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SUBJECT and GRADEMathematical Literacy Grade 10TERM 1Week 2TOPICRounding RatioAIMS OF LESSONYou should understand and be able to perform calculations with rounding and ratio in context. Calculations with rounding: You should be able to round:off (to a specified number of decimal places or a specific whole number)off to the nearest 5/ 10 / 100 etc.updownRounding in context: we need to remember that the context will determine how the answer must be rounded. We need to remember that early rounding can influence the accuracy of the final answer.Calculations with ratio:48482255524500convert between different forms of a ratiodetermine missing numbers in a ratiodivide or share an amount in a given ratiodifferent formats for expressing ratios equivalent ratios how to write a ratio in unit formRatio in context:Make sense of situations and calculations involving:mixing quantitiesproportionrates (e.g. Electricity tariffs; speed)percentage calculationsconversionsscaleexpressions of probabilityany other scenarios in the five main topics of Mathematical Literacy.RESOURCES Paper based resourcesDigital resources Your textbook should have units on Rounding and Ratio. Look under the heading NUMBER CONCEPTS for these units. Online study guides: videos: realizing it you have been using these concepts of rounding and ratio regularly in your daily life. This includes rounding off the prices of items when you want to check if you have enough money. Using ratio’s when mixing your Oros (or other diluted cool drinks). We need to always look at the context in which the rounding / ratio calculation must take place. It is therefore important to read carefully and then apply your mathematical knowledge correctly to the given context. CONCEPTS AND SKILLS50918685769700ROUNDING:You have been performing calculations with rounding for a while. You can be asked to round off, round up or round down. If you are unsure about how exactly to round, remember the following: Remember to keep the context of the problem in mind (sometimes you cannot have an answer with a decimal, and sometimes you can.) Let’s look at some examples of rounding off: Round 334,657 offQuestion:Solution:a) to the nearest whole number. 335b) to the nearest ten. 330c) to the nearest hundred.300d) to two decimal places.334,66Let’s look at some examples of rounding in context: This is often the point where some answers cannot have a decimal. You will need to ROUND UP to the nearest whole number or ROUND DOWN to the nearest whole number depending on the context. Question:Solution:Kayla is having a class party. She plans on buying cupcakes for everyone. If there will be 34 people attending the party and the cupcakes are sold in packs of six, how many packs must Kayla buy?34÷6=5,67≈6 packetsA school is planning a sport tour. They want to use the school’s minibuses that can transport 12 learners each. If there is a total of 70 learners going on tour, how many minibuses do they need?70÷12=5,83 busses≈6 bussesA classroom wall is 750 cm long. How many tables will fit along the wall if each table is 120 cm long? 750÷120=6,25 tables≈6 tablesA seamstress has 4,5 m of material and plans to cut out a pattern that uses 80 cm of material for each pattern. How many times can she cut out the pattern?4,5÷0,8=5,625 ≈5 times952571120When we round up or down, we often have some of the item left over. In many cases, this is an advantage in case something breaks or you need some extra material. 00When we round up or down, we often have some of the item left over. In many cases, this is an advantage in case something breaks or you need some extra material. For each of the questions above (1-4) calculate how much was left.Question:6×6=36 36-34=2 left 6×12=72 72-70=2 left120×6=720 cm 750-720=30 cm left5×0,80=4m 4,5m-4m=0,5m leftLet’s look at some examples of cash rounding:When we go to the shops, we normally have the option of paying by cash or by card. 525780057785Can you think why it is rounded down to the nearest 10 cent?0Can you think why it is rounded down to the nearest 10 cent?If you pay by card the exact amount will be taken from your account. If you however decide to pay with cash, the price is usually rounded DOWN to the closest ten cents. Example 1: Did the client receive any cash rounding on this purchase? Motivate your answer. No, as they paid using a debit card.How much change would a person receive if they gave the cashier R130 cash?R129,99 Cash rounding : R129,90R130 – R129,90=R0,10Example 2: extract from a till slip: Total:R204,62Cash Rounding:aCash:R210Change: bUse what you have learnt above to calculate the missing values a and b. -R0,02R210 – R204,60 = R5,40RATIOS:A ratio is a comparison of two or more numbers that are usually of the same type or measurement. If the numbers have different units, it is important to convert the units to be the same before doing any calculations.We write the numbers in a ratio with a colon (:) between them.When we write ratios, we do not add units to them. When asked to write a ratio in unit form it will need to be in the form 1: …Remember that 1:7 is not the same as 7:1If you are asked to write a ratio, note the ORDER that the ratio must be in. e.g: “Yellow to green smarties” Yellow : green We should also be able to simplify ratios or find equivalent ratiose.g: 1:2 = 3:6 (equivalent)e.g: 9:3 = 3:1 (simplified)When we do calculations with ratios we can be asked to: Determine quantities using the ratio. Divide an amount into the ratio that is given. 43624502730500e.g 1 Let’s look at an example: What is the ratio of boys to girls? B:G3:2How many people are there in total? 3+2 = 5Write the ratio of boys to girls in unit form. 3:2 ÷3 both sides 1: 0,67 e.g 2 Let’s look at an example: How to divide a ratio. 2847975320675There are two ways to approach this problem:Try and understand both methods:0There are two ways to approach this problem:Try and understand both methods:Nonhlanhla wants to divide R 1 800 between her employees. She decides to divide it in the ratio 3:2:1 for John, Sam and Zintle. How much does each person receive? 3 :2 :1John: Sam: Zintle Option 1:Option 2:3+2+1 = 6 R1 800 ÷6=R 300John:3 ×R 300=R 900Sam:2 ×R 300=R600Zintle 1 ×R 300=R3003+2+1 = 6 John: 36×R 1 800=R 900Sam:26×R1800= R 600Zintle:16×R 1 800=R 300 507682593980You can check your answer by adding all the amounts together to see if it gives you R 1 80000You can check your answer by adding all the amounts together to see if it gives you R 1 800 95259334500e.g 3 Let’s look at an example: How to determine quantities using a ratio Oros is a popular drink in South Africa. It is sold in various sizes, including a 2liter bottle. The recommended mixing instructions are 3 parts water to 1 part Oros concentrate. Write the ratio of Oros to Water. 1:3If you have a 2l bottle of Oros, how much water will you need to mix it with, if you want to make the whole bottle? 393065055245X200X2299085031115X200X23781425311153400425501651:32:6∴You will need 6? of WaterIf you use 75 ml of Oros, how much water will you use? 409575024765X7500X75326707568580276225044450X7500X753895725304801:375:225∴You will need 225m? of WaterIf you want to make 1 liter of already mixed cooldrink, how much water and how much Oros will you need? Now here the question is not asking about the separate components, but the combined product, so: 1+3=4 oros:14×1liter=0,25 literwater:34×1liter=0,75 liter0-254000e.g 4 Let’s look at an example: How to determine quantities using a ratioA basic cookie recipe will require a ratio for flour: butter: sugar of 3:2:1If a recipe for a specific cookie requires 375 ml butter, how much flour and Sugar will be needed?F: B :S3: 2 :1?: 375 :?375÷2=187,5so we must multiply flour and sugar by 187,5Flour:3 ×187,5=562,5 mlSugar:1 × 187,5=187,5 ml If one batch of cookies requires 3? cups of flour and Sandra needs to make 8 batches of cookies, how much of each ingredient will she need to buy? F: B :S3 :2 :13? : ? :?3,75÷3=1,25 cupsso we must multiply butter and sugar by 1,25 cupsbutter:2 ×1,25=2,5 cupsSugar:1 × 1,25=1,25 cupsNow we know how much we need for ONE batch. But remember Sandra needs to bake 8 batches. So: Flour: 3? × 8 = 30 cupsButter: 2,5 × 8 = 20 cupsSugar: 1,25 ×8=10 cupsCAN YOU?5314950127000Round off answers accurately in relation to the context of the question?Round off answers to the appropriate decimal place or number as asked? Explain and apply the concept of cash rounding? Write ratios from given information? Simplify ratios? Write ratios in unit form? Determine quantities from ratios? Use ratios to divide an amount? ACTIVITIES/ASSESSMENTRounding: The population of South Africa was 59 663 549 in 2020.485775011874500Round this off to the nearest: 101 0001 000 000Krispy Kreme offers the following deal online: If Kara wants to buy 66 doughnuts, how many dozen must she buy? (remember a dozen is 12). A school wants to buy a doughnut for all of their grade 10 learners. If they have 212 learners, calculate the cost of the doughnuts for the grade. Khanya buys two punnetts of papayas from Spar and pays for it in cash. 51117504508500Calculate the total cost. What would the cash rounding amount be?If she received R60,10 change, how much cash did she give the cashier?Ratio: Simplify the following ratios as far as possible: a)27:9b)45:50c)6:72d)0,25:0,5e)38:114f)4:14An animal shelter said that they have 4 cats for every 6 dogs at their shelter. If the shelter buys 54 bags of dog food monthly, how many bags of cat food should they buy? If the shelter has a total of 850 spaces available for animals, how many cats and dogs can they accommodate? In a class there are 15 girls and 20 boys. Give the ratio of boys to girls. If the teacher has to buy a total of 105 prizes for her class, how many will be for boys and how many for girls? If another 10 girls join the class, write down the simplified ratio of boys to girls. Dane, Michael and Byron want to sell their old PlayStation 4 for R 5 250. How much should they each get if they bought the playstation together and contributed to it as follows: Dane R 2 181,82 Byron: R 1090,91 and Michael: R 2727,27.Cement, sand and stone are used to mix concrete in the ratio 2:1,5 : 1. If the total mass of sand used is 150 kg, how many bags of cement are needed( one bag of cement is 50 kg). SOLUTIONS TO ACTIVITIES:Rounding:1a) 59 663 550 b) 59 664 000 c) 60 000 0002a) 66÷12=5,5 ≈6 b) 212÷12=17,67 ≈18 dozen 18 ×114 =R 20523a) 19,99 ×2=R 39,98 b) R0,08 or -R0,08 c) R39,90 + R60,10 = R100Ratio:1. a)3:1b)9:10c)1:12d)1:2e)1:3f)2:72. cats: dogs a) 4: 6 ?: 54 54÷6=9 bagsso we must multiply cat food by 9 bagscat food:4×9=36 bagsb) Cats: 410×850=340 Dogs : 610 ×850=570320:15 simplified 4:320+15=35 learnersBoys: 2035×105=60Girls: 1535×105=4520:25 simplified 4:5 4. Dane : Byron : Michael R2181,82 :R1090,91 : R2727,27R2181,82+R1090,91+R2727,27= R 6 000Dane : 2181,826 000 ×5 250=R 1909, 09Byron : 1090,916 000 ×5 250=R 954,55Michael : 2727,276 000 ×5 250=R 2 386,365. Cement : Sand : Stone 2 : 1,5 : 1 ? : 150 :1501,5=100cement :2 ×100=200 kg200 kg50 kg a bag=4 bags CONSOLIDATIONGo through the aims of the lesson and make sure that you can answer questions on ratio and rounding. Make sure that you understand how a context can change the way you answer a question. Remember that you will use ratio & rounding concepts in all other topics that we will discuss, so make sure that you have mastered the skills in this lesson! VALUES If you have mastered the skills in this lesson, it should help you develop your COMPETENCE in the subject. You can also be HELPFUL by explaining this to others who did not understand. ................
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