DECIMALS AND PERCENTAGES Archives

Fractions and Percentages A fraction can be converted to decimal by dividing the numerator by its denominator. It can be changed to percentage by simply multiplying by 100. Example 5.1 Change 3/8 into a decimal and percentage Convert 0.145 to percentage Solution 1) 3/8 0.375 in decimal 3/8 x 100% 37.5% 2) 0.145x10014.5% Example 5.2 To change percentage to decimal fraction, simply divide by 100 and then convert to decimal fraction. E.g. convert 92% to decimal Solution 92 100 920 900 200 200 0.92 Example 5.3 Change the following to percentages (a) 0.125 (b) 0.002 Solution (a) 0.125x100% 12.5% (b) 0.002 0.002x100% 0.2% Change the following to decimal fractions (A) 45 % ( b) 8/3% Solution 45/1000.45 8/3 8/3 ÷100/1 8/3 x 1/100 8/300 4/150 2/75 0.02666 75 200 150 500 450 500 450 500 0.0267 Class work Change the following to percentage (a) 0.264 (b) 0.875 Change the following to decimal fractions (A) 60% (b) 52/3% APPLICATION OF DECIMAL FRACTIONS AND PERCENTAGES Consider the following examples. Find 15% of 2.8kg Express 3.3 mass a percentage of 7.5 Find 331/3 % of8.16litres Solution 15/100 of 2.8kg 15/100 x 2.8 x 1000g 15/100 x 2800 420g 420/1000 0.420kg b. 3.3/7.5 x 100/1 33/75 x 100/1 11x4 44% c. 331/3% of 8.16litres 100/3 of 8.16litres 100/3 of 8.16litres 100/3 x 8.16litres 100/3 x 8.16 x 1000 (1litre1000cm3) 100/3 x 8160 100/3 ÷100/1 x 8160 100/3 x 1/100 x 8160 2700/1000 2.720litres Class work Express1.5 as a percentage of 2.5 m Find 662/3 % of2.4m Proportion Proportion can be solved either by unitary method or inverse method. When solving by unitary method, always write in sentence the quantity to be found at the end. decide whether the problem is either an example of direct or inverse method find the rate for one unit before answering the problem. Examples A worker gets N 900 for 10 days of work, find the amount for (a) 3 days (b) 24 days (c) x days Solution For 1 day N 900 1 day 900/10 N90 For 3 days 3 x 90 270 For 24 days 24x90 N 2,160 For x days X x 90 N 90 x Inverse Proportion Example Seven workers dig a piece of ground in 10 days. How long will five workers take? Solution For 7 workers 10 days For 1 worker 7x1070 days For 5 workers70/5 14 days 5 people took 8 days to plant 1,200 trees, How long will it take 10 people to plant the same number of trees Solution For 5 people 8 days For 1 person 8x540 days For 10 people 40/10 4 days Class Work A woman is paid N 750 for 5 days, Find her pay for (a) 1 day (b) 22 days A piece of land has enough grass to feed 15 cows for x days. How long will it last (a) 1 cow (b) y cows A bag of rice feeds 15 students for 7 days .How long would the same bag feed 10 students Note on direct proportion: this is an example of direct proportion .The less time worked (3 days) the less money paid (#270) the more time worked (24 days) the more money paid (N N 2,160) Ratio Ratio behaves the same way as fraction. Ratios are often used when sharing quantities.. Example 600/800600/8003/4 300-400600-8001200-160034 Example Express the ratio of 96 c: 120c as simple as possible Solution 96c: 120c96/1204/54.5 Fill in the gap in the ratio of 2:728 Solution let the gap be X 2/7 X/28 7X 2 x 28 X2 x 28/7 X2 x 4 X 8 Two students shared 36 mangoes in the ratio 2:3 How many mangoes does each student get? Solution Total ratio 2+35 First share2/5x35/121 mangoes Rate Rate is the change in one quantity to the other. Examples are 45km/hr, a km, 1 litre etc Worked examples A car goes 160 km in 2 hrs what is the rate in km/hr? Solution In 2 hrs the car travels 160 km In 1 hr the car travels 160/280km Therefore the rate of the car is 80km/hr A car uses 10 litres of petrol to travel 74 km. Express its petrol consumption as a rate in km per litre. Solution 10 litres 74 km 1 litres 74/10 km 7.4 km Class work A car factory made 375 cars in 5 days, Find its rate in cars per day. A car travels 126 km in 11/2 hrs. Find the rate in km per hr. WEEKEND ASSIGNMENT 5 men build in 10 days, how long would it take 25 men? (a) 3 days (b) 2 days (c) 5 days (d) 10 days A girl buys 7 pens for N How would ten pens cost? (a)#300(b)#30(c)#3(d)#200 Fill in the gap in m: a 16:24 (a) 10 (b) 12 (c) 4 (d) 6 Express 90km /hr: 120km /hr as simple as possible (a) 4:3 (b) 3:4 (c) 2:3 (d) 3:2 A factory makes N 2000 pencils in 10 days, Find its production rate of pencils per day (a) N 20 per day (b) N 100 per day(c) N 50 per day (d) N 200 per day THEORY Find 50% of 3.5m A bag of corn can feed 100 chicks for 12 days. How long would the same bag feed 80 chickens? See also H.C.F & L.C.M AND PERFECT SQUARES WHOLE NUMBERS AND DECIMAL NUMBERS BASIC OPERATION OF INTEGERS WEIGHT VOLUME OF CYLINDER

FRACTIONS, RATIOS, DECIMALS AND PERCENTAGES