Samacheer Class 6 Maths Fractions Book Back Answers & Solutions

Q: Fill in the blanks: (i) 7\frac{3}{4} + 6\frac{1}{2} ……….. (ii) The sum of a whole number and a proper fraction is called ………. (iii) 5\frac{1}{3} – 3\frac{1}{2} ……….. (iv) 8 ÷ \frac{1}{2} ……….. (v) The number which has its own reciprocal is ……….

(ii) Mixed Fraction (iii) 5\frac{1}{3} – 3\frac{1}{2} = \frac{16}{3} – \frac{7}{2} = \frac{32-21}{6} = \frac{11}{6} = 1\frac{5}{6} (iv) 8 ÷ \frac{1}{2} = 8 × \frac{2}{1} = 16 (v) 1 The first step would be to write the mix number 223 as an improper fraction.

Q: Answer the following: (i) Find the sum of \frac{1}{7} and \frac{3}{9}. (ii) What is the total of 3\frac{1}{3} and 4\frac{1}{6}? (iii) Simplify: 1\frac{3}{5}+5\frac{4}{7}. (iv) Find the difference between \frac{8}{9} and \frac{2}{7} (v) Subtract: 1\frac{3}{5} from 2\frac{1}{3}. (vi) Simplify: 7\frac{2}{7} – 3\frac{4}{21}

(i) \frac{1}{7} + \frac{3}{9} = \frac{9+21}{63} = \frac{30}{63} = \frac{10}{21}

Q: Convert mixed fractions into improper fractions and vice versa: (i) 3\frac{7}{18} (ii) \frac{99}{7} (iii) \frac{47}{6} (iv) 12\frac{1}{9}

(i) 3\frac{7}{18} = \frac{61}{18} (ii) \frac{99}{7} = 14\frac{1}{7} (iii) \frac{47}{6} = 7\frac{5}{6} (iv) 12\frac{1}{9} = \frac{109}{9}

Q: Multiply the following: (i) \frac{2}{3} × 6 (ii) 8\frac{1}{3} × 5 (iii) \frac{3}{8} × \frac{4}{5} (iv) 3\frac{5}{7} × 1\frac{1}{13}

(i) \frac{2}{3} × 6 = 4 (ii) 8\frac{1}{3} × 5 = \frac{25}{3} × 5 = \frac{125}{3} = 41\frac{2}{3} (iii) \frac{3}{8} × \frac{4}{5} = \frac{12}{40} = \frac{3}{10} (iv) 3\frac{5}{7} × 1\frac{1}{13} = \frac{26}{7} × \frac{14}{13} = \frac{4}{1} = 4

Q: Divide the following (i) \frac{3}{7} ÷ 4 (ii) \frac{4}{3} ÷ \frac{5}{9} (iii) 4\frac{1}{5} ÷ 3\frac{3}{4} (iv) 9\frac{2}{3} ÷ 1\frac{2}{3}

(i) \frac{3}{7} ÷ 4 = \frac{3}{7} × \frac{1}{4} = \frac{3}{28} (ii) \frac{4}{3} ÷ \frac{5}{9} = \frac{4}{3} × \frac{9}{5} = \frac{12}{5} = 2\frac{2}{5}

Q: Nilavan can walk 4\frac{1}{2} km in an hour. How much distance will he cover in 3\frac{1}{2} hours?

Distance walked in an hour = 4\frac{1}{2} km Distance covered in 3\frac{1}{2} Hours

Q: Ravi bought a curtain of length 15\frac{3}{4} m. If he cut the curtain into small pieces each of length 2\frac{1}{4} m, then how many small curtains will he get?

Total length = 15\frac{3}{4} Length of the small pieces = 2\frac{1}{4} Small curtains obtained = 7 Objective Type Questions

Q: Which of the following statement is incorrect?

(d) \frac{10}{11} > \frac{9}{10}

Your Progress - Chapter 10% complete

1Book Back Questions28 questions

Q.1Fill in the blanks: (i) 7\(\frac{3}{4}\) + 6\(\frac{1}{2}\) ……….. (ii) The sum of a whole number and a proper fraction is called ………. (iii) 5\(\frac{1}{3}\) – 3\(\frac{1}{2}\) ……….. (iv) 8 ÷ \(\frac{1}{2}\) ……….. (v) The number which has its own reciprocal is ……….v

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 1
(ii) Mixed Fraction
(iii) 5\(\frac{1}{3}\) – 3\(\frac{1}{2}\)
= \(\frac{16}{3}\) – \(\frac{7}{2}\) = \(\frac{32-21}{6}\) = \(\frac{11}{6}\)
= 1\(\frac{5}{6}\)
(iv) 8 ÷ \(\frac{1}{2}\)
= 8 × \(\frac{2}{1}\)
= 16
(v) 1

The first step would be to write the mix number 223 as an improper fraction.

Answer:

Q.2Say True or False (i) 3\(\frac{1}{2}\) can be written as 3 + \(\frac{1}{2}\). (ii) The sum of any two proper fractions is always an improper fraction. (iii) The mixed fraction of \(\frac{13}{4}\) is 3\(\frac{1}{4}\). (iv) The reciprocal of an improper fraction is always a proper fraction. (v) 3\(\frac{1}{4}\) × 3\(\frac{1}{4}\) = 9\(\frac{1}{16}\)v

Solution

(i) True
(ii) False
(iii) True
(iv) True
(v) False

Answer:

(i) True
(ii) False
(iii) True
(iv) True
(v) False

Q.3Answer the following: (i) Find the sum of \(\frac{1}{7}\) and \(\frac{3}{9}\). (ii) What is the total of 3\(\frac{1}{3}\) and 4\(\frac{1}{6}\)? (iii) Simplify: 1\(\frac{3}{5}\)+5\(\frac{4}{7}\). (iv) Find the difference between \(\frac{8}{9}\) and \(\frac{2}{7}\) (v) Subtract: 1\(\frac{3}{5}\) from 2\(\frac{1}{3}\). (vi) Simplify: 7\(\frac{2}{7}\) – 3\(\frac{4}{21}\)v

Solution

(i) \(\frac{1}{7}\) + \(\frac{3}{9}\)
= \(\frac{9+21}{63}\) = \(\frac{30}{63}\) = \(\frac{10}{21}\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 2

Answer:

(i) \(\frac{1}{7}\) + \(\frac{3}{9}\)
= \(\frac{9+21}{63}\) = \(\frac{30}{63}\) = \(\frac{10}{21}\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 2

Q.4Convert mixed fractions into improper fractions and vice versa: (i) 3\(\frac{7}{18}\) (ii) \(\frac{99}{7}\) (iii) \(\frac{47}{6}\) (iv) 12\(\frac{1}{9}\)v

Solution

(i) 3\(\frac{7}{18}\) = \(\frac{61}{18}\)
(ii) \(\frac{99}{7}\) = 14\(\frac{1}{7}\)
(iii) \(\frac{47}{6}\) = 7\(\frac{5}{6}\)
(iv) 12\(\frac{1}{9}\) = \(\frac{109}{9}\)

Answer:

(i) 3\(\frac{7}{18}\) = \(\frac{61}{18}\)
(ii) \(\frac{99}{7}\) = 14\(\frac{1}{7}\)
(iii) \(\frac{47}{6}\) = 7\(\frac{5}{6}\)
(iv) 12\(\frac{1}{9}\) = \(\frac{109}{9}\)

Q.5Multiply the following: (i) \(\frac{2}{3}\) × 6 (ii) 8\(\frac{1}{3}\) × 5 (iii) \(\frac{3}{8}\) × \(\frac{4}{5}\) (iv) 3\(\frac{5}{7}\) × 1\(\frac{1}{13}\)v

Solution

(i) \(\frac{2}{3}\) × 6 = 4
(ii) 8\(\frac{1}{3}\) × 5
= \(\frac{25}{3}\) × 5
= \(\frac{125}{3}\)
= 41\(\frac{2}{3}\)
(iii) \(\frac{3}{8}\) × \(\frac{4}{5}\)
= \(\frac{12}{40}\) = \(\frac{3}{10}\)
(iv) 3\(\frac{5}{7}\) × 1\(\frac{1}{13}\)
= \(\frac{26}{7}\) × \(\frac{14}{13}\)
= \(\frac{4}{1}\)
= 4
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1

Answer:

Q.6Divide the following (i) \(\frac{3}{7}\) ÷ 4 (ii) \(\frac{4}{3}\) ÷ \(\frac{5}{9}\) (iii) 4\(\frac{1}{5}\) ÷ 3\(\frac{3}{4}\) (iv) 9\(\frac{2}{3}\) ÷ 1\(\frac{2}{3}\)v

Solution

(i) \(\frac{3}{7}\) ÷ 4
= \(\frac{3}{7}\) × \(\frac{1}{4}\) = \(\frac{3}{28}\)
(ii) \(\frac{4}{3}\) ÷ \(\frac{5}{9}\)
= \(\frac{4}{3}\) × \(\frac{9}{5}\)
= \(\frac{12}{5}\)
= 2\(\frac{2}{5}\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 4

Answer:

Q.7Gowri purchased 3\(\frac{1}{2}\) kg of tomatoes, \(\frac{3}{4}\) kg of brinjal and 1\(\frac{1}{4}\) kg of onion. What is the total weight of the vegetables she bought?v

Solution

Total weight of vegetables bought
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 5

Answer:

Total weight of vegetables bought
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 5

Q.8An oil tin contains 3\(\frac{3}{4}\) litres of oil of which 2\(\frac{1}{2}\) litres of oil is used. How much oil is left over?v

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 6

Answer:

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 6

Q.9Nilavan can walk 4\(\frac{1}{2}\) km in an hour. How much distance will he cover in 3\(\frac{1}{2}\) hours?v

Solution

Distance walked in an hour = 4\(\frac{1}{2}\) km
Distance covered in 3\(\frac{1}{2}\)
Hours
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 7

Answer:

Distance walked in an hour = 4\(\frac{1}{2}\) km
Distance covered in 3\(\frac{1}{2}\)
Hours
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 7

Q.10Ravi bought a curtain of length 15\(\frac{3}{4}\) m. If he cut the curtain into small pieces each of length 2\(\frac{1}{4}\) m, then how many small curtains will he get?v

Solution

Total length = 15\(\frac{3}{4}\)
Length of the small pieces = 2\(\frac{1}{4}\)
Small curtains obtained
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1 8
= 7

Objective Type Questions

Answer:

Q.11Which of the following statement is incorrect?v

A. \(\frac{1}{2}\) > \(\frac{1}{3}\)
B. \(\frac{7}{8}\) > \(\frac{6}{7}\)
C. \(\frac{8}{9}\) < \(\frac{9}{10}\)
D. \(\frac{10}{11}\) > \(\frac{9}{10}\)

Solution

(d) \(\frac{10}{11}\) > \(\frac{9}{10}\)

Answer:

(d) \(\frac{10}{11}\) > \(\frac{9}{10}\)

Q.12The difference between \(\frac{3}{7}\) and \(\frac{2}{9}\) isv

A. \(\frac{13}{63}\)
B. \(\frac{1}{9}\)
C. \(\frac{1}{7}\)
D. \(\frac{9}{16}\)

Solution

(a) \(\frac{13}{63}\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1

Answer:

(a) \(\frac{13}{63}\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1

Q.13The reciprocal of \(\frac{53}{17}\) isv

A. \(\frac{53}{17}\)
B. 5\(\frac{3}{17}\)
C. \(\frac{17}{53}\)
D. 3\(\frac{5}{17}\)

Solution

Answer:

Q.14If \(\frac{6}{7}=\frac{\mathbf{A}}{49}\), then the value of A isv

A. 42
B. 36
C. 25
D. 48

Solution

(a) 42
Hint: \(\frac{6 \times 49}{7}=42\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1

Answer:

(a) 42
Hint: \(\frac{6 \times 49}{7}=42\)
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.1

Q.15Pugazh has been given four choices for his pocket money by his father. Which of the choices should he take in order to get the maximum money?v

A. \(\frac{2}{3}\) of Rs 150
B. \(\frac{3}{5}\) of Rs 150
C. \(\frac{4}{5}\) of Rs 150
D. \(\frac{1}{5}\) of Rs 150

Solution

(c) \(\frac{4}{5}\) of Rs 150
Posted in Class 6 on January 6, 2025 January 7, 2025
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Answer:

Q.1Sankari purchased 2\(\frac{1}{2}\) m cloth to stich a long skirt and 1\(\frac{3}{4}\) m cloth to stitch blouse. If the cost is Rs. 120 per metre then find the cost of cloth purchased by her.v

Solution

Total cloth purchased
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 1
cost of 1 metre = Rs. 120
Total cost of cloth purchased
= Rs. 120 × \(\frac{17}{4}\)
= Rs. 510

Answer:

Total cloth purchased
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 1
cost of 1 metre = Rs. 120
Total cost of cloth purchased
= Rs. 120 × \(\frac{17}{4}\)
= Rs. 510

Q.2From his office, a person wants to reach his house on foot which is at a distance of 5\(\frac{3}{4}\) km. If he had walked 2\(\frac{1}{2}\) km, how much distance still he has to walk to reach his house?v

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 2

Answer:

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 2

Q.3Which is smaller? The difference between 2\(\frac{1}{2}\) and 3\(\frac{2}{3}\) or the sum of 1\(\frac{1}{2}\) and 2\(\frac{1}{4}\).v

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 3
∴ The difference of 2\(\frac{1}{2}\) and 3\(\frac{2}{3}\) is smaller

Answer:

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 3
∴ The difference of 2\(\frac{1}{2}\) and 3\(\frac{2}{3}\) is smaller

Q.4Mangai bought 6\(\frac{3}{4}\) kg of apples. If Kalai 1 bought 1\(\frac{1}{2}\) times a Mangai bought, then how many kilograms of apples did Kalai buy?v

Solution

Apples bought by Mangai = 6\(\frac{3}{4}\) kg
Apples bought by Kalai
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 4

Answer:

Apples bought by Mangai = 6\(\frac{3}{4}\) kg
Apples bought by Kalai
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 4

Q.5The length of the staircase is 5\(\frac{1}{2}\) m. If one step is set at \(\frac{1}{4}\) m, then how many steps will be there in the staircase? Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 5

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 5

Solution

Total length of the staircase = 5\(\frac{1}{2}\) m
length of each step = \(\frac{1}{4}\) m
No of steps in the stair case
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 6
= 22 steps

Challenge Problems

Answer:

Q.6By using the following clues, find who am I? (i) Each of my numerator and denominator is a single-digit number. (ii) The sum of my numerator and denominator is a multiple of 3. (iii) The product of my numerator and denominator is a multiple of 4.v

Solution

The numerator may be any one of!, 2, 3,4, 5, 6, 7, 8, 9 and the denominator may be any one of 1, 2,3,4, 5,6, 7,8,9. Sum of numerator and denominator is a multiple of 3.
∴ Possible proper fractions are \(\frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \frac{2}{4}, \frac{2}{7}, \frac{3}{6}, \frac{3}{9}, \frac{4}{5}, \frac{4}{8}, \frac{5}{7}, \frac{6}{9}\)
Also given the product of numerator and denominator is a multiple of 4.
∴ Possible fractions are \(\frac{1}{8}, \frac{2}{4}, \frac{4}{5}, \frac{4}{8}\)

Answer:

Q.7Add the difference between 1\(\frac{1}{3}\) and 3\(\frac{1}{6}\) and the difference between 4\(\frac{1}{6}\) and 2\(\frac{1}{3}\)v

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 7
Adding Difference

Answer:

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 7
Adding Difference

Q.8What fraction is to be subtracted from 9\(\frac{3}{7}\) to get 3\(\frac{1}{5}\)?v

Solution

Let the fraction be x
According to the problem
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 9
The fraction to be subtracted is 6\(\frac{8}{35}\)

Answer:

Let the fraction be x
According to the problem
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 9
The fraction to be subtracted is 6\(\frac{8}{35}\)

Q.9The sum of two fractions is 5\(\frac{3}{9}\). If one of the fractions is 2\(\frac{3}{4}\), find the other fraction.v

Solution

Let the other fraction be x
According to the problem,
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 10
∴ The other fraction is 2\(\frac{7}{12}\)

Answer:

Let the other fraction be x
According to the problem,
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 10
∴ The other fraction is 2\(\frac{7}{12}\)

Q.10By what number should 3\(\frac{1}{16}\) be multiplied to get 9\(\frac{3}{16}\)?v

Solution

Let the number be x
According to the problem,
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 11
x = 3
The number is 3

Answer:

Let the number be x
According to the problem,
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 11
x = 3
The number is 3

Q.11Complete the fifth row in the Leibnitz triangle which is based on subtraction. Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 12

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 12

Solution

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 13

Answer:

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 13

Q.12A painter painted \(\frac{3}{8}\) of the wall of which one third is painted in yellow colour. What fraction is the yellow colour of the entire wall? Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 14

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 14

Solution

yellow colour of the entire wall
= \(\frac{3}{8}\) × \(\frac{1}{3}\)
= \(\frac{1}{8}\)

Answer:

yellow colour of the entire wall
= \(\frac{3}{8}\) × \(\frac{1}{3}\)
= \(\frac{1}{8}\)

Q.13A rabbit has to cover 26\(\frac{1}{4}\) m to fetch its food. If it covers 1\(\frac{3}{4}\) m in one jump, then how many jumps will it take to fetch its food? Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 15

Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 15

Solution

Total distance = 26\(\frac{1}{4}\) m
Distance covered in one jump = 1\(\frac{3}{4}\) m
Number of jumps required to fetch the food
Samacheer Kalvi 6th Maths Guide Term 3 Chapter 1 Fractions Ex 1.2 16
= 15

Answer:

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