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Application of Mathematics in Practical Situations of Life

Application of Mathematics in Practical Situations of Life. Presented By: Vardaan Sahgal, Eshan Uniyal, Salman Nehru, Bhavesh Kaushik, Ritvik Kumar, Harshul Siddharth, & Rishabh Mishra From Class VII-F. By : Vardaan Sahgal. IN THIS PRESENTATION YOU WILL LEARN ABOUT

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Application of Mathematics in Practical Situations of Life

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  1. Application of Mathematics in Practical Situations of Life Presented By: Vardaan Sahgal, Eshan Uniyal, Salman Nehru, Bhavesh Kaushik, Ritvik Kumar, Harshul Siddharth, & Rishabh Mishra From Class VII-F By : VardaanSahgal

  2. IN THIS PRESENTATION YOU WILL LEARN ABOUT APPLICATION OF MATHEMATICS IN PRACTICAL SITUATION OF LIFE WITH REFERANCE TO RATIO AND PROPIRTION By : VardaanSahgal

  3. By: VardaanSahgal Ratio And Proportion Ratio Proportion • We compare the two quantities in terms of ‘how many times’. • This comparison is known as the ratio. • We donate ratio using symbol ‘: ’ • Eg.2:4=2/4=1:2 • If two ratios are not equal, then we say that they are not in proportion . • In a statement of proportion, the four quantities involved when taken in order are known as respective terms. • First and fourth terms are known as extreme terms. • Second and third terms are known as middle terms. • E.g.. 35 : 70 :: 2 : 4;- 35,70,2,4 are the four terms.35 and 4 are the extreme terms and 70 and 2 are the middle terms.

  4. By: VardaanSahgal Example Of Ratio • EXAMPLE- Length & breadth of a rectangular field are 50m & 15m respectively. Find the ratio of the length to the breadth of the field. • SOLUTION :- • Length of the rectangular field=50 m • Breadth of the rectangular field=15m • The ratio of the length to the breadth is 50:15 • 50 50/5 10 • The ratio can be written as ,--- = ---------- =--- = 10 : 3 • 15 15/5 3 • Thus , the required ratio is 10 : 3 .

  5. EXAMPLE OF RATIO Example:The area of a rectangular field is 75 m2 whose length is 10 m. Find the ratio of breadth to the length of this rectangular field. Solution: Length of the rectangular field = 10 m = 10 × 100 cm = 1000 cm Area of the rectangular field = 75 m2 = 75 × 100 × 100 cm2 = 750000 cm2 We know that: Area of rectangular field = Length × Breadth Therefore, ratio of breadth to the length of the rectangle  Thus, the required ratio is 3:4. By: HarshulSiddharth

  6. EXAMPLE OF PROPORTION Check whether the following ratios form a proportion. (a) 24 sec: 2 min and 40 cm: 2 m (b) Rs 5:60 paise and 2 L: 240 ml (c) 60 kg: 1 quintal and 45 min: 1 hour Solution: (a) 24 sec: 2 min = Clearly, 24 sec: 2 min = 40 cm: 2 m Hence, the given ratios form a proportion. (b)  Clearly, Rs 5:60 paise = 2 L: 240 mL Hence, the given ratios form a proportion. (c) 60 kg: 1 quintal  45 min: 1 hour  Clearly, 60 kg: 1 quintal ≠ 45 min: 1 hour Hence, the given ratios do not form a proportion. By: HarshulSiddharth

  7. WE USE RATIO IN OUR DAILY LIFE By: BhaveshKaushik • EXAMPLE: Suppose that Kunal weights 28kg and Tanya weights 32kg. • SOLUTION:(Kunal’s weight):(Tanya's weight)=28kg:32kg • =28/32=28/32 divided by 4=7/8=7:8 • Therefore, ratio of Kunal’s weight and Tanya's weight is 7:8 Kg

  8. WE USE PROPORTION IN OUR DAILY LIFE By: BhaveshKaushik EXAMPLE: Are the two ratios 45g:60 g and 36kg:48kg in proportion ? SOLUTION:1- 45g:60g=45:60=45/60=3/4=3:4 SOLUTION:2-36kg:48kg=36:48=36/48=3/4=3:4 Therefore,the ratios 45g:60g and 36kg:48kg are in proportion.

  9. Ratio • In a ratio x:z, x is called the antecedent and z is called the consequent. • A ratio is always equivalent to itself multiplied by a nonzero no. Eg. 1 A company wants to reduce its operating cost in the ratio 2 : 3.If the operating cost was $51000 last year, what would be its target cost? Sol. Cost is to be reduced in the ratio 2:3 Therefore, target cost : Old Cost= 2:3 Let the target cost be x x:51000=2:3 x=(51000*2)/3 Therefore, x=102000/3 Therefore, the company’s target cost =34000 would be $34000. By: EshanUniyal

  10. Proportion • Proportion is expressing the equality of ratios such as A:B and C:D which is written as A:B=C:D or A:B::C:D. The latter form, when spoken or written in the English language, is often expressed as: A is to B as C is to D. • Again, A, B, C, D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means. The equality of three or more proportions is called a continued proportion. Eg. The first three terms of a proportion are 3, 5 and 21 respectively. Find the fourth term: Sol. Let the fourth term be x. 3:5::21:x =3*x=5*21 Therefore, the fouth term is 35. =3*x=105 =x=105/3 =35 By: EshanUniyal

  11. Ratio • In the ratio a:b,we call a as the first term or antecedent and b as the second term or consequent • A ratio remains unchanged if both of it’s terms are multiplied by the same nonzero quantity. Let m ≠ 0,then clearly we have • a∕b=ma∕mb & therefore,(a:b)=(ma:mb) • a∕b=(a∕m)÷(b∕m)and therefore (a:b)=(a∕m:b∕m) Eg: Divide 60$ in the ratio in the ratio ¼ : 1/6 Sol: lcm of 4 & 6 is 12 1/4 :1/6 = ¼ * 12 : 1/6 * 12 = 3: 2 Sum of the ratios = 3+2 = 5 First part = 360* 3/5=216$ Second part = 2/5*360=144$ Eg: The cost of an eraser is 80 paise & the cost of a pencil is 200 paise. What is the ratio of their costs in the simplest form ? Sol: cost of an eraser = 80 paise cost of a pencil = 2 rupees = 200 paise cost of an eraser : cost of the pencil = 80 : 200 =2 : 5 By: Salman Nehru

  12. Proportion 4 Four numbers a,b,c,d are said to be in proportion,if a:b=c:d and we write, 1 If a:b::c:d,then a,b,c,d are respectively known as first, second,third and fourth term. a and d are called extremes while b and c are called means If all four a,b,c,d, are in proportion then product of the means is equal to the product of the extremes. We say that d is the fourth proportional to a,b,c. Examples 1)Are 22,33,42,63 in proportion Sol-Product of extremes=Product of means (22*63) =(33*42) 1386=1386 Therefore,22,33,42,63 are in proportion 2) 2A = 3B =4C find A: B: C LET 2A = 3B = 4C = K A= K/2, B= K/3, C= K/4 K/2 * 12= 6K, K/3 * 12 =4K, K/4*12=3K 6:4:3 By: Salman Nehru

  13. Ratio If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2. In mathematical language, thatrelationship can be written in two ways:1/2 or 1:2 Both of these express the ratio of eggs to cups of flour: 1 to 2. If you mistakenly alter that ratio, the results may not be edible By: Ritvik Kumar

  14. Examples of ratio and proportion Suppose the price of oranges is Rs.20 a dozen, If we want to buy six oranges, how do we determine their cost ?As the number of oranges is half of one dozen, their cost also has to behalf. Therefore, the cost of 6 oranges is to their number half of rs.20 i.e. Rs 10. In other words, we think that the cost of oranges in proportion Real life applications of ratio and proportion are numerous! When we prepare recipes, paint our house, or repair gears in a large machine or in a car transmission, we use ratios and proportions By: Ritvik Kumar

  15. Ratio & proportion(by –rishabh ,class –vii f) • Uses of ratio &proportion in our daily life :- • 1)For knowing the value of currencies . Like 1$=Rs.50 • 2)For knowing the value of units. For example 1km=1000m • 3)For knowing the strength of a school , college etc. like 1 boy:2 girls • 4)To understand fractions in a simpler way.

  16. By VardaanSahgal THANK YOU AND HAVE A NICE DAY

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