Class VI�CHAPTER 12�TOPIC: RATIO AND PROPORTION�PART-2� (NCERT Syllabus)

PREPARED BY: MRS. KALPITA J. ZOPE

T.G.T. MATHS

JNV SATARA (MAHARASHTRA)

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Contents:

• What is Proportion?
• Explanation with Example.
• Numbers are in Proportion (General Form)
• Examples of Proportion.
• Unitary Method.
• Examples of Unitary method.
• What we have learnt.
• Assignments : Multiple choice question

Practice Questions

PISA Based Question

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What is Proportion?

• Proportion means equal or even ratio.
• Now we will understand it with the help of example-

A nature drawing drawn in a rectangular

sheet of length 5 inch and breadth 7 inches.

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If we want to expand the picture we can increase its length or breadth. But if we increase only its length 2 times or only its breadth 2 times then the picture is not like the original one.

How can we get expanded picture?

If we expand length and breadth both 2 times then we get expanded picture of original picture.

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To get expanded picture looking like original, we have to increase its length and breadth both in equal ratio.

OR Ratio of length of the original picture to its breadth is equal to ratio of length of expanded picture to its breadth.

Ratio of length and breadth of given picture = 5 : 7

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If we multiply length and breadth with same number then we get the expanded picture looking like original one.

So 5 : 7 = 10 : 14

If two ratios are equal then we say that they are in proportion.

The symbol = OR : : is use to show the proportion or equal ratio.

So we can say that 5, 7, 10, 14 are in same proportion.

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5 : 7 : : 10 : 14

We cannot write, 5 : 7 : : 14 : 10

because 14 / 10 ≠ 5 / 7

In proportion sequence of numbers are very important.

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In General Form:

• If a, b, c, d four numbers are in proportion.
• Then we can write,

a : b = c : d OR a : b : : c : d OR a / b = c / d

• Here a, b, c and d are called Terms.
• In which ‘a’ and ‘d’ called extreme terms or end terms and ‘b’ and ‘c’ are called middle terms.
• If four numbers a, b, c and d are in proportion,

So, Product of extreme terms = Product of middle terms

a x b = b x c

To understand proportion very clear, let us solve another example.

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Example : Leena and Sheena made 7 garlands. Out of 7 garlands Sheena made 4 garlands and Leena made 3 garlands. By selling these garlands they got Rs. 35. How much money got Sheena and Leena?

Solution :

Sheena’s garland Leena’s garland

Out of 7 garlands, Sheena works 4/7 part and Leena works 3/7 part.

Therefore, ratio of work of Sheena to Leena = 4 : 3

In this proportion,

Amount got by Sheena =

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Amount got by Leena =

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Ratio of amount for Sheena to Leena = 20 : 15 = 4 : 3

Therefore 4 : 3 = 20 : 15 OR 4 : 3 : : 20 : 15

So numbers 4, 3, 20 and 15 are in proportion.

Examples:

1. Are the ratios 1500 gm : 3 kg and 300 cm : 6 m in proportion?

Ratio 1500 gm : 3 kg Ratio 300 cm : 6 m

= 1500 gm : 3000 gm = 300 cm : 600 cm

= 1500 : 3000 = 300 : 600

= 1 : 2 = 1 : 2

Both ratios are equal.

Therefore 1500 gm : 3 kg = 300 cm : 6 m

1500 gm, 3 kg, 300 cm and 6 m are in proportion.

2. Are the ratio 15 cm to 2 m and 10 sec to 3 min are in proportion?

Ratio 15 cm : 2 m Ratio 10 sec : 3 min

= 15 cm : 200 cm =10 sec : 180 sec

(1m = 100cm) (1min = 60 sec)

= 15 : 200 = 10 : 180

= 3 : 40 = 1 : 18

Here 3 : 40 ≠ 1 : 18

Ratios are not equal

Therefore 15 cm, 2 m, 10 sec and 3 min are not in proportion.

Unitary Method :

• Unit means finding for one.
• In daily life we see many examples that, If we know one value of an object then we can find values for required object.
• EXAMPLE 1:

If price of 1 dozen banana = Rs. 40

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1 dozen ½ dozen 2 dozen

Rs. 40 Rs. 20 Rs. 80

Then we can find price of half dozen or two dozen banana’s with the help of given price.

So, “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.”

• EXAMPLE 2:

Rohan fence his house with wire. He made 3 round wire fence of expenditure Rs. 9072. Then find the expenditure of 5 round wire.

House with wire fence

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Solution- Given,

Expenditure for making fence for 3 rounds = Rs. 9072

Therefore, expenditure for fence of 1 round of wire = 3072 ÷ 3

= Rs. 3024

Therefore, expenditure for fence of 5 round of wire = 5 x 3024

= Rs. 15120.

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• * When we go to a shop to purchase pen or pencil, shopkeeper told that the price of one pen or pencil.

With the help of this we can purchase what we want.

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* Like wise a vegetable seller told us price of 1 kg of any vegetable.

* To find the required distance covered in given quantity of petrol, a scooter driver see that his scooter goes how many distance in 1 litre petrol.

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In this way,

“ To find the value of required units, first we find the value of one unit, this method is called Unitary Method.”

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• EXAMPLE : A car goes 50 km in 2 hours, how many distance covered by car in 6 min.
• SOLUTION: To solve the question first we see that all value are in same ratio.

Given, Distance covered by car in 2 hours = 50 km

1 hour = 60 min, So 2 hours = 120 min

so, distance covered by car in 120 min = 50 km

Therefore, Distance covered by car in 1 min = 150 ÷ 120

=

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Therefore distance covered by car in 6 min =

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What we have learnt :

• Comparison of two quantities by division is called ratio.
• If least value of two ratios are equal then they are called equivalent ratio.
• The ratio may occur in different situations.
• The ratio 3 : 2 is different from 2 : 3. Thus the order in which quantities are taken to express their ratio is important.
• A ratio may be treated as fraction. Ex. 10 : 3 may treated as 10/3
• To find the ratio of two quantities their units should be same.
• Four quantities are in proportion. If the ratio of first and second quantities are equal to the ratio of third and fourth quantities.
• The order of terms in proportion is Important.
• The method in which we first find the value of one unit and then find the value of required number of units is known as unitary method.

Assignment:�MULTIPLE CHOICE QUESTIONS:

1. To make a cup of tea ratio of water to milk is 3 : 1. So, to make 4 cups of tea the ratio of water to milk is :

(a) 4 : 1 (b) 4 : 2 (c) 12 : 4 (d) 7 : 5

2. A car travels 81 km in 3 hours. Distance travelled by car in 5 hours is :

(a) 27 km (b) 135 km (c) 45 km (d) none of these

3. In the word “ MATHEMATICS” the ratio of numbers of consonants to the numbers of vowel is :

(a) 1 : 7 (b) 1 : 4 (c) 7 : 4 (d) 5 : 3

4. The ratio of complete angle to right angle is :

(a) 4 : 1 (b) 1 : 4 (c) 1 : 2 (d) 2 : 1

5. In the simplest form of the ratio of 72 to 180 is :

(a) 4 : 10 (b) 18 : 45 (c) 2 : 5 (d) 4 : 5

PRACTICE QUESTIONS:

1. Find the ratio of 30 min to 2 hours.

2. Check 7, 56, 13, 104 are in proportion.

3. For 25 : 10, 10 : 4 find the mean proportion.

4.In the given proportion 9 : 3, 36 : 12 extremes are?

5.12 Sarees costs Rs. 3600. Find cost of 1 saree.

6.Cost of 12 apples is Rs. 96. Then what is the cost of 15 apples.

7.Cost of 5 kg wheat is Rs. 80. Then what will be cost of 8 kg of wheat?

8.Mohit earns Rs. 7650 and saves Rs. 918 per month. Find the ratio of (1) his income and saving.

(2) his expenditure and saving.

9. Out of 30 students in a class 12students like football , 10 students like cricket and the remaining students like tennis. Find the ratio of (a) Number of student liking football to number of students liking

tennis.

(b) Number of students liking cricket to total number of students.

10. Divide 20 pens between Pooja and Riya in the ratio of 2 : 3.

PISA BASED QUESTION :

• On a particular day the sales (in Rs.) of different items of a Baker’s Shop are given below:

From above information, give answers of the followings :

1. Find the ratio of sales of biscuits to the sales of the fruit bread.

2. Find the ratio of the sales of ordinary bread to the total sales .

3. Find the ratio of sales of cakes and pastries to biscuits and the ratio of biscuits to the sales of ordinary bread. Are they in proportion?

4. The ratios of cakes and pastries to ordinary bread and ratios of sales of biscuits to the sales of others. Are they in proportion?

5. If there are 5 fruit bread packet sold on that day then find the price of 8 fruit bread packets?

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THANK YOU