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mathematics

class VII

#### Key Concepts

First term, second term, comparision of ratios, proportion, mean proportional, direct variation, inverse variation

#### essential questions

1. How is a ratio or rate used to compare two quantities or values? Where can examples of ratios and rates be found?
2. How can I model and represent rates, ratios, and proportions?
3. What is a proportion?
4. How are cross products and unit rates helpful in determining whether two ratios are equivalent?
5. What is the use of unitary method? How do we use proportions in this concept?

#### Remembering:

1. A ratio equivalent to 3:7 is : a) 3:9  b) 6:10  c) 9:21  d) 18: 49
2. The ratio 35: 84 in the simplest form is: a) 5:7  b) 7:12  c) 5:12  d) None
3. The first, second and fourth terms of a proportion are 16, 24 and 54 respectively. Then the third term is: a) 36  b) 28  c) 48  d) 32
4. If 12, 21, 72, 126 are in proportion, then: i) 12× 21 =72 × 126   ii) 12 × 72 = 21× 126  iii) 12 × 126 = 21 × 72  iv) None
5. If x, y and z are in proportion then: i) x : y :: z : x  ii) x: y :: y: z  iii) x:y :: z: y  iv) x: z :: y : z
6. 7:12 is equivalent to : i) 28 : 40   ii) 42 : 71  iii) 72 : 42  iv) 42: 72
7. We can get ____ ratios by multiplying or divinding the numerator and denominator by the same number. a) equivalent  b) simple  c) unlike
8. If two ratios are equal, we say that they are in____ a) congruence  b) proportion  c) simplest form
9. In 35:70:: 2:4 , 35 and 4 are known ar_____ a) middle terms  b) extreme terms  c) first term
10. If you divide Rs 100 in the ratio of 2:3 between Monu and Sonu, the amount Sonu gets is____ a) 40  b) 60  c) 80
11. The method in whihc first we find the value of one unit and the value of required number of units is known as_____ a) unitary method  b) simplest method  c) Integration method
12. Two quantity can be compared only if they are in the ____ unit. a) Same b) different  c) None
13. The lowest form of the ratio 4:16 is____ a) 1:4  b) 4:1  c) 2:5
14. In 4:7 :: 16:28 , 7 & 16 are called: a) extreme terms  b) middle terms  c) Middle and extreme  d) None
15. Show the numbers are in proportion. a) 22,33, 42, 63

Unitary method:

1. If cost of 9 toys is Rs 333, find the cost of 76 such toys.
2. If 25 meters cloth cost Rs 1575, what will be the cost of 1 meter of cloth?

#### understanding:

1. In a class there are 20 boys and 15 girls. The ratio of boys and girls is : a) 4:3  b) 3:4  c) 4:5 d) none
2. The ratio of 1.5 m to 10 cm is : a) 1:15  b) 15:10  c) 10:15  d) 15:1
3. Which of the following are in proportion: a) 33, 121, 9 ,96  b) 15, 45, 40, 120  c) 24,28,36,48
4. If A: B= 5: 8  and B: C- 18:25  find A:C
5. If 2A =3B= 4C, find A: B: C
6. Arrange the ratios in ascending order: a) 5:6 , 7:10 , 13: 15 and 23:30   b) 5:6, 8:9 (11:18)  c) 11:14, 17:21, 5:7 and 2:3
7. Which is greater 4:5 or 16: 25?
8. Find the fourth term if first 3 terms are 3,5 and 21 respectively
9. Find the third proportional to 9 and 12
10. Find the mean proportion between 8 and 18

Unitary method:

1. If 15 oranges cost Rs 110, what do 39 oranges cost?
2. If 8 Kg sugar cost Rs 260, how much sugar can be brought for Rs 877.50?
3. A worker makes a toy every 2/3 hour. If he works for 7 1/3 hours, then how many toys will he make?

#### Application:

1. Two numbers are in the ratio 7:9. If the sum of the numbers is 112, then the larger number is: a) 49  b) 72  c) 63 d) 42
2. The number of students in 3 classes is in the ratio 2:3:4 If 12 students are increased in each class this ratio changes to 8:11:14. Find the total number of students in beginning.
3. If a:b:c = 3:4:7 then ratio (a+b+c) :c is equal to : i) 2:1  ii) 14:3  iii) 7:2  iv) 1:2
4. The length and breadth of a rectangle are in the ratio 3:1 . If the breadth is 7 cm then the length of the rectangle is: a) 14 cm  b) 16 cm  c) 18 cm  d) 21 cm
5. The value of m, if 3,18,m, 42 are in proportion is: a) 6  b) 54  c) 7  d) none
6. Length and width of a field are in the ratio 5: 3. If the width of the field is 42 m then its length is : a) 100m  b) 80m  c) 50m  d) 70m
7. A box has 210 coins of denominations  one rupee and fifty paise only. The ratio of their respective values is 13: 11. The number of one rupee coin is  a) 65  b) 66  c) 77  d) 78
8. If 2/3 of A= 75% of B= 0.6 of C, then find A:B: C
9. If A and B are in the ratio 3:4 and B & C in the ratio 12:13 then A& C will be in the ratio: a) 3:13  b) 9:13  c) 36:13  d) 13:9
10. If x : y = 3 : 2 find (2 x +3 y) : ( 3 x +5 y)
11. What must be added to each term of the ratio 3:5 so that the new ratio becomes 5:6?
12. The ratio of monthly income to the savings of a family is 11: 2. if the savings be Rs 2500, find the income and expenditure
13. Divide Rs 1350 among A,B and C in the ratio 2:3:4
14. The ages of A and B are in the ratio 5: 7. Eight years ago, their ages were in ratio 7:13. Find their present age.
15. Find x if x:18:: 5:3
16. What number must be added to each of the number 10, 18 , 22, 38 to get the numbers which are in proportion?
17. What must be subtracted from each of the numbers 23, 40, 57 and 108 so that the remainders are in proportion?

Unitary method:

1. A train covers a distance of 51 km in 45 minutes. How long will it take to cover 221 Km?
2. If 36 men can finish a piece of work in 25 days, how many days will 15 men take to do it?
3. If 48 men can dig a trench in 14 days how long will 28 men take to dig a similar trench?
4. 6 dozen eggs are bought for Rs 108, how much will 18 eggs cost?
5. 10 men can finish the construction of a wall in 8 days. How many men are added to finish the work in half a day?
6. If 21 cows eat as much as 15 buffaloes. How many cows will eat as much as 35 buffaloes?
7. In a fort, 120 men had provision for 30 days. For how many days is the food sufficient for 100 men?

#### Analysis:

1. The ratio of 1 hour to 300 seconds is: a) 1:12  b) 12:1  c) 1:5  d) 5:1
2. Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. The sum of the numbers will be____
3. If (3a + 5b): (3a-5b)=5:1  Find a:b

Unitary Method:

1. The length of the shadow of a 3 meter high pole at a certain time of the day is 3.6 m What is the length of another poles whose shadow at that time is 54 m long?
2.  The extension in an elastic string varies directly as the weight hung on it. If a weight of 10 grams produces an extension of 2.8 m, what weight would produce an extension of 19.6 cm?
3. If 4/5 of cistern is filled in 1 minute, how much more time will be required to fill the rest of it?
4. 10 pipes of the same diameter can fill a tank in 24 minutes. if 2 pipes go out of order how long will remaining pipe take to fill the tank?
5. A tree, 6 m tall, cast 4 m long shadow. At the same time, a flag pole casts a 50 m long shadow. How long is the flag pole?
6. In a map 1 cm represents 8km. How much distance will be represented by 80.5 cm? a) 640 Km  b) 642 Km  c) 644 Km  d) 648 Km