Exercises 1.2

Exercises 1.2

Miscellaneous Practice problems

 1. Sankari purchased 2 1/2 m cloth to stich a long skirt and 1 3/4  m cloth to stitch blouse. If the cost is ₹120 per metre then find the cost of cloth purchased by her.

Length of long skirt = 2 ½ m

Length of blouse = 1 ¾  m

Total length of cloth she bought = (2 ½ + 1 ¾ ) m

The cost of cloth purchased by her = ₹ 510

2. From his office, a person wants to reach his house on foot which is at a distance of 5 3/4 km. If he had walked 2 1/2 km, how much distance still he has to walk to reach his house?

The distance between office and house = 5 ¾ km

The distance he had walked = 2 ½ km

Distance still he has to walk to reach his house = (5 ¾ − 2 ½ ) km

= ( (23 / 4) – (5 / 2) ) km

= ( [23 – 10] / 4) km 13/4 km

= 3 ¼  km

Distance still he has to walk to reach his house = 3 ¼ km

3. Which is smaller? The difference between 2 1/2 and 3 2/3 or the sum of 1 1/2 and 2 1/4 .

The difference between 2 ½  and 3 2/3  = 3 2/3  − 2 ½  

= [11 / 3] – [5/2] =   [22 – 15] / 6 =  7 / 6 = 1 (1/6)

The sum of 1 ½ and 2 ¼ = 1 ½ + 2 ¼

= 3/2 + 9/4 = (6 + 9) / 4 = 15 / 4

= 3 3/4

1 1/6 < 3 3/4

The difference between 2 ½  and 3 2/3 is smaller.

4. Mangai bought 6 3/4kg of apples. If Kalai bought 1 1/2 times as Mangai bought, then how many kilograms of apples did Kalai buy?

Weight of apples bought by Mangai = 6 ¾  kg.

Weight of apples bought by Kalai = weight of apples bought by Mangai x 1 ½  kg

= (6 ¾ × 1 ½ ) kg

= 27/4 × 3/2 kg = 81/8 kg = 10 1/8 kg

Weight of apples bought by Kalai = 10 1/8 kg

5. The length of the staircase is 5 1/2 m. If one step is set at 1/4 m, then how many steps will be there in the staircase?

The length of the staircase = 5 ½  m

Height of one step set at = ¼  m

The length of the staircase = The length of the staircase / Height of one step set at

= 5 ½ / ¼  = 11/2 ÷ 1/4

= 11/2 × 4/1  = 22

Number of steps in the stair case = 22 

Challenge Problems

6. By using the following clues, find who am I?

i) Each of my numerator and denominator is a single digit number.

5/7 , 3/4 , 8/9

ii) The sum of my numerator and denominator is a multiple of 3.

1/5, 3/6 , 4/5, 1/8 , 2/7, 2/4

iii) The product of my numerator and denominator is a multiple of 4.

2/4, 3/4, 4/6, 4/8, 3/8

7. Add the difference between 1 1/3  and 3 1/6  and the difference between 4 1/6 and 2 1/3 .

 8. What fraction is to be subtracted from 9 3/7  to get 3 1/5 ?

 9. The sum of two fractions is 5 3/9. If one of the fractions is 2 3/4 , find the other fraction.

10. By what number should 3 1/16 be multiplied to get 9 3/16?

11. Complete the fifth row in the Leibnitz triangle which is based on subraction.

12) A painter painted 3/8 of the wall of which one third is painted in yellow colour. What fraction is the yellow colour of the entire wall?

13. A rabbit has to cover 26 1/4 m to fetch its food. If it covers 1 3/4 m in one jump, then how many jumps will it take to fetch its food?

14. Look at the picture and answer the following questions:

i) What is the distance from School to Library via Bus stop?

ii) What is the distance between School and Library via Hospital?

iii) Which is the shortest distance between (i) and (ii)?

The distance from school to Library via Bus stop is the shortest distance.

iv) The distance between School and Hospital is ________ times the distance between School and Bus stop.

The distance between school and Hospital = 4 ½ km

The distance between school and Bus stop = ¾ km

 = 9/2 × 4/3 = 6

The distance between school and Hospital is 6 times the distance between school and Bus stop. 

ANSWERS:

Exercise 1.2

1.  510

 2. 3 1/4 km

3. The difference between 2 1/2 and 3 2/3 is smaller

4. 10 1/8 kg

 5. 22 steps

6. 4/8 & many answers

7. 3 2/3

 8. 6 8/35

9. 2 7/12

10. 3

11. 1/20, 1/30, 1/20

12. 1/8

13. 15

14. i) 4 1/4 km ii) 5 3/4 km iii) Via Bus Stand  iv) 6 times

Exercises 1.2

Miscellaneous Practice problems

 1. Sankari purchased 2 1/2 m cloth to stich a long skirt and 1 3/4  m cloth to stitch blouse. If the cost is ₹120 per metre then find the cost of cloth purchased by her.

Length of long skirt = 2 ½ m

Length of blouse = 1 ¾  m

Total length of cloth she bought = (2 ½ + 1 ¾ ) m

= ( 5/2 + 7/4) m

= ( (10 + 7) / 4) m = 17 / 4 m

= 4 ¼  m

Cost of 1 metre cloth = ₹ 120

Cost of 4 ¼  metres cloth = ₹ 120 × 4 ¼

= ₹120 × (17/4)

= ₹ 510

The cost of cloth purchased by her = ₹ 510

2. From his office, a person wants to reach his house on foot which is at a distance of 5 3/4 km. If he had walked 2 1/2 km, how much distance still he has to walk to reach his house?

The distance between office and house = 5 ¾ km

The distance he had walked = 2 ½ km

Distance still he has to walk to reach his house = (5 ¾ − 2 ½ ) km

= ( (23 / 4) – (5 / 2) ) km

= ( [23 – 10] / 4) km 13/4 km

= 3 ¼  km

Distance still he has to walk to reach his house = 3 ¼ km

3. Which is smaller? The difference between 2 1/2 and 3 2/3 or the sum of 1 1/2 and 2 1/4 .

The difference between 2 ½  and 3 2/3  = 3 2/3  − 2 ½  

= [11 / 3] – [5/2] =   [22 – 15] / 6 =  7 / 6 = 1 (1/6)

The sum of 1 ½ and 2 ¼ = 1 ½ + 2 ¼

= 3/2 + 9/4 = (6 + 9) / 4 = 15 / 4

= 3 3/4

1 1/6 < 3 3/4

The difference between 2 ½  and 3 2/3 is smaller.

4. Mangai bought 6 3/4kg of apples. If Kalai bought 1 1/2 times as Mangai bought, then how many kilograms of apples did Kalai buy?

Weight of apples bought by Mangai = 6 ¾  kg.

Weight of apples bought by Kalai = weight of apples bought by Mangai x 1 ½  kg

= (6 ¾ × 1 ½ ) kg

= 27/4 × 3/2 kg = 81/8 kg = 10 1/8 kg

Weight of apples bought by Kalai = 10 1/8 kg

5. The length of the staircase is 5 1/2 m. If one step is set at 1/4 m, then how many steps will be there in the staircase?

The length of the staircase = 5 ½  m

Height of one step set at = ¼  m

The length of the staircase = The length of the staircase / Height of one step set at

= 5 ½ / ¼  = 11/2 ÷ 1/4

= 11/2 × 4/1  = 22

Number of steps in the stair case = 22 

Challenge Problems

6. By using the following clues, find who am I?

i) Each of my numerator and denominator is a single digit number.

5/7 , 3/4 , 8/9

ii) The sum of my numerator and denominator is a multiple of 3.

1/5, 3/6 , 4/5, 1/8 , 2/7, 2/4

iii) The product of my numerator and denominator is a multiple of 4.

2/4, 3/4, 4/6, 4/8, 3/8

7. Add the difference between 1 1/3  and 3 1/6  and the difference between 4 1/6 and 2 1/3 .

The difference between 1 1/3 and 3 1/6

= 3 (1/6) – 1 (1/3)

= 19/6 – 4/3 = [19 – 8] / 6 = 11 / 6

The difference between 4 1/6 and 2 1/3

= 4 (1/6) – 2 (1/3)

= 25/6 – 7/3 = [25 – 14] / 6 = 11 / 6

Sum of the differences, 11/6 + 11/6 = 22/6

= 11 / 3 = 3 2/3

 8. What fraction is to be subtracted from 9 3/7  to get 3 1/5 ?

The fraction is to be subtracted = 9 3/7 – 3 1/5

= 66/7 – 16/5 = [330 – 112] / 35 = 218 / 35

= 6 8/35

6 8/35 is to be subtracted from 9 3/7 to get 3 1/5

 9. The sum of two fractions is 5 3/9. If one of the fractions is 2 3/4 , find the other fraction.

The sum of two fractions = 5 3/9

One of the fractions = 2 ¾

The other fraction = 5 (3/9) – 2 (3/4)

= 48/9 – 11/4

= [192 – 99] / 36 = 93 / 36 = 31 / 12

= 2 (7/12)

The other fraction = 2 (7/12)

10. By what number should 3 1/16 be multiplied to get 9 3/16?

The number should be multiplied =  [ 9 3/16 ] / [ 3 1/16 ] 

= 9 3/16 ÷ 3 1/16

= 147/16 ÷ 49/16

= 147/16 ÷ 16/49 = 3

3 (1/16) × 3 = 9 (3/16)

3 Should be multiplied with 3 (1/16) to get 9 (3/16).

11. Complete the fifth row in the Leibnitz triangle which is based on subraction.

12) A painter painted 3/8 of the wall of which one third is painted in yellow colour. What fraction is the yellow colour of the entire wall?

The part painted in the wall = 3/8

The part painted in yellow colour of the entire wall = 1/3 part of 3/8

= 3/8 × 1/3 = 1/8

The part painted in yellow colour of the entire wall = 1/8 

13. A rabbit has to cover 26 1/4 m to fetch its food. If it covers 1 3/4 m in one jump, then how many jumps will it take to fetch its food?

The distance has to cover by a rabbit to fetch its food = 26 ¼ m = 105/4 m

The distance covers in one jump = 1 3/4 m = 7/4 m

The number of jumps it will take to fetch is food = Distance has to cover / Distance cover in one jump

= 105/4 ÷ 7/4

= 105/4 × 4/7 = 15

The rabbit will take 15 jumps to fetch its food.

14. Look at the picture and answer the following questions:

i) What is the distance from School to Library via Bus stop?

The distance from school to library via Bus stop

= ( 3/4 + 3 1/2 ) km (3/4 + 7/2) km

= ( [3 + 14] / 4 ) km = 17/4 km = 4 (¼) km

ii) What is the distance between School and Library via Hospital?

The distance between school and Library via Hospital

= 4 1/2 + 1 1/4 km = 9/2 + 5/4 km

= [18 + 5] / 4 km = 23/4 km = 5 (3/4) km

iii) Which is the shortest distance between (i) and (ii)?

The distance from school to Library via Bus stop is the shortest distance.

iv) The distance between School and Hospital is ________ times the distance between School and Bus stop.

The distance between school and Hospital = 4 ½ km

The distance between school and Bus stop = ¾ km

4 (1/2) ÷ 3/4 = 9/2 × 4/3 = 6

The distance between school and Hospital is 6 times the distance between school and Bus stop. 

ANSWERS:

Exercise 1.2

1.  510

 2. 3 1/4 km

3. The difference between 2 1/2 and 3 2/3 is smaller

4. 10 1/8 kg

 5. 22 steps

6. 4/8 & many answers

7. 3 2/3

 8. 6 8/35

9. 2 7/12

10. 3

11. 1/20, 1/30, 1/20

12. 1/8

13. 15

14. i) 4 1/4 km ii) 5 3/4 km iii) Via Bus Stand  iv) 6 times