Class 6

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 6 Decimals Ex 6.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 6 Decimals Ex 6.2

1. Convert the following decimal numbers into fractions and reduce it to lowest form.

Question (i)
1.4
Solution:
1.4 = \(\frac{14}{10}=\frac{14 \div 2}{10 \div 2}\)
(H.C.F. of 14 and 10 is 2)
= \(\frac {7}{5}\)

Question (ii)
2.25
Solution:
2.25 = \(\frac{225}{100}=\frac{225 \div 25}{100 \div 25}\)
(H.C.F. of 225 and 100 is 25)
= \(\frac {9}{4}\)

Question (iii)
18.6
Solution:
18.6 = \(\frac{186}{10}=\frac{186 \div 2}{10 \div 2}\)
(H.C.F. of 186 and 10 is 2)
= \(\frac {93}{5}\)

Question (iv)
4.04
Solution:
4.04 = \(\frac{404}{100}=\frac{404 \div 4}{100 \div 4}\)
(H.C.F. of 404 and 100 is 4)
= \(\frac {101}{25}\)

Question (v)
21.6
Solution:
21.6 = \(\frac{216}{10}=\frac{216 \div 2}{10 \div 2}\)
(H.C.F. of 216 and 10 is 2)
= \(\frac {108}{5}\)

2. Convert the following fractions into decimal numbers:

Question (i)
\(\frac {7}{100}\)
Solution:
\(\frac {7}{100}\) = 0.07
(Here denominator is 100)

Question (ii)
\(\frac {12}{10}\)
Solution:
\(\frac {12}{10}\) = 1.2
(Here denominator is 10)

Question (iii)
\(\frac {215}{100}\)
Solution:
\(\frac {215}{100}\) = 2.15
(Here denominator is 100)

Question (iv)
\(\frac {18}{1000}\)
Solution:
\(\frac {18}{1000}\) = 0.018
(Here denominator is 1000)

Question (v)
\(\frac {245}{10}\)
Solution:
\(\frac {245}{10}\) = 24.5
(Here denominator is 10)

3. Convert the following fractions into decimal numbers by equivalent fraction method:

Question (i)
\(\frac {5}{2}\)
Solution:
Here denominator is 2.
Convert into equivalent fraction with denominator 10 by multiplying it by 5.
∴ \(\frac{5}{2}=\frac{5 \times 5}{2 \times 5}=\frac{25}{10}\) = 2.5

Question (ii)
\(\frac {3}{4}\)
Solution:
Here denominator is 4.
Convert into equivalent fraction with denominator 100 by multiplying it by 25.
∴ \(\frac{3}{4}=\frac{3 \times 25}{4 \times 25}=\frac{75}{100}\) = 0.75

Question (iii)
\(\frac {28}{5}\)
Solution:
Here denominator is 5.
Convert into equivalent fraction with denominator 10 by multiplying it by 2.
∴ \(\frac{28}{5}=\frac{28 \times 2}{5 \times 2}=\frac{56}{10}\) = 5.6

Question (iv)
\(\frac {135}{20}\)
Solution:
Here denominator is 20.
Convert into equivalent fraction with denominator 100 by multiplying it by 5.
∴ \(\frac{135}{20}=\frac{135 \times 5}{20 \times 5}=\frac{675}{100}\)
= 6.75

Question (v)
\(\frac {17}{4}\)
Here denominator is 4.
Convert into equivalent fraction with denominator 100 by multiplying it by 25.
∴ \(\frac{17}{4}=\frac{17 \times 25}{4 \times 25}=\frac{425}{100}\)
= 4.25

4. Convert the following fractions into decimals by long division method:

Question (i)
\(\frac {17}{2}\)
Solution:

= 8.5

Question (ii)
\(\frac {33}{4}\)
Solution:

= 8.25

Question (iii)
\(\frac {76}{5}\)
Solution:

= 15.2

Question (iv)
\(\frac {24}{25}\)
Solution:

= 0.96

Question (v)
\(\frac {5}{8}\)
Solution:

= 0.625

5. Represent the following decimals on number line:

Question (i)
(i) 0.7
(ii) 1.6
(iii) 3.7
(iv) 6.3
(v) 5.4
Solution:

6. Write three decimal numbers between:

Question (i)
1.2 and 1.6
Solution:
Three decimal numbers between 1.2 and 1.6 are:
1.3, 1.4, 1.5

Question (ii)
2.8 and 3.2
Solution:
Three decimal numbers between 2.8 and 3.2 are:
2.9, 3, 3.1

Question (iii)
5 and 5.5.
Solution:
Three decimal numbers between 5 and 5.5 are:
5.1, 5.2, 5.3, 5.4.

7. Which number is greater:

Question (i)
0.4 or 0.7
Solution:

Since, 7 > 4
So, 0.7 > 0.4

Question (ii)
2.6 or 2.5
Solution:

Since, 6 > 5
So, 2.6 > 2.5

Question (iii)
1.23 or 1.32
Solution:

Since, 3 > 2
So, 1.32 > 1.23

Question (iv)
12.3 or 12.4
Solution:

Since, 4 > 3
So, 12.4 > 12.3

Question (v)
18.35 or 18.3
Solution:

Since, 5 > 0
So, 18.35 > 18.30

Question (vi)
12 or 1.2
Solution:

Since, 12 > 1
So, 12 > 1.2

Question (vii)
5.06 or 5.061
Solution:

Since, 1 > 0
So, 5.061 > 5.060

Question (viii)
2.34 or 23.3
Solution:

Since, 23 > 2
So, 23.3 > 2.34

Question (ix)
13.08 or 13.078
Solution:

Since, 8 > 7
So, 13.08 > 13.078

Question (x)
2.3 or 2.03.
Solution:

Since, 3 > 0
So, 2.3 > 2.03

8. Arrange the decimal numbers in ascending order:

Question (i)
2.5, 2, 1.8, 1.9
Solution:
Ascending order is :
1.8, 1.9, 2, 2.5

Question (ii)
3.4, 4.3, 3.1, 1.3
Solution:
Ascending order is :
1.3, 3.1, 3.4, 4.3

Question (iii)
1.24, 1.2, 1.42, 1.8.
Solution:
Ascending order is :
1.2, 1.24, 1.42, 1.8.

9. Arrange the decimal numbers in descending order:

Question (i)
4.1, 4.01, 4.12, 4.2
Solution:
Descending order is :
4.2, 4.12, 4.1, 4.01

Question (ii)
1.3, 1.03, 1.003, 13
Solution:
Descending order is :
13, 1.3, 1.03, 1.003

Question (iii)
8.02, 8.2, 8.1, 8.002.
Solution:
Descending order is :
8.2, 8.1, 8.02, 8.002.

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 6 Decimals Ex 6.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 6 Decimals Ex 6.1

1. Write each of the following in figures:

Question (i)
Seventy-two point one four.
Solution:
Seventy-two point one four = 72.14

Question (ii)
Two hundred fifty-seven point zero eight
Solution:
Two hundred fifty-seven point zero eight = 257.08

Question (iii)
Eight point two five-six.
Solution:
Eight point two five six = 8.256

Question (iv)
Forty-five and twenty-three hundredths.
Solution:
Forty five and twenty three hundredths
= 45 + \(\frac {23}{100}\)
= 45.23

Question (v)
Six hundred twenty-one and two hundred fifty-three thousandths
Solution:
Six hundred twenty-one and two hundred fifty-three thousandths
= 621 + \(\frac {253}{1000}\)
= 621.253

Question (vi)
Twelve and eight thousandths.
Solution:
Twelve and eight thousandths
= 12 + \(\frac {8}{1000}\)
= 12.008

2. Write the following decimal numbers in words:

Question (i)
12.52
Solution:
12.52 = Twelve point five two or twelve and fifty-two hundredths.

Question (ii)
7.148
Solution:
7.148 = Seven point one four eight or seven and one hundred forty-eight thousandths.

Question (iii)
0.24
Solution:
0.24 = Zero Point two four or twenty-four hundredths.

Question (iv)
5.018
Solution:
5.018 = Five-point zero one eight or five and eighteen thousandths.

Question (v)
.009.
Solution:
.009 = Point zero zero nine or nine thousandths.

3. Write the following decimals in the place value table:

Question (i)
(i) 21.569
(ii) 0.64
(iii) 3.51
(iv) 14.087
(v) 3.002.
Solution:

Number	Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousandths
1. 21.569	–	–	2	1	5	6	9
2. 0.64	–	–	–	0	6	4	–
3. 3.51	–	–	–	3	5	1	–
4. 14.087	–	–	1	4	0	8	7
5. 3.002	–	–	–	3	0	0	2

4. Write the following as decimals:

Question (i)
40 + \(\frac {2}{10}\)
Solution:
40 + \(\frac {2}{10}\) = 40.2

Question (ii)
700 + 5 + \(\frac {3}{10}\) + \(\frac {4}{100}\)
Solution:
700 + 5 + \(\frac {3}{10}\) + \(\frac {4}{100}\) = 705.34

Question (iii)
100 + \(\frac {5}{100}\) + \(\frac {3}{1000}\)
Solution:
100 + \(\frac {5}{100}\) + \(\frac {3}{1000}\) = 10.053

Question (iv)
100 + \(\frac {7}{10}\) + \(\frac {4}{1000}\)
Solution:
100 + \(\frac {7}{10}\) + \(\frac {4}{1000}\) = 0.704

Question (v)
\(\frac {5}{1000}\)
Solution:
\(\frac {5}{1000}\) = 0.005

5. Write the decimals shown in the following place value table:

Question (i)

Thousands	Hundreds	Tens	Ones	Tenth	Hundredths	Thousandths
–	5	2	4	1	2	–
2	0	3	4	2	1	–
–	–	6	1	0	2	3
–	–	–	4	0	0	1
–	1	0	0	0	3

Solution:
(i) 524.12
(ii) 2034.21
(iii) 61.023
(iv) 4.001
(v) 100.03

6. Expand the following decimals.

Question (i)
2.5
Solution:
2.5 = 2 + 0.5
= 2 + \(\frac {5}{10}\)

Question (ii)
18.43
Solution:
18.43 = 10 + 8 + 0.4 + 0.03
= 10 + 8 + \(\frac {4}{10}\) + \(\frac {3}{100}\)

Question (iii)
4.05
Solution:
4.05 = 4 + 0.05
= 4 + \(\frac {5}{100}\)

Question (iv)
13.123
Solution:
13.123 = 10 + 3 + 0.1 + 0.02 + 0.003
= 10 + 3 + \(\frac {1}{10}\) + \(\frac {2}{100}\) + \(\frac {3}{1000}\)

Question (v)
245.456
Solution:
245.456 = 200 + 40 + 5 + 0.4 + 0.05 + 0.006
= 200 + 40 + 5 + \(\frac {4}{10}\) + \(\frac {5}{100}\) + \(\frac {6}{1000}\)

Question (vi)
20.057
Solution:
20.057 = 20 + 0.05 + 0.007
= 20 + \(\frac {5}{100}\) + \(\frac {7}{1000}\)

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions MCQ Questions with Answers.

PSEB 6th Class Maths Chapter 5 Fractions MCQ Questions

Multiple Choice Questions

Question 1.
Which of the following does not represent any fraction?

Answer:

Question 2.
Which of the following is a proper fraction?
(a) \(\frac {5}{5}\)
(b) \(\frac {12}{11}\)
(c) \(\frac {7}{9}\)
(d) 7
Answer:
(c) \(\frac {7}{9}\)

Question 3.
Which of the following is an improper fraction?
(a) \(\frac {5}{8}\)
(b) \(2\frac {3}{4}\)
(c) \(\frac {7}{11}\)
(d) \(\frac {15}{16 }\)
Answer:
(b) \(2\frac {3}{4}\)

Question 4.
The fractions having las numerator are called …………. fractions.
(a) Like
(b) Unlike
(c) Unit
(d) Proper.
Answer:
(c) Unit

Question 5.
The fractions having same denominators are called …………. fractions.
(a) Proper
(b) Unit
(c) Improper
(d) Like.
Answer:
(d) Like.

Question 6.
The fraction having different denominators are called ……………. fractions.
(a) Unlike
(b) Like
(c) Improper
(d) Unit.
Answer:
(a) Unlike

Question 7.
Express 8 hours as a fraction of 1 day.
(a) \(\frac {2}{3}\)
(b) \(\frac {1}{3}\)
(c) \(\frac {8}{1}\)
(d) \(\frac {1}{8}\)
Answer:
(b) \(\frac {1}{3}\)

Question 8.
Find : \(\frac {2}{5}\) of ₹ 20.
(a) ₹ 8
(b) ₹ 10
(c) ₹ 12
(d) ₹ 40.
Answer:
(a) ₹ 8

Question 9.
Write \(\frac {19}{4}\) as mixed fraction.
(a) \(3\frac {4}{5}\)
(b) \(4\frac {4}{3}\)
(c) \(4\frac {3}{4}\)
(d) \(5\frac {1}{4}\)
Answer:
(c) \(4\frac {3}{4}\)

Question 10.
\(7\frac {2}{3}\) = ……………….
(a) \(\frac {17}{3}\)
(b) \(\frac {23}{3}\)
(c) \(\frac {13}{3}\)
(d) \(\frac {42}{3}\)
Answer:
(b) \(\frac {23}{3}\)

Question 11.
Which of the following represents an improper fraction?

Answer:

Question 12.
Which of the following is an equivalent of \(\frac {5}{7}\)?
(a) \(\frac {25}{49}\)
(b) \(\frac {20}{35}\)
(c) \(\frac {35}{49}\)
(d) \(\frac {35}{28}\)
Answer:
(c) \(\frac {35}{49}\)

Question 13.

(a) 32
(b) 24
(c) 40
(d) 16
Answer:
(a) 32

Question 14.
Which of the following are in ascending order?
(a) \(\frac{2}{3}, \frac{2}{7}, \frac{2}{5}\)
(b) \(\frac{2}{3}, \frac{2}{5}, \frac{2}{7}\)
(c) \(\frac{2}{7}, \frac{2}{3}, \frac{2}{5}\)
(d) \(\frac{2}{7}, \frac{2}{5}, \frac{2}{3}\)
Answer:
(d) \(\frac{2}{7}, \frac{2}{5}, \frac{2}{3}\)

Question 15.
Which of the following are in descending order?
(a) \(\frac{1}{8}, \frac{1}{3}, \frac{1}{9}\)
(b) \(\frac{1}{3}, \frac{1}{8}, \frac{1}{9}\)
(c) \(\frac{1}{8}, \frac{1}{9}, \frac{1}{3}\)
(d) \(\frac{1}{3}, \frac{1}{9}, \frac{1}{8}\)
Answer:
(b) \(\frac{1}{3}, \frac{1}{8}, \frac{1}{9}\)

Question 16.
\(\frac{4}{6}+\frac{3}{6}\) = …………. .
(a) \(\frac {7}{12}\)
(b) \(\frac {7}{8}\)
(c) \(1\frac {1}{6}\)
(d) \(1\frac {1}{12}\)
Answer:
(c) \(1\frac {1}{6}\)

Question 17.
\(\frac{4}{9}+\frac{5}{9}-\frac{2}{9}\) = ……………. .
(a) \(\frac {7}{9}\)
(b) \(\frac {7}{18}\)
(c) \(\frac {11}{9}\)
(d) \(\frac {5}{9}\)
Answer:
(a) \(\frac {7}{9}\)

Question 18.
\(\frac{2}{3}+\frac{1}{6}\) = ………………
(a) \(\frac {3}{9}\)
(b) \(\frac {5}{6}\)
(c) \(\frac {7}{6}\)
(d) \(\frac {5}{9}\)
Answer:
(b) \(\frac {5}{6}\)

Question 19.
4 – \(\frac {1}{3}\) = …………….
(a) \(4\frac {1}{3}\)
(b) \(3\frac {1}{3}\)
(c) \(4\frac {2}{3}\)
(d) \(3\frac {2}{3}\)
Answer:
(d) \(3\frac {2}{3}\)

Question 20.
Divide \(\frac {1}{6}\) by 2
(a) \(\frac {1}{3}\)
(b) \(\frac {1}{12}\)
(c) \(\frac {1}{18}\)
(d) 12
Answer:
(b) \(\frac {1}{12}\)

Question 21.
Which fraction is represented by point P on the adjoining number line?

(a) \(\frac {4}{5}\)
(b) \(\frac {5}{6}\)
(c) \(\frac {3}{4}\)
(d) \(\frac {3}{5}\)
Answer:
(a) \(\frac {4}{5}\)

Question 22.
Which fraction is represented by point P on the adjoining number line?

(a) \(\frac {1}{2}\)
(b) \(\frac {3}{5}\)
(c) \(\frac {4}{5}\)
(d) \(\frac {2}{5}\)
Answer:
(d) \(\frac {2}{5}\)

Question 23.
Which of the following fractions are in ascending order?
(a) \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)
(b) \(\frac{5}{10}, \frac{5}{11}, \frac{5}{12}\)
(c) \(\frac{1}{10}, \frac{1}{100}, \frac{1}{1000}\)
(d) \(\frac{3}{10}, \frac{4}{10}, \frac{7}{10}\)
Answer:
(d) \(\frac{3}{10}, \frac{4}{10}, \frac{7}{10}\)

Question 24.
Which of the following fractions are in descending order?
(a) \(\frac{1}{3}, \frac{1}{4}, \frac{1}{5}\)
(b) \(\frac{4}{11}, \frac{4}{12}, \frac{4}{13}\)
(c) \(\frac{1}{10}, \frac{1}{100}, \frac{1}{1000}\)
(d) \(\frac{7}{10}, \frac{9}{10}, \frac{11}{10}\)
Answer:
(a) \(\frac{1}{3}, \frac{1}{4}, \frac{1}{5}\)

Question 25.
Which of the following fraction is shown in the shaded portion of the figure?

(a) \(\frac {1}{3}\)
(b) \(\frac {2}{4}\)
(c) \(\frac {3}{4}\)
(d) \(\frac {2}{5}\)
Answer:
(b) \(\frac {2}{4}\)

Fill in the blanks:

Question (i)
The fraction shown in the shaded portion of the figure is ……………..,

Answer:
\(\frac {1}{4}\)

Question (ii)
The fraction of the shaded portion shown by the following figure is …………. .

Answer:
\(\frac {1}{8}\)

Question (iii)
The fraction of the shaded portion shown by the given figure is …………… .

Answer:
\(\frac {3}{7}\)

Question (iv)
The upper part of the fraction is called ……………. .
Answer:
numerator

Question (v)
The lower part of the fraction is called ……………. .
Answer:
denominator

Write True/False:

Question (i)
The fraction \(\frac {3}{5}\) is read as three fifth. (True/False)
Answer:
True

Question (ii)
The fraction whose numerator is less than the denominator is called the proper fraction. (True/False)
Answer:
True

Question (iii)
\(\frac {7}{8}\) is an improper fraction. (True/False)
Answer:
False

Question (iv)
Mixed fraction is a combination of a whole number and a proper fraction. (True/False)
Answer:
True

Question (v)
Fraction with the same denominator are called unlike fractions. (True/False)
Answer:
False

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.6 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.6

1. Multiply:

Question (i)
(i) \(\frac {1}{5}\) × 4
(ii) \(\frac {2}{7}\) × 3
(iii) \(\frac {5}{8}\) × 2
(iv) \(\frac {7}{12}\) × 4
(iv) 10 × \(\frac {4}{5}\)
Solution:

2. Divide:

Question (ii)
(i) \(\frac {1}{4}\) ÷ 5
(ii) \(\frac {3}{5}\) ÷ 3
(iii) \(\frac {5}{8}\) ÷ 3
(iv) \(\frac {6}{7}\) ÷ 2
(iv) \(\frac {12}{15}\) ÷ 6.
Solution:

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.5

1. Add the following:

Question (i)

Solution:

2. Subtract the following:

Question (i)

Solution:

3. Simplify the following:

Question (i)

Solution:

4. An iron pipe of length \(6 \frac{2}{3}\) metres long was cut into two pieces. One piece is \(4 \frac{3}{7}\) metre long. What is the length of other pieces?
Solution:
Total length of an iron pipe
= \(6 \frac{2}{3}\) m = \(\frac{20}{3}\) metre
Length of one piece
= \(4 \frac{3}{7}\) metre = \(\frac{31}{7}\) metre
∴ Length of other piece

5. Ashok bought \(\frac{7}{10}\)kg of mangoes and Taran \(\frac{11}{15}\)kg of apples. How much fruit did he buy in all?
Solution:

6. Avi did \(\frac{3}{5}\) of his homework on Saturday and \(\frac{1}{10}\) of the same homework on Sunday. How much of the homework did he do over the weekend?
Solution:
Homework he did weekend
\(\frac{3}{5}+\frac{1}{10}=\frac{3 \times 2}{5 \times 2}+\frac{1}{10}=\frac{6}{10}+\frac{1}{10}\)
∴ Home work done in weekend
\(\frac{6+1}{10}=\frac{7}{10}\)

7. Charan spent \(\frac {1}{4}\) of his pocket money on a movie and \(\frac {3}{8}\) on a new pen and \(\frac {1}{8}\) on a pencil. What fraction of his pocket money did he spend?
Solution:
Total money he spent
= \(\frac{1}{4}+\frac{3}{8}+\frac{1}{8}=\frac{1}{4} \times \frac{2}{2}+\frac{3}{8}+\frac{1}{8}\)
= \(\frac{2}{8}+\frac{3}{8}+\frac{1}{8}=\frac{2+3+1}{8}\)
= \(\frac{6}{8}=\frac{3}{4}\)
So, pocket money spent = \(\frac {3}{4}\)

8. Simar lives at a distance of 4 km from the school. Prabhjot lives at a distance of \(\frac {2}{3}\) km less than Simar’s distance from the school. How far does Prabhjot live from the school?
Solution:
Distance of Simar from school = 4 km Distance of Prabhjot from school

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.4

1. Find the different set of like fractions:

Solution:

2. Write any three like fractions of:

Question (i)
(i) \(\frac {2}{5}\)
(ii) \(\frac {1}{4}\)
(iii) \(\frac {11}{6}\)
Solution:

3. Encircle unit fractions:

Solution:
\(\frac{1}{8}, \frac{1}{9}, \frac{1}{7}\)

4. Fill in the boxes with >, < or =

Question (i)

Solution:

5. Compare using >, < or =

Question (i)

Solution:

6. Compare using >, < or =

Question (i)

Solution:

7. Arrange the following fractions in ascending order:

Question (i)

Solution:
We know that in fractions having the same denominator the greater the numerator, the greater the value of the fractional numbers. Therefore the given fractions in:
(i) Ascending order is : \(\frac{3}{10}, \frac{5}{10}, \frac{7}{10}\)
(ii) Ascending order is : \(\frac{1}{7}, \frac{4}{7}, \frac{6}{7}\)
(iii) Ascending order is : \(\frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}\)
We know that in fractions having the same numerator, the fractions with smaller denominator is greater:
(iv) Ascending order is : \(\frac{5}{9}, \frac{5}{7}, \frac{5}{3}\)
(v) Ascending order is : \(\frac{3}{13}, \frac{3}{11}, \frac{3}{7}\)
(vi) First find L.C.M. of denominators 4, 6, 12. Now, we convert the given fractions into fractions with denominator 12, we have:

(vii) First find L.C.M. of denominators 7, 35, 14, 28. Now, we convert the given fraction into fractions with denominators 140, we have

(viii) First find HCF of 3, 9, 12, 15. Now we convert the given fractions into fractions with denominator 180, we have:

8. Arrange the following fractions in descending order:

Question (i)
\(\frac{5}{9}, \frac{7}{9}, \frac{1}{9}\)
Solution:
If two or more fractions having the same denominator then fraction with greater numerator is greater fraction:
(i) Descending order is : \(\frac{7}{9}, \frac{5}{9}, \frac{1}{9}\)

Question (ii)
\(\frac{3}{11}, \frac{5}{11}, \frac{2}{11}, \frac{7}{11}\)
Solution:
Descending order is : \(\frac{7}{11}, \frac{5}{11}, \frac{3}{11}, \frac{2}{11}\)
If two or more fractions having the same numerator then the fraction with a small denominator is greater.

Question (iii)
\(\frac{2}{7}, \frac{2}{13}, \frac{2}{9}\)
Solution:
Descending order is : \(\frac{2}{7}, \frac{2}{9}, \frac{2}{13}\)

Question (iv)
\(\frac{1}{5}, \frac{1}{3}, \frac{1}{8}, \frac{1}{2}\)
Solution:
Descending order is : \(\frac{1}{2}, \frac{1}{3}, \frac{1}{5}, \frac{1}{8}\)

Question (v)
\(\frac{1}{6}, \frac{5}{12}, \frac{5}{18}, \frac{2}{3}\)
Solution:
First find L.C.M. of denominators 6, 12, 18, 3.
Now, we convert the given fractions into a fraction with denominator 36, we have:

Question (vi)
\(\frac{3}{4}, \frac{9}{20}, \frac{11}{15}, \frac{17}{30}\)
Solution:
First find L.C.M. of denominator 4, 20,15, 30. Now, we convert the given fractions into a fraction with denominator 60, we have:

9. Kasvi covered \(\frac {1}{3}\) of her journey by car, \(\frac {1}{5}\) by rickshaw and \(\frac {2}{15}\) on foot. Find by which means, she covered the major part of her journey.
Solution:
Journey covered by car = \(\frac {1}{3}\)
Journey covered by Rickshaw = \(\frac {1}{5}\)
Journey covered on foot = \(\frac {2}{15}\)

We observe that \(\frac {5}{15}\) i.e. \(\frac {1}{3}\) is the greatest.
Hence the major part of journey was covered by car.

10. Father distributed his property among his three sons. The eldest one got \(\frac {3}{10}\), the middle got \(\frac {1}{6}\) and the youngest got \(\frac {1}{5}\) part of the property. State how the property was distributed in ascending order.
Solution:
Property eldest son got = \(\frac {3}{10}\) part
Property middle son got = \(\frac {1}{6}\) part
and Property youngest son got = \(\frac {1}{5}\) part

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.3

1. Write the fraction for the shaded part and check whether these fractions are equivalent or not?

Question (i)

Solution:

2. Find four equivalent fractions of the followings:

Question (i)
(i) \(\frac {1}{4}\)
(ii) \(\frac {3}{5}\)
(iii) \(\frac {7}{9}\)
(iv) \(\frac {5}{11}\)
(v) \(\frac {2}{3}\)
Solution:

3. Write the lowest equivalent fraction (simplest form) of :

Question (i)
(i) \(\frac {10}{25}\)
(ii) \(\frac {27}{54}\)
(iii) \(\frac {48}{72}\)
(iv) \(\frac {150}{60}\)
(v) \(\frac {162}{90}\)
Solution:

4. Are the following fractions equivalent or not?

Question (i)
\(\frac{5}{12}, \frac{25}{60}\)
Solution:
We have

By cross product,
5 × 60 = 300 and 12 × 25 = 300
Since two cross products are same
So, the given fractions are equivalent.

Question (ii)
\(\frac{6}{7}, \frac{36}{42}\)
Solution:
We have

By cross product,
6 × 42 = 252 and 7 × 36 = 252
Since two cross products are same
So, the given fractions are equivalent.

Question (iii)
\(\frac{7}{9}, \frac{56}{72}\)
Solution:
We have

By cross product,
7 × 72 = 504 and 9 × 56 = 504
Since two cross products are same
So, the given fractions are equivalent.

5. Replace [ ] 1 in each of the following by the correct number.

Question (i)
\(\frac{2}{7}\) = 12 / [ ]
Solution:
Observe the numerators we have 12 ÷ 2 = 6
So, we multiply both numerator and denominator of \(\frac {2}{7}\) by 6
We get \(\frac{2}{7}=\frac{2 \times 6}{7 \times 6}=\frac{12}{42}\)
Hence, the correct number in [ ] 1 is 42

Question (ii)
\(\frac{5}{8}\) = 35 / [ ]
Solution:
Observe the numerators we have 35 ÷ 5 = 7
So, we multiply both numerator and denominator of \(\frac {5}{8}\) by 7
We get \(\frac{5}{8}=\frac{5 \times 7}{8 \times 7}=\frac{35}{56}\)
Hence, the correct number in [ ] is 56.

Question (iii)
\(\frac{24}{36}\) = 6 / [ ]
Solution:
Observe the numerators we have 24 ÷ 6 = 4
So, we divide both numerator and denominator of \(\frac {24}{36}\) by 4
We get \(\frac{24}{36}=\frac{24 \div 4}{36 \div 4}=\frac{6}{9}\)
Hence, the correct number in [ ] is 9

Question (iv)
\(\frac{30}{48}\) = 8 / [ ]
Solution:
Observe the denominators we have 48 ÷ 8 = 6
So, we divide both numerator and denominator of \(\frac {30}{48}\) by 6
We get \(\frac{30}{48}=\frac{30 \div 6}{48 \div 6}=\frac{5}{8}\)
Hence, the correct number in ⊇ is 5

Question (v)
\(\frac{7}{4}\) = 42 / [ ]
Solution:
Observe the numerators we have 42 ÷ 7 = 6
So, we multiply both numerator and denominator of \(\frac {7}{4}\) by 6
We get \(\frac{7}{4}=\frac{7 \times 6}{7 \times 6}=\frac{42}{24}\)
Hence, the correct number in [ ] is 24

6. Find the equivalent fraction of \(\frac {3}{5}\), having

Question (i)
numerator 18
Solution:
(i) Equivalent fraction of \(\frac {3}{5}\), having numerator 18 is
\(\frac{3}{5}\) = 18 / [ ]
Observe the numerators, we have 18 ÷ 3=6
So, we multiply both numerator and denominator of \(\frac {3}{5}\) by 6
∴ \(\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}\)
Thus, required equivalent fraction of \(\frac{3}{5}=\frac{18}{30}\)

Question (ii)
denominator 20
Solution:
Equivalent fraction of \(\frac {3}{5}\), having denominator 20 is \(\frac{3}{5}\) = [ ] / 20
Observe the denominators, we have 20 ÷ 5 = 4
So, we multiply both numerator and denominator of \(\frac {3}{5}\) by 4
Thus, required equivalent fraction of \(\frac{3}{5}=\frac{12}{20}\)
∴ \(\frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}\)
Thus, required equivalent fraction of
\(\frac{3}{5}=\frac{12}{20}\)

Question (iii)
numerator 24.
Solution:
Equivalent fraction of \(\frac {3}{5}\) , having numerator 24 is
\(\frac{3}{5}\) = 24 / [ ]
Observe the numerators, we have 24 ÷ 3 = 8
So, we multiply both numerator and denominator of \(\frac {3}{5}\) by 8
∴ \(\frac{3}{5}=\frac{3 \times 8}{5 \times 8}=\frac{24}{40}\)
Thus, required equivalent fraction of
\(\frac{3}{5}=\frac{24}{40}\)

7. Find the equivalent fraction of \(\frac {24}{40}\), having

Question (i)
(i) numerator 6
(ii) numerator 48
(iii) denominator 20
Solution:
(i) Equivalent fraction of \(\frac {24}{40}\), numerator 6 is
\(\frac{24}{40}\) = 6 / [ ]
Observe the numerators, we have 24 ÷ 6 = 4
So, we divide both numerator and denominator of \(\frac {24}{40}\) by 4
∴ \(\frac{24}{40}=\frac{24 \div 4}{40 \div 4}=\frac{6}{10}\)
Thus, required equivalent fraction of
\(\frac{24}{40}=\frac{6}{10}\)

Question (ii)
numerator 48
Solution:
Equivalent fraction of \(\frac {24}{40}\), having numerator 48 is
\(\frac{24}{40}\) = 48 / [ ]
Observe the numerators, we have 48 ÷ 24 = 2
So, we multiply both numerator and denominator of \(\frac {24}{40}\) by 2
∴ \(\frac{24}{40}=\frac{24 \times 2}{40 \times 2}=\frac{48}{80}\)
Thus, required equivalent fraction of
\(\frac{24}{40}=\frac{48}{80}\)

Question (iii)
denominator 20
Solution:
Equivalent fraction of \(\frac {24}{40}\), having denominator 20 is
\(\frac{24}{40}\) = [ ] / 20
Observe the denominators, we have 40 ÷ 20 = 2
So, we divide both numerator and denominator of \(\frac {24}{40}\) by 2
\(\frac{24}{40}=\frac{24 \div 2}{40 \div 2}=\frac{12}{20}\)
∴ Thus, required equivalent fraction of
\(\frac{24}{40}=\frac{12}{20}\)

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.2

1. Classify the following as proper and improper fractions:

Question (i)

Solution:

2. Express each of the following as mixed fractions, Also represent with diagrams:

Question (i)
\(\frac {27}{5}\)
Solution:

∴ Mixed fraction
= Quotient \(\frac {Remainder}{Divisor}\) = \(5\frac {2}{5}\)

Question (ii)
\(\frac {13}{4}\)
Solution:

∴ Mixed fraction
= Quotient \(\frac {Remainder}{Divisor}\) = \(3\frac {1}{4}\)

Question (iii)
\(\frac {43}{8}\)
Solution:

∴ Mixed fraction
= Quotient \(\frac {Remainder}{Divisor}\) = \(5\frac {3}{8}\)

Question (iv)
\(\frac {51}{7}\)
Solution:

∴ Mixed fraction
= Quotient \(\frac {Remainder}{Divisor}\) = \(7\frac {2}{7}\)

Question (v)
\(\frac {20}{3}\)
Solution:

∴ Mixed fraction
= Quotient \(\frac {Remainder}{Divisor}\) = \(6\frac {2}{3}\)

3. Express each of the following mixed fractions as improper fractions:

Question (i)
(i) \(\)2 \frac{1}{3}\(\)
(ii) \(\)5 \frac{2}{7}\(\)
(iii) \(\)4 \frac{3}{5}\(\)
(iv) \(\)3 \frac{3}{4}\(\)
(v) \(\)9 \frac{5}{8}\(\)
Solution:

4. Express the shaded portion as Improper Fraction and Mixed fraction:

Question (i)

Solution:

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 5 Fractions Ex 5.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 6 Maths Chapter 5 Fractions Ex 5.1

1. Write the fraction representing the shaded portion:

Solution:

2. Colour the part according to the given fraction:

Solution:

3. Write the fraction for each of the following:

Question (i)
(i) Three-Fourth
(ii) Seven-Tenth
(iii) A Quarter
(iv) Five-Eighth
(v) Three-Twelvth.
Solution:
(i) \(\frac {3}{4}\)
(ii) \(\frac {7}{10}\)
(iii) \(\frac {1}{4}\)
(iv) \(\frac {5}{8}\)
(v) \(\frac {3}{12}\)

4. Write the fraction for the followings:

Question (i)
numerator = 5
denominator = 9
Answer:
\(\frac {5}{9}\)

Question (ii)
numerator = 2
denominator = 11
Answer:
\(\frac {2}{11}\)

Question (iii)
numerator = 6
denominator = 7
Answer:
\(\frac {6}{7}\)

5. Write the numerator and the denominator for the followings:

Question (i)
\(\frac {2}{3}\)
Solution:
Given fraction is \(\frac {2}{3}\) = \(\frac {Numerator}{Denominator}\)
∴ Numerator = 2
and Denominator = 3

Question (ii)
\(\frac {1}{4}\)
Solution:
Given fraction is \(\frac {1}{4}\) = \(\frac {Numerator}{Denominator}\)
∴ Numerator = 1
and Denominator = 4

Question (iii)
\(\frac {5}{11}\)
Solution:
Given fraction is \(\frac {5}{11}\) = \(\frac {Numerator}{Denominator}\)
∴ Numerator = 5
and Denominator = 11

Question (iv)
\(\frac {9}{13}\)
Solution:
Given fraction is \(\frac {9}{13}\) = \(\frac {Numerator}{Denominator}\)
∴ Numerator = 9
and Denominator = 13

Question (iv)
\(\frac {17}{16}\) = \(\frac {Numerator}{Denominator}\)
∴ Numerator = 17 and
Denominator = 16

6. Express:

Question (i)
1 day as a fraction of 1 week.
Solution:
We know 1 week = 7 days
∴ Required fraction= \(\frac {1}{7}\)

Question (ii)
40 seconds as a fraction of 1 minute.
Solution:
We know 1 minute = 60 seconds
∴ Required fraction = \(\frac {40}{60}\) or \(\frac {2}{3}\)
(Dividing both terms by 20)

Question (iii)
15 hours as fraction of 1 day.
Solution:
We know 1 day = 24 hours
∴ Required fraction = \(\frac {15}{24}\) or \(\frac {5}{8}\)
(Dividing both terms by 3)

Question (iv)
2 months as a fraction of 1 year.
Solution:
We know 1 year = 12 months
∴ Required fraction = \(\frac {2}{12}\) or \(\frac {1}{6}\)
(Dividing both terms by 2)

Question (v)
45 cm as a fraction of 1 metre.
Solution:
We know 1 metre = 100 cm
∴ Required fraction = \(\frac {45}{100}\) or \(\frac {9}{20}\)
(Dividing both terms by 5)

7. Write the numbers from 1 to 25.

Question (i)
What fraction of them are even numbers?
Solution:
Numbers from 1 to 25 are:
1,2, 3, 4,5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 i.e. 25 in number.
Even numbers out of these numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18; 20, 22, 24 i.e. 12 in number
∴ Required fraction = \(\frac {12}{25}\)

Question (ii)
What fraction of them are prime numbers?
Solution:
Prime number out of these numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23 i.e. 9 in number
∴ Required fraction = \(\frac {9}{25}\)

Question (iii)
What fraction of them are multiples of 3?
Solution:
Multiples of 3 out of these numbers are:
3, 6, 9, 12, 15, 18, 21, 24 i.e. 8 in number
∴ Required fraction = \(\frac {8}{25}\)

8. In class 6th, there are 24 boys and 18 girls. What fraction of total students represent boys and girls?
Solution:
Boys = 24
Girls = 18
Total students = 24 + 18 = 42
Fraction which represents boys
= \(\frac {24}{42}\) or \(\frac {4}{7}\)
(Dividing both terms by 6)
Fraction which represents girls
= \(\frac {18}{42}\) or \(\frac {3}{7}\)
(Dividing both terms by 6)

9. A bag contains 6 red balls and 7 blue balls. What fraction of balls represent red and blue colour?
Solution:
Red balls = 6
Blue balls = 7
Total number of red and blue balls = 6 + 7 = 13
Fraction which represents red balls = \(\frac {6}{13}\)
Fraction which represents blue balls = \(\frac {7}{13}\)

10. Sidharth has a cake. He cuts it into 10 equal parts. He gave 2 parts to Naman, 3 parts to Nidhi, 1 parts to Seema and the remaining four parts he kept for himself. Find:

Question (i)
What fraction of cake, he gave to Naman?
Solution:
Total parts = 10
Fraction of cake, he gave to Naman = \(\frac {2}{10}\) or \(\frac {1}{5}\)

Question (ii)
What fraction of cake, he gave to Nidhi?
Solution:
Fraction of cake, he gave to Nidhi = \(\frac {3}{10}\)

Question (iii)
What fraction of cake, he kept for himself?
Solution:
Fraction of cake, he kept for himself = \(\frac {4}{10}\) or \(\frac {2}{5}\)

Question (iv)
Who has more cake than others?
Solution:
Sidharth has more cake than others

11. In a box, there are 12 apples, 7 oranges and 5 guavas. What fraction of fruits in box represents each?
Solution:
Apples = 12, Oranges = 7
and Gauvas = 5
Total fruits = 12 + 7 + 5 = 24.
Fraction which represents apples
= \(\frac {12}{24}\) or \(\frac {1}{2}\)
Fraction which represents oranges
= \(\frac {7}{24}\)
Fraction which represents Gauvas
= \(\frac {5}{24}\)

12. Dishmeet has 20 pens. He gives one-fourth to Balkirat. How many pens Dishmeet and Balkirat have?
Solution:
Total pens = 20
Pens Balkirat has = One-fourth of 20
= \(\frac {22}{7}\) × 20 = 5
Pens Dishmeet has = 20 – 5 = 15

13. Represent the following fraction on the number line?

Question (i)
\(\frac {2}{5}\)
Solution:
In order to represent \(\frac {2}{5}\) on number line, we divide the gap between 0 and 1 into 5 equal parts, which are, (as shown)

Question 2.
\(\frac {5}{7}\)
Solution:
In order to represent \(\frac {5}{7}\) on number line, we divide the gap between 0 and 1 into 7 equal parts, which are, (as shown)

Question 3.
\(\frac {3}{10}\), \(\frac {5}{10}\), \(\frac {1}{10}\)
Solution:
In order to represent \(\frac {3}{10}\), \(\frac {5}{10}\), \(\frac {1}{10}\) on number line, we divide the gap between 0 and 1 into 10 equal parts, which are (as shown)

Question 4.
\(\frac {3}{8}\), \(\frac {5}{8}\), \(\frac {7}{8}\)
Solution:
In order to represents \(\frac {3}{8}\), \(\frac {5}{8}\), \(\frac {7}{8}\) on number line, we divide the gap between 0 and 1 into 8 equal parts, which are (as shown)

14. Find:

(i) \(\frac {3}{5}\) of 20 books
(ii) \(\frac {5}{8}\) of 32 pens
(iii) \(\frac {1}{6}\) of 36 copies 6
(iv) \(\frac {4}{7}\) of 21 apples
(v) \(\frac {3}{4}\) of 28 pencils.
Solution:

15. Balkirat had a box of 36 erasers. He gave \(\frac {1}{2}\) of them to Rani, \(\frac {2}{9}\) of them to Yuvraj and keeps the rest.

Question (i)
(i) How many erasers does Rani get?
(ii) How many erasers does Yuvraj get?
(iii) How many erasers does Harnik keep?
Solution:
Total erasers = 36

(iii) Erasers Harnik gets = 36 – (18 + 8)
= 36 – 26
= 10

16. State True/False

Question (i)

Solution:
(i) False
(ii) True
(iii) True
(iv) True

Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 4 Integers MCQ Questions with Answers.

PSEB 6th Class Maths Chapter 4 Integers MCQ Questions

Multiple Choice Questions

Question 1.
How many integers are between -3 to 3?
(a) 5
(b) 6
(c) 4
(d) 3.
Answer:
(a) 5

Question 2.
Which of the following integer is greater than -3?
(a) -5
(b) -4
(c) 0
(d) -10.
Answer:
(c) 0

Question 3.
Which of the following integers are in ascending order?
(a) -5, -9, -7, -8
(b) -9, -8, -7, -5
(c) -5, -7, -8, -8, -9
(d) -8, -5, -9, -7.
Answer:
(b) -9, -8, -7, -5

Question 4.
Which of the following integers are in descending order?
(a) 3, 0, -2, -5
(b) -5, -2, 0, 3
(c) -5, 3,-2, 0
(d) -2, 0, -5, 3.
Answer:
(a) 3, 0, -2, -5

Question 5.
The given number line represents:

(a) 5 + 1
(b) 1 + 5
(c) 1 + 1 + 1 + 1 + 1
(d) 5 + 5 + 5 + 5 + 5.
Answer:
(c) 1 + 1 + 1 + 1 + 1

Question 6.
3 less than -2 =
(a) -5
(b) -6
(c) 5
(d) 6.
Answer:
(a) -5

Question 7.
(-2) + 8 =
(a) -6
(b) -10
(c) 10
(d) 6.
Answer:
(d) 6.

Question 8.
Which of the following statements is true about the given number line:

(a) Value of A is greater than value of B.
(b) Value of A is greater than value of C.
(c) Value of B is less than value of C.
(d) Value of C is less than value of B.
Answer:
(c) Value of B is less than value of C.

Question 9.
(-7) + (-12) + 11 =
(a) -19
(b) 30
(c) -23
(d) -8.
Answer:
(d) -8.

Question 10.
15 – (-12) + (-27) =
(a) 0
(b) -54
(c) -24
(d) 54.
Answers :
(a) 0

Question 11.
What is the number of integers between -4 and -1?
(a) 3
(b) 4
(c) 5
(d) 6.
Answer:
(b) 4

Question 12.
What is the number of integers between -8 and -2?
(a) 3
(b) 4
(c) 5
(d) 6.
Answer:
(c) 5

Question 13.
Which is the largest integers among -7, -6, -5, -4 and -3?
(a) -6
(b) -5
(c) -4
(d) -3.
Answer:
(d) -3.

Question 14.
Which is the smallest integer among -3, -2, 0 and 1?
(a) -3
(b) -2
(c) 0
(d) 1.
Answer:
(a) -3

Question 15.
The value of (-7) + (-9) + 4 + 16 is:
(a) 36
(b) 22
(c) 4
(d) 27.
Answer:
(c) 4

Fill in the blanks:

Question (i)
The sum of (-9) + (+4) + (-6) + (+3) is …………. .
Answer:
– 8

Question (ii)
The successor of -5 is ……………. .
Answer:
– 4

Question (iii)
-19 + …………. = 0.
Answer:
19

Question (iv)
100 + …………. = 0.
Answer:
– 100

Question (v)
50 + (-50) = ……………. .
Answer:
0

Write True/False:

Question (i)
-8 is to the right of -10 on number line. (True/False)
Answer:
True

Question (ii)
-100 is to the right of -50 on number line. (True/False)
Answer:
False

Question (iii)
Smallest negative integer is -1. (True/False)
Answer:
False

Question (iv)
-26 is larger than -25. (True/False)
Answer:
False

Question (v)
The sum of two integers is always an integer. (True/False)
Answer:
True