366 =369 =204 =405 =324 =497 =488 =357 =243 =455 =189 =102 =549 =255 =142 =364 =63 =168 =355 =42 =427 =284 =328 =205 =82 =729 =246 =213 =147 =426 =162 =305 =639 =105 =244 =306 =93 =567 =273 =459 =155 =62 =819 =248 =164 =546 =186 =124 =217 =728 =183 =123 =182 =486 =279 =84 =648 =153 =408 =122 =568 =637 =126 =Extra Number Facts Practice 3: Subtraction and Division – Answers238629359482 294948375275756427865386 62895739459849266774434578334484727853393493672653894588764658925657339649839227267428556792394598574926677448375275756427865386628943657833238629359482 29494645887658925657922726744484727867265389533934933396498328556792Extra Number Facts Practice 4 – Addition and Subtraction PRIVATE 23629871213412812141878910712691415126131081411PRIVATE 632346111081671614125398131129131587111359614 PRIVATE 276414310111291314913171347513109118811221251310Extra Number Facts Practice 4 – Multiplication and DivisionPRIVATE 2362987353643283245811012141610359945542764224124824PRIVATE 632346301686476349276318154224214365415102836520648PRIVATE 27641432424329364520427236472854025202816824242763624Mental Arithmetic Practice – Level 16 + 1718 + 4022 – 5100 – 4417 214 1036 3100 5301 + 3416 + 8205 – 732 – 94 + 1831 – 1712 723 480 5160 2154 + 983 10022 + 137 + 9170 – 9072 – 1312 512 6040 490 332 + 15028 – 2859 + 60311 + 46400 – 3156 – 2813 317 10064 440 51000 – 6039 106 + 4760 + 4530 – 2652 – 1223 315 540 2075 1525 + 11712 + 54170 – 12050 + 34020 – 13300 + 19921 36 1434 238 2160 4077 – 7449 + 7335 + 4531 – 1840 – 127 1324 651 384 415 + 41025 + 199600 – 410432 – 33267 – 14601 – 30027 370 1428 231 618 10140 10Mental Arithmetic Practice – Level 1 – continued26 + 817 + 11271 – 1245 – 1825 524 449 764 2175 –928 + 2327 + 34125 – 11245 – 171189 – 20032 51 7360 1042 34000 1007 103130 + 110016 + 0137 – 1534 – 028 327 0440 20 330 + 1510 + 31443 – 17148 – 9960 – 25100 – 3934 341 452 474 221 100371 + 6063 + 1959 + 835 – 1652 – 148 1511 1036 475 52 + 405123 + 4516 + 15370 + 151453 – 20040 1035 237 263 366 6756 – 301000 200142 + 3618 + 34120 – 738 – 1832 452 364 468 21600 + 6328 + 2718 + 34450 – 2742 – 28700 – 39931 2065 257 365 542 100020 20Mental Arithmetic Practice – Level 26 + 1918 + 41220 – 51000 – 4418 214 1036 3100 53 + 3.41.6 + 0.82.5 – 0.73.2 – 0.94 + 1.83.1 – 1.712 723 480 552 23/10 + 4/104/5 – 1/522 + 1497 + 917 – 972 – 1512 5013 10040 490 33.2 + 1.52.81 – 2.85.9 + 6.03.11 + 0.46.4 – 3.15.6 – 2.813 517 1064 440 55/8 – 3/89/10 – 3/106 + 5760 + 45340 – 26452 – 1423 315 1240 2075 152.5 + 1.71.2 + 5.51.7 – 1.24.6 + 3.42.0 – 1.33 + 1.9921 36 1434 238 22/7 + 3/72/7 – 1/7149 + 703335 + 4531 – 1840 – 1270 1324 651 384 41.5 + 4.12.5 + 1.616 – 1.64.32 – 4.12.67 – 0.046 – 3.6527 3070 1428 231 1112/10 – 3/102/5 + 6/5Mental Arithmetic Practice – Level 2 – continued26 + 87 + 102701 – 1345 – 1825 526 4490 762 25 – 0.928 + 2.32.7+ 3.40.25 + 0.124.5 – 1.719 – 2.532 1001 7360 1242 31/9 + 4/94/13 + 5/1330 + 11016 + 4037 – 1534 – 926 327 1004400 100 3513 + 1.510 + 0.3144.3 – 1.74.8 + 2.56.0 – 1.2510 – 3.733 3041 4052 474 211/4 – 3/41/6 + 5/663 + 21959 + 8135 – 11652 – 148 1411 10056 475 52 + 4.051.23 + 0.451.6 + 1.993.7 + 1.514.53 – 1.22.8 – 0.0935 237 263 366 65/5 – 4/54/7 + 5/7142 + 3618 + 30170 – 71038 – 12532 420 1364 448 20.03 + 6.32.8 + .271.8 + 3.44.5 – 2.74.2 – 2.87 – 0.3467 265 2057 365 52/3 + 5/33/12 – 1/12Mental Arithmetic Practice – Level 317 4430 – 128122 + 3942/7 as an improper fr’n? of 247/10 of 0.63/10 as a decimal3.71 100.6 as a percent88 40$3.50 10$1.90 52.5 560 + 40 3add 20% to $4060% as a decimal2 + 5 64/5 as a percent4.8 – 4add 5% to $802.03 – 1.55.4 –1.914/5 as a mixed number0.6 20002.5 0.530 1001/5 of $4030 – 12 4 53/5 of $201.2 as a percent62% as a common fraction0.8 512% of $2000.8 0.51 5 as a decimal428 + 175add 10% to $50take 80% off $25012 – 8 + 40.4 3524/40 in simplest form16 891 7 40 – 12.761.6 0.51/8 as a decimal12 – 4.835/7 of 424/5 of 10600 30? of 3.20.2 0.053 5 as a common fraction$90 discounted 20%16 – 4 104 5 – 7 22.5 40121% as a mixed no.take 25% off $2000.03 5how many hours in a week12 13100 – 28.46.3 – 2.8520 30030% of $400.2 of 42.41 as an improper fr’n0.4 0.22.5 50016% of 5022 2 56 (3 + 5)11.7 32.6 + 1.812.5% of $4003/5 + 1/53/8 of $44 as a decimal6% as a decimal2.6 + 0.027Mental Arithmetic Practice – Level 3 – continued17 5470 – 269119 + 9943/8 as an improper fr’n? of 289/10 of 0.67/10 as a decimal3.77 1000.75 as a percent88 40$6.50 20$2.95 62.2 570 + 30 3add 40% to $4050% as a decimal5 + 5 62/5 as a percent4.8 – 3add 20% to $802.11 – 1.55.6 –1.917/5 as a mixed number0.7 2002.4 0.270 1001/5 of $6040 – 12 4 53/5 of $401.25 as a percent32% as a common fr’n0.3 512% of $3008 0.51 2 as a decimal432 + 175add 10% to $60take 60% off $25016 – 6 + 40.4 4524/42 in simplest form16 898 7 40 – 12.762.4 0.51/8 as a decimal10 – 4.235/7 of 423/5 of 10600 30? of 3.60.2 0.053 8 as a common fr’n$90 discounted 30%16 – 6 105 5 – 7 22.5 400101% as a mixed no.take 25% off $1200.03 5minutes in a day12 14100 – 33.36.25 – 2.7520 50015% of $400.2 of 402.3 as an improper fr’n0.4 0.32.6 20015% of $5022 2 66 (8 – 5)11.5 52.6 + 1.412.2% of $4003/5 – 1/53/8 of $362% as a decimal2.6 + 0.227Mental Arithmetic Practice – Level 4170 5430 – 128.510.22 – 4.393 5003/4 of 2407/10 of 0.613/4 as a decimal3.2 10243–8.7 –3068 3 – 20 32 –5? + 1? add 22% to $404 – 27/8–2 + 5 65/8 as a percent4 – 4.5add 6% to $602.03 – 2.55–5.4 –1.90.03 0.70.4 250013.5 –1.533 – 524/15 of $3020 – 12 4 5540.375 as a percent? of 2/32? ? 12% of $1500.6 –0.5square root of 10 0004.28 + 17.5add 10% to $52take 85% off $30012 – 8 (4 + 3)3/5 of ? 1.81 516.7 + 2.998–2.5 –6 441.8 0.05? – 1/10 as a decimal10 – 4.4330 22.54/5 of 151500 30730.2 0.063 15 as a percent$50 discounted 24%16 – 20 20 104 5 – 0.7 –22.5 10.148/56 in simplest form21 700.03 6how many hours in July1.2 11101 – 49.56 – 2 2230 300.535% of $40111/4 as a mixed number0.415 as a percent0.4 0.253 ? 22/6 + 3 5/625 –2 516 – (–3 + 5)10.8 32.6 + 1.816329? as an improper fr’n(52 – 42) 27/90 of 18Mental Arithmetic Practice – Level 4 – continued160 5430 – 179.510.23 – 4.492 5003/8 of 2403/10 of 0.613/5 as a decimal4.2 103638.4 –3083–2 –8? + 1? add 12% to $406 – 25/8–2 + –3 63/8 as a percent4 – 5.8add 7% to $602.04 – 2.445.4 – –1.70.05 0.70.4 25012 –1.534 – 437/15 of $30030 – 16 4 5270.007 as a percent? of 2/53? ? 12% of $1201.6 –0.54.98 + 17.5add 10% to $45take 95% off $30012 – 3 (4 + 3)1/5 of ? 1.9 516.7 – 2.998–2 –6.5 1618 0.05? – 1/20 as a decimal20 – 4.7340 20.54/5 of 20250 30930.02 0.056 15 as a percent$50 discounted 16%20 – 10 20 54 3 – 0.7 –22.5 1142/64 in simplest form21 7000.04 8hours in 3 weeks1.1 21220 – 49.86 – 2 2330 100.130% of $4571/4 as a mixed no.0.017 as a percent0.4 0.26 2/3 25/6 + 1 5/624 2 –1516 – (–4 – 5)7.8 32.9 + 1.713522? as an improper fr’n(52 – 32) 2 – 27/40 of 16Mental Arithmetic Practice – Level 5212 – 28.3430 – 128.521 173.3 6003/8 + 1/127/10 of 0.86 ? 3.2 52(–4.5)2–5.7 0.31.5367 3 – 20 623.5% of $500? + 12/5 as a mixed no.16 + 4 6 34.1 – 27/8 as a decimal44% as a common fr’n5/16 as a percentadd 12% to $23.50add 0.6% to $65632 5 as a decimal–5.4 +1.95 30.03 0.750.41 25018 –0.1536 – 544/19 of $11.404/9 3/8 – ? 5533 48? of 2/3 of 0.722? ? as a mixed no.47 250.6 –0.45 as a mixed no.105 404.28 + 16.5 3add 9% to $52take 15% off $34.6012 – 8 (4 + 3) –4 3/5 – 1/7 1.8 5156.72 + 2.298cube root of 1728 0.054 in scientific not’n33/5 17/9 as a mixed no.? – 1/9 to 4 decimal places10 – 2.83197540 27.54/5 of 121500 350.73minutes in 3.85 hours1 32 as a percent$70 discounted 27%16 – 200 20 10004 0.52 – 0.71 –22.5 4.01100 – 2.5 5623.8 7000.042 350hours in 120 days1.2 11111.1 0.0371 + 3 + 5 + 7 + . . . + 23 + 2530 344.532.1% of 401359/14 as mixed number44 3150.47 0.02514 ? to 3 decimal places21/6 – 35/12 as a mixed no.34.5 (4 + 4 2.3 – 1.7) + 6.516 – –3 0.5510.5 30 0.72.6 52()4(–9)429? as an improper fr’n10 7 to 2 decimal places17/90 of 4.5 as a decimalMental Arithmetic Practice – Level 5 – continued432 – 58.7126.32 – 129.521 273.9 6003/8 + 1/67/10 of 0.74 ? as a mixed no.3.7 52(–2.1)2–11.7 0.031.2368 3 – 40 616% of $550? + 12/5 as a mixed no.16 + 4 –6 124.7 – 27/8 as a decimal35% as a common fr’n4/9 as a % to 2 dec placesadd 12% to $44add 1.6% to $65735 15 –5.4 –1.95 50.3 0.450.44 750180 –0.4536 – 634/13 of $11.707/12 –3/8 + ? 21333 998? of 2/5 of 0.082? 3/5 as a mixed no.73 250.6 0.25 as a mixed no.105 8004.008 + 11.05 3add 14% to $52take 40% off $34.6012 + 0.8 (4 + 3) –5 3/5 – 1/8 1.9 5106.72 + 2.289square root of 484 0.033 in scientific not’n33/5 22/9 ? – 1/6 to 3 decimal places10 – 4.71107540 17.24/5 of 13500 550.63seconds in 3.1 hours13 40 as a percent$40 discounted 27%10.6 – 250 20 10003 0.52 – 0.77 –225 411198 – 2.5 6697.6 8000.049 35minutes in 3 days10125.16 0.0322 222 55 555 as a decimal30 312.525.1% of 40200/9 as a mixed number44 1150.417 0.0511 ? to 3 decimal places21/6 + 35/9 as a mixed no.11 9.9 as a mixed no. 4.7 + –3 0.8511.2 20 0.72.6 81()8(–9)3107? as an improper fr’n10 9 to 3 decimal places13/30 of 4.5 as a decimalAnswers to Mental Arithmetic Practice – Level 12358341291756592734140125961220732335241665119823611322142898984921607316806001425230040721351612301680591223460720840103022001820453241193152649636928356139170010216416813379403902100431531058267440193869751201102591514266407168503903152174992534007847074171921114372651228017852132811320911441281561721163442522416635519039952423253301143018156201301418619131801442 000400Answers to Mental Arithmetic Practice – Level 22559341092159566882736140125 104122070316.42.44.130.31.82.36.10.375.81.42.816.584923200736265147/10 3/5 5/9 9/13 361061405685722256001300782700103044004.70.014.510.31411.93.512.67.33.32.84.756.365170990164016813372/8 or 1/46/10 or 3/58/4 or 26/6 or 1631052826731443819386918011211002514154.26.76.051680.583.595.210.74.993.332.7163847074171921115/7 1/71/5 9/7 or 12/7852380178319132863913910144128260172116245.64.116.333.074.40.225.21.82.632.351.46.66810513413001434119139/10 8/5 or 13/57/3 or 21/32/12 or 1/6Answers to Mental Arithmetic Practice – Level 3683028520116130/721835/860.4270.540.337.10.737760%2.275%2.2$35$9.50$130$17.7012.518011160$480.6$560.53280%3540%0.8$841.8$960.533.50.613.724/5120032/514050.3120.7$815$1225$12120%$24125%62/100 or 31/500.1632/100 or 8/250.06$241.6$40160.26030.5607$55$50$66$10081414183/51284/71281327.241427.240.80.1251.20.1257.17305.7730818 000618 0000.80.010.90.013/5$723/8$6315.6615.411100121/100100011/100$1500.006$900.006168156144016871.63.4566.73.56000$1210 000$60.8241/100823/100.080.0050.120.013855$7.5066483.9182.34.41$104.01$8.804/516.52/5$13.500.062.6270.022.827Answers to Mental Arithmetic Practice – Level 4850301.5800250.55.830.0067.740.0041800.42900.183.253202.60.0042640.29216–0.289161512–102? 162? $48.8011/8$44.8033/82862.5%–2037.5%–0.5$63.60–1.8$64.20–0.52–7.3–0.47.10.02110000.035100–72–817$85$1401062537.5%1280.7%1/3101/53? 18–1.2$14.40–3.210021.78822.48$57.20$45$49.50$15–443/10–91/109.0519.6989.513.702152561310.090.150.90.25.5767515.278201245 0001675003430.0127290.00120%$3840%$42–2421.2–2013.425.256/72.7521/320.30.0050.030.0057441.3250423.151.5–2170.2–109015$143003$13.5027? 41.5%17? 1.7%0.140.08961/6–62.544/6 or 42/3–180143.6252.64.412164.6124311119/41091/44.51.4302.8Answers to Mental Arithmetic Practice – Level 5183.7301.5373.33.183570.00555670.006511/24 0.5613/240.498 851/392.520.25–194.41–3903.375191.78816$117.5019/10 $8823/20181.22581.82511/2531.25%7/2044.44%$29.32$65.39$49.28$66.04126.40.4547–15.150.025102.50.135330–120104–0.04513$2.40– 7/12 $3.6017/1831251584819232 9340.2431/30.00841/61175–11/3182522/5250053.7812537.158$56.68$29.43$59.28$20.761116/35 13.1219/4091.859.0189699.00912 6.25 10–6222.7 10562/5 0.138980.0837.16802511005.2889256889.652 50010.427 5000.3432310.21611 1603.125%$51.1032.5%$29.20123.55.63.110.025–4010 275330.0340.000120.1220.00142880133.2432010 2013001691720.410 33512.84937510.04971/14 13 860222/950600.0117518.6670.0208514.667–1? 9.5513/1811/917.650.52.150.7135.2576210.612966561119/4729431/41.430.851.1111.95 ................
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