MATHEMATICS FORM 1 – DECIMALS AND PERCENTAGES msomimaktaba, August 17, 2024August 17, 2024 DECIMALS AND PERCENTAGES Are fractions of tenth, they are written using a point which is a result of division of a normal fractionE.g. 0.34, 0.5, 0.333——–In the fraction 0.2546 the place values areOnes0Tenth2Hundredths5Thousandths4Ten Thousandths6Decimals can be converted into fractions and vice versaE.g. Change in to decimalsSolution: = 0.75This fraction which ends after dividing is called terminating fraction. Other fractions do not end, these ones are called recurring or repeating decimals.E.g. Conversion of Repeating decimal into fractionsSolution:0.3 = 0.333…….Subtract (i) from (ii)9t = 3.0 = t = Exercise 1 Insert or between each pair of fractions questions 4 to 121. , Solution L.C.M = 33 = 23 = 1 2. , SolutionL.C.M = 63 63 = 7 63 = 9 3. Solution 12 = 10 12 = 9 4. , Solution 20 = 16 20 = 15 5. , Solution L.C.M of 20 and 4 = 80 80 = 60 80 = 140 6. , Solution L. C. M of 4 and 4 = 4 4 = 1 4 = 3 7. , Solution L. C. M of 5 and 6 = 30 30 = 12 30 = 5 8. , Solution L. C. M of 9 and 6 = 18 18 = 16 18 = 15 9. Which numbers are denominators in each of the following fractions?(a) 16 is the denominator. (b) 93 is the denominator(c) 3 5 is the denominator 10. Which numbers are numerators in each of the following fractions?(a) Numerators is 3(b) 3 Numerators is 4(c) Numerators is 12 12. Which is greater(a) or Solution Find the L.C.M of 5 and 4 = 20 20 = 12 20 = 15 (b) or Solution Find the L.C.M of 3 and 2 = 6 x 6 = 4 x 6 = 3 13. What is the condition for a fraction to be called improper?The numerator is bigger than the denominator. 14. Change the following improper fractions into mixed numbers(a) = 1(b) = 4(c) = 3(d) = 116 15. Change the following mixed numbers into improper fractions(a) 3 Solution = (b) 15 Solution = (c) 24 Solution = 3.3 PERCENTAGESPercentages are fractions expressed out of 100. That is – are the ones whose denominator is one hundred, they are denoted by (%) called percentExample: 12% means 12 = 70% = etc.Examples: 1. convert the following percentage into fraction (i) 65% (ii)75% (iii)12 % Solution (i) 65%65 = = = (ii) 75%75 = = = (iii) 12 %12 = = 12 % = 2. Change(i) 40% into decimal(ii) 35% into fractions(iii) 0.125 into percentageSolution (i) 40% = = = 0.4(ii) 35% 35 = = (iii) 0.125Solution0.125 = 100%= 12.5%3. Change the recurring decimals into fractions(i)0Solution Let x = 0.……………………….. (i)100x = 21.……………………. (ii)Take away equation (i) from (ii)100x = 21.= = x = (ii) Solution Let x = 0.9……………………….. (i)10x = 9.…………………………. (ii)100x = 93.3 ………………………(iii)Take equation (ii) away from equation (iii)100x = 93.3= = x = (iii)0.6Solution Let x = 0.6………………………….. (i)1000x = 567.567 ……………………. (ii)Take away equation (i) from (ii)1000x = 567.567X = 0.567 x = (iv) 0.35Solution Let x = 0.35……………………….. (i)10000x = 1352.1352 ……………………. (ii)Take (ii) – (i)10000x = 1352.1352= = x = (v) 0.1Solution Let x = 0.1………………………….. (i)1000x = 219.219 ……………………. (ii)Take away equation (i) from (ii)1000x = 219.219= = x = (vi)0.8Solution Let x = 0.8………………………….. (i)1000x = 186.186 ……………………. (ii)Take away equation (i) from (ii)1000x = 186.186= = x = (vii) 0.63Solution Let n = 0.63………………………….. (i)10000n = 8634.8634 ……………………. (ii)Take away equation (i) from (ii)10000n = 8634.8634= = n = (viii) 0.7Solution Let x = 0.7……………………….. (i)10x =0.7 …………………………. (ii)1000x = 792. ………………………(iii)Take away equation (ii) from equation (iii)100x = 792.1000x – 10x = 792. – 7. 990x = 785 x = (ix) 0.4Solution Let y = 0.4………………………….. (i)1000y = 645.4……………….. (ii)Take away equation (i) from (ii)1000y – y = 645-4 999y=645 = y = (x)0.Solution Let b = 0.………………………….. (i)100b = 64. ……………………. (ii)Take away equation (i) from (ii)100b – b = 64.-0. 99b = 64 = b = (xi)0.2Solution Let m = 0.2………………………….. (i)1000m = 627.2……………………. (ii)Take away equation (i) from (ii)1000m – m = 627.2– 0.2 999m = 627 = m = 4.In question (i) to (v) change the fractions into decimals.Solution 1 ÷ 3 = = 0.33 ii. Solution 5 ÷ 6 = = 0.833 iii.Solution 4 ÷ 11 = = 0.3636 iv. Solution 1 ÷ 9 = = 0.111 v.Solution 7 ÷ 13 = = 0.538461Solution Let b = 0.2………………………….. (i)1000b = 123.2……………….. (ii)Take equation (i) away from equation (ii)1000b – b = 123.2 – 0.2 999b = 123– b = Operations on Decimals Operations with decimals are similar to operations with whole numbers:AdditionNote: The decimal points must be in line, put zeros at the end to give the same number of decimal places in each number.MultiplicationNote:When multiplying decimals the answer must have the same number of decimal places as the total number of decimal places in the number being multiplied.First carry out the multiplication in the usual way, without any decimal points, then put the point to the total decimal places.DivisionNote:It is not easy to divide by a decimal, so you multiply each number by a power of 10 in order that you are dividing by a whole number.Example:- (i) Find (a) 68.32 ÷ 1.4(b) 9.66 ÷ 0.23Solution(a) 68.32÷ 1.4 = 68.32 x 10 ÷1.4 x 10682.2÷14By long division Therefore 68.32÷ 1.4 = 48.8 (b)Therefore 9.66÷ 0.23 = 42(c) 7.32 1.2 = 7.32 x 10 1.2 x 10 73.2t Therefore 7.32÷ 1.2 = 6.1Mariam was given 20,000 shillings by her father, she spent 48% of it to buy shoes. How much money remained.Solution 20,000 =9,60020,000– 9,60011,600∴The remained money was 11,600/= PERCENTAGES APPLIED TO REAL LIFE PROBLEMS The examples below show the wide range of application Examples:- 1. In one week, Flora earned 48,000/=, she spent 4,000/= on travel to and from work. What percentage of her money was left? Solution: Percentage of a quantity When finding a percentage of a quantity, it is often helps to change the percentage to a decimal and multiply it by the quantity. Example:- Find (a) 20% of 840,000 Percentage increase and Decrease There are two steps to calculate percentage increase (or decrease) Example: In 1975 the population of a village was 90. It increased by 30% the following year. What was the population in the year 1976? ALL NOTES FOR ALL SUBJECTS QUICK LINKS:AGRICULTURE O LEVEL PURE MATHEMATICS A LEVELBAM NOTES A LEVELBASIC MATH O LEVELBIOLOGY O/A LEVELBOOK KEEPING O LEVELCHEMISTRY O/A LEVELCIVICS O LEVELCOMPUTER(ICT) O/A LEVELECONOMICS A LEVELENGLISH O/A LEVELCOMMERCE O/A LEVELACCOUNTING A LEVELGENERAL STUDIES NOTESGEOGRAPGY O/A LEVELHISTORY O/A LEVELKISWAHILI O/A LEVELPHYSICS O/A LEVELMOCK EXAMINATION PAPERSNECTA PAST PAPERS Basic Mathematics Study Notes Form 1 Basic Mathematics Study Notes FORM 1MATHEMATICSPost navigationPrevious postNext postRelated Posts Basic Mathematics Study Notes Form 3 Mathematics – ACCOUNTS November 13, 2018August 17, 2024ACCOUNTS Accountsis a place in a ledger where all the transactions are relating to a particular asset, liabilities and capital, expenses,or revenue items were recorded. Accounts is a wider concept with identifying measuring and communicating economic information to permit informed judgments and decisions by users of the information. 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