6th Maths : Term 3 Unit 1 : Fractions : Exercises 1.2 : Miscellaneous Practice problems, Challenge Problems , Text Book Back Exercises Questions with Answers, Solution

**Exercises 1.2 **

__Miscellaneous Practice problems __

** 1. Sankari purchased 2 1/2 m cloth to stich a long skirt and 1**

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 o****ﬃ****ce, 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 3/4***kg*** 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 3/4*kg* 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

Tags : Questions with Answers, Solution | Fractions | Term 3 Chapter 1 | 6th Maths , 6th Maths : Term 3 Unit 1 : Fractions

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6th Maths : Term 3 Unit 1 : Fractions : Exercises 1.2 | Questions with Answers, Solution | Fractions | Term 3 Chapter 1 | 6th Maths

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