New Microsoft Office PowerPoint Presentation

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WELCOME TO MATHS PROJECT

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PRESENTED BY:- A.S.SELVARAJ & P.NITHIN REDDY

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RATIOS & PROPORTIONS

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CONTENTS RATIOS PROPORTIONS EQVIVALENTRATIOS UNITARY METHO0D

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RATIOS

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In our daily life, many a times we compare two quantities of the same type. For example, Avnee and Shari collected flowers for scrap notebook. Avnee collected 30 flowers and Shari collected 45 flowers. So, we may say that Shari collected 45 – 30 = 15 flowers more than Avnee . Also, if height of Rahim is 150 cm and that of Avnee is 140 cm then, we may say that the height of Rahim is 150 cm – 140 cm = 10 cm more than Avnee . This is one way of comparison by taking difference. INTRODUCTION

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Isha’s weight is 25 kg and her father’s weight is 75 kg. How many times Father’s weight is of Isha’s weight? It is three times. Cost of a pen is Rs 10 and cost of a pencil is Rs 2. How many times the cost of a pencil is the cost of a pen? Obviously it is five times. In the above examples, we compared the two quantities in terms of how many times’. This comparison is known as the Ratio . RATIOS

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We denote ratio using symbol ‘:’ Consider the earlier examples again. We can say, The ratio of father’s weight to Isha’s weight = 75 /25 = 3 /1 = 3:1 The ratio of the cost of a pen to the cost of a pencil = 10 /2 = 5 1 = 5:1 RATIOS SYMBOL

CONSIDER AN ANOTHER EXAMPLE:

CONSIDER AN ANOTHER EXAMPLE Length of a house lizard is 20 cm and the length of a crocodile is 4 m. I am 5 times bigger than you”, says the lizard. As we can see this is really absurd. A lizard’s length cannot be 5 times of the length of a crocodile. So, what is wrong? Observe that the length of the lizard is in centimetres and length of the crocodile is in metres . So, we have to convert their lengths into the same unit. Length of the crocodile = 4 m = 4 × 100 = 400 cm. Therefore, ratio of the length of the crocodile to the length of the lizard = 400 /20 = 20 /1=20 :1.

TWO QUANTITIES CAN BE COMPARED ONLY IF THEY ARE IN SAME UNIT:

TWO QUANTITIES CAN BE COMPARED ONLY IF THEY ARE IN SAME UNIT Now what is the ratio of the length of the lizard to the length of the crocodile? It is 20 /400 = 1/20 = 1: 20 . Observe that the two ratios 1 : 20 and 20 : 1 are different from each other. The ratio 1 : 20 is the ratio of the length of the lizard to the length of the crocodile whereas, 20 : 1 is the ratio of the length of the crocodile to them length of the lizard.

SAME RATIOS IN DIFFERENT SITUATIONS:

SAME RATIOS IN DIFFERENT SITUATIONS Length of a room is 30 m and its breadth is 20 m. So, the ratio of length of the room to the breadth of the room = 30/20 = 3/2 =3:2 There are 24 girls and 16 boys going for a picnic. Ratio of the number of girls to the number of boys = 24/16 = 3/2 =3:2 The ratio in both the examples is 3 : 2. Note the ratios 30 : 20 and 24 : 16 in lowest form are same as 3 : 2. These are equivalent ratios .

EQUALENT RATIOS:

EQUALENT RATIOS Ravi and Rani started a business and invested money in the ratio 2 : 3. After one year the total profit was Rs 40,000. Ravi said “we would divide it equally”, Rani said “I should get more as I have invested more”. It was then decided that profit will be divided in the ratio of their investment. Here, the two terms of the ratio 2 : 3 are 2 and 3. Sum of these terms = 2 + 3 = 5 What does this mean? This means if the profit is Rs 5 then Ravi should get Rs 2 and Rani should get Rs 3. Or, we can say that Ravi gets 2 parts and Rani gets 3 parts out of the 5 parts.

Let us take an example:

Let us take an example EXAMPLE :Length and breadth of a rectangular field are 50 m and 15 m 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 = 15 m The ratio of the length to the breadth is 50 : 15 The ratio can be written as 50/15 =50 5 /15 5 = 10/3 = 10 : 3 Thus, the required ratio is 10 : 3.

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Example 4 : Give two equivalent ratios of 6: 4. Solution : Ratio 6 : 4 = 6/4 =6 * 2 / 4 * 2 = 12 /8 . Therefore, 12 : 8 is an equivalent ratio of 6 : 4 Similarly, the ratio 6 : 4 = 6/4=6 *2/4 *2 = 3/2 So, 3:2 is another equivalent ratss . Therefore, we can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number .

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PROPORTIONS

INTRODUCTION:

INTRODUCTION Two friends Ashma and Pankhuri went to market to purchase hair clips. They purchased 20 hair clips for Rs 30. Ashma gave Rs 12 and Pankhuri gave Rs 18. After they came back home, Ashma asked Pankhuri to give 10 hair clips to her. But Pankhuri said, “since I have given more money so I should get more clips. You should get 8 hair clips and I should get 12”. Can you tell who is correct, Ashma or Pankhuri? Why? Ratio of money given by Ashma to the money given by Pankhuri = Rs 12 : Rs 18 = 2 : 3 According to Ashma’s suggestion, the ratio of the number of hair clips for Ashma to the number of hair clips for Pankhuri = 10 : 10 = 1 : 1 According to Pankhuri’s suggestion, the ratio of the number of hair clips for Ashma to the number of hair clips for Pankhuri = 8 : 12 = 2 : 3. Now, notice that according to Ashma’s distribution, ratio of hair clips and the ratio of money given by them is not the same. But according to the Pankhuri’s distribution the two ratios are the same. Hence, we can say that Pankhuri’s distribution is correct.

SHARING A RATIO:

SHARING A RATIO Raj purchased 3 pens for Rs 15 and Anu purchased 10 pens for Rs 50. Whose pens are more expensive? Ratio of number of pens purchased by Raj to the number of pens purchased by Anu = 3 : 10. Ratio of their costs = 15 : 50 = 3 : 10 Both the ratios 3 : 10 and 15 : 50 are equal. Therefore, the pens were purchased for the same price by both.

PROPORTIONS:

PROPORTIONS If two ratios are equal, we say that they are in PROPORTIONS and use the symbol ‘::’ or ‘=’ to equate the two ratios. We can say 3, 10, 15 and 50 are in proportion which is written as 3 : 10 :: 15 : 50 and is read as 3 is to 10 as 15 is to 50 or it is written as 3 : 10 = 15 : 50. For the second example, we can say 2, 4, 60 and 120 are in proportion which is written as 2 : 4 :: 60 : 120 and is read as 2 is to 4 as 60 is to 120.

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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.

FOR EXAMPLE::

FOR EXAMPLE: Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion? Solution : Ratio of 15 cm to 2 m = 15 : 2 × 100 (1 m = 100 cm) = 3 : 40 Ratio of 10 sec to 3 min = 10 : 3 × 60 (1 min = 60 sec) = 1 : 18 Since, 3 : 40 ≠ 1 : 18, therefore, the given ratios do not form a proportion.

UNITARY METHOD:

UNITARY METHOD The method in which first we find the value of one unit and then the value of required number of units is known as UNITARY METHOD

FOR EXAMPLE::

Two friends Reshma and Seema went to market to purchase notebooks. Reshma purchased 2 notebooks for Rs 24. What is the price of one notebook? Cost of 2 notebooks is Rs 24. Therefore, cost of 1 notebook = Rs 24/2 = Rs 12. Now, if you were asked to find cost of 5 such notebooks. It would be = Rs 12 × 5 = Rs 60. A scooter requires 2 litres of petrol to cover 80 km. How many litres of petrol is required to cover 1 km? For 80 km, petrol needed = 2 litres . Therefore, to travel 1 km, petrol needed = 2/80 = 1/40 litres . Now, if you are asked to find how many litres of petrol are required to cover 120 km? Then petrol needed = 1/40×120 litres = 3 litres . FOR EXAMPLE:

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THANKS TO MATHS DEPARTMENT

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THANKS TO COMPUTER DEPARTMENT