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PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 9 Rational Numbers Ex 9.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

1. Write two equivalent rational numbers of the following :

Question (i).
\frac {4}{5}
Solution:
\frac {4}{5} = \frac {4}{5} × \frac {2}{2}
= \frac {8}{10}
\frac {4}{5} = \frac {4}{5} × \frac {3}{3}
= \frac {12}{15}
∴ Equivalent rational numbers of \frac {4}{5} are \frac {8}{10} and \frac {12}{15}

Question (ii).
\frac {-5}{9}
Solution:
\frac {-5}{9} = \frac {-5}{9} × \frac {2}{2}
= \frac {-10}{18}
\frac {-5}{9} = \frac {-5}{9} × \frac {3}{3}
= \frac {-15}{27}
∴ Equivalent rational numbers of \frac {-5}{9} are \frac {-10}{18} and \frac {-15}{27}

Question (iii).
\frac {3}{-11}
Solution:
\frac {3}{-11} = \frac {3}{-11} × \frac {2}{2}
= \frac {6}{-22}
\frac {3}{-11} = \frac {3}{-11} × \frac {3}{3}
= \frac {9}{-33}
∴ Equivalent rational numbers of \frac {3}{-11} are \frac {6}{-22} and \frac {9}{-33}

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

2. Find the standard form of the following rational numbers :

Question (i).
\frac {35}{49}
Solution:
\frac {35}{49}
∵ H.C.F. of 35 and 49 is 7
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 1
So dividing both the numerator and denominator by 7 we get.
\frac {35}{49} = \frac{35 \div 7}{49 \div 7} = \frac {5}{7}
∴ Standard form of \frac {35}{49} is \frac {5}{7}

Question (ii).
\frac {-42}{56}
Solution:
\frac {-42}{56}
∵ H.C.F. of -42 and 56 is 14
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 2
So dividing both the numerator and denominator by 14 we get.
\frac {-42}{56} = \frac{-42 \div 14}{56 \div 14} = \frac{-3}{4}
∴ Standard form of \frac {-42}{56} is \frac{-3}{4}

Question (iii).
\frac {19}{-57}
Solution:
\frac {19}{-57}
∵ H.C.F. of 59 and 57 is 19
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 3
So dividing both the numerator and denominator by 19 we get.
\frac {19}{-57} = \frac{-19 \div 19}{-57 \div 19} = \frac{1}{-3}
∴ Standard form of \frac {19}{-57} is \frac{1}{-3}

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question (iv).
\frac{-12}{-36}
Solution:
\frac{-12}{-36}
∵ H.C.F. of 12 and 36 is 12.
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 4
So dividing both the numerator and denominator by 12 we get.
\frac{-12}{-36} = \frac{-12 \div 12}{-36 \div 12} = \frac{1}{3}
Standard form of \frac{-12}{-36} is \frac{1}{3}

3. Which of the following pairs represent same rational number ?

Question (i).
\frac{-15}{25} and \frac{18}{-30}
Solution:
\frac{-15}{25} = \frac{-15 \div 5}{25 \div 5}
= \frac{-3}{5}
\frac{18}{-30} = \frac{18 \div-6}{-30 \div-6}
= \frac{-3}{5}
\frac{-15}{25} and \frac{18}{-30} represents the same number.

Question (ii).
\frac{2}{3} and \frac{-4}{6}
Solution:
\frac{2}{3} = \frac{2}{3} × \frac{1}{1}
= \frac{2}{3}
\frac{-4}{6} = \frac{-4 \div 2}{6 \div 2}
= \frac{-2}{3}
\frac{-2}{3} and \frac{-4}{6} doesnot represents the same rational numbers.

Question (iii).
\frac{-3}{4} and \frac{-12}{16}
Solution:
\frac{-3}{4} = \frac{-3}{4} × \frac{4}{4}
= \frac{-12}{16}
\frac{-12}{16} = \frac{-12}{16}
\frac{-3}{4} and \frac{-12}{16} represents the same rational number.

Question (iv).
\frac{-3}{-7} and \frac{3}{7}
Solution:
\frac{-3}{4} = \frac{-3 \div-1}{-7 \div-1}
= \frac{-3}{4}
\frac{-3}{-7} and \frac{3}{7} represents the same rational number.

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

4. Which is greater in each of the following ?

Question (i).
\frac{3}{7}, \frac{4}{5}
Solution:
Given rational nrnnbere are \frac{3}{7} and \frac{4}{5}
L.C.M. of 7 and 5 is 35
\frac{3}{7} = \frac{3 \times 5}{7 \times 5}
= \frac{15}{35}
and \frac{4}{5} = \frac{4 \times 7}{5 \times 7}
= \frac{28}{35}
∵ Numerator of second is greater than first i.e. 28 > 15
So \frac{4}{5} > \frac{3}{7}

Question (ii).
\frac{-4}{12}, \frac{-8}{12}
Solution:
Given rational numbere are \frac{-4}{12} and \frac{-8}{12}
∵ Numerator of first is greater than second i.e. -4 > – 8
\frac{-4}{12} > \frac{-8}{12}

Question (iii).
\frac{-3}{9}, \frac{4}{-18}
Solution:
Given rational numbers are \frac{-3}{9}, \frac{4}{-18}
\frac{-3}{9} = \frac{-3 \times 2}{9 \times 2}
= \frac{-6}{18}
\frac{4}{-18} = \frac{4 \times-1}{-18 \times-1}
\frac{-4}{18}
Since -4 > – 6.
\frac{4}{-18} > \frac{-3}{9}

Question (iv).
-2\frac{3}{5}, -3\frac{5}{8}
Solution:
-2\frac{3}{5} = \frac{-13}{5} \times \frac{8}{8}
= \frac{-104}{40}
-3\frac{5}{8} = \frac{-29}{8} \times \frac{5}{5}
= \frac{-135}{40}
∵ -104 > -135
\frac{-13}{5} > \frac{-29}{8}
Thus, -2\frac{3}{5} > -3\frac{5}{8}

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

5. Write the following rational numbers in ascending order.

Question (i).
\frac{-5}{7}, \frac{-3}{7}, \frac{-1}{7}
Solution:
\frac{-5}{7}, \frac{-3}{7}, \frac{-1}{7}
Here -5 < -3 < -1
i.e. \frac{-5}{7}, \frac{-3}{7}, \frac{-1}{7}
Therefore, the ascending order is:
\frac{-5}{7}, \frac{-3}{7}, \frac{-1}{7}

Question (ii).
\frac{-1}{5}, \frac{-2}{15}, \frac{-4}{5}
Solution:
\frac{-1}{5}, \frac{-2}{15}, \frac{-4}{5}
L.C.M of 5, 15, 5 is 15
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 5

Question (iii).
\frac{-3}{8}, \frac{-2}{4}, \frac{-3}{2}
Solution:
\frac{-3}{8}, \frac{-2}{4}, \frac{-3}{2}
L.C.M of 8, 4, 2 is 8
\frac{-3}{8}=\frac{-3}{8} \times \frac{1}{1}=\frac{-3}{8}
\frac{-2}{4}=\frac{-2 \times 2}{4 \times 2}=\frac{-4}{8}
\frac{-3}{2}=\frac{-3 \times 4}{2 \times 4}=\frac{-12}{8}
∴ -12 < -4 < -3
or \frac {-12}{8} < \frac {-4}{8} < \frac {-3}{8}
Hence assending order is \frac{-3}{2}, \frac{-2}{4}, \frac{-3}{8}

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

6. Write five rational numbers between following rational numbers.

Question (i).
-2 and -1
Solution:
Given rational numbers are -2 and -1
Let us write -2 and -1 as rational numbers with 5 + 1 = 6 as denominator.
We have -2 = -2 × \frac {6}{6}
= \frac {-6}{6}
\frac {-12}{6} < \frac {-11}{6} < \frac {-10}{6} < \frac {-9}{6} < \frac {-8}{6} < \frac {-7}{6} < \frac {-6}{6}
Hence five rational numbers between -2 and -1 are :
\frac {-11}{6},\frac {-10}{6},\frac {-9}{6},\frac {-8}{6},\frac {-7}{6}
i.e. \frac {-11}{6},\frac {-5}{3},\frac {-3}{2},\frac {-4}{3},\frac {-7}{6}

Question (ii).
\frac {-4}{5} and \frac {-2}{3}
Solution:
Given rational numbers are \frac {-4}{5} and \frac {-2}{3}
First we find equivalent rational numbers having same denominator
Thus \frac {-4}{5} = \frac{-4 \times 9}{5 \times 9}
= \frac {-36}{45}
and \frac {-2}{3} = \frac{-2 \times 15}{3 \times 15}
= \frac {-30}{45}
Now, we choose any five integers -35, -34, -33, -32, -31 between the numerators -36 and -30
Then the five rational numbers between \frac {-36}{45} and \frac {-30}{45} are:
\frac{-35}{45}, \frac{-34}{45}, \frac{-33}{45}, \frac{-32}{45}, \frac{-31}{45}
Hence, five rational numbers between \frac {-4}{5} and \frac {-2}{3} are
\frac{-35}{45}, \frac{-34}{45}, \frac{-33}{45}, \frac{-32}{45}, \frac{-31}{45}
i.e. \frac{-7}{9}, \frac{-34}{45}, \frac{-11}{15}, \frac{-32}{45}, \frac{-31}{45}

Question (iii).
\frac {1}{3} and \frac {5}{7}
Solution:
Given rational numbers are \frac {1}{3} and \frac {5}{7}
First we find equivalent rational numbers having same denominator
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 6
<\frac{4}{7}<\frac{13}{21}<\frac{2}{3}<\frac{5}{7}
Hence, five rational numbers between \frac {1}{3} and \frac {5}{7} are
\frac{8}{21}, \frac{3}{7}, \frac{10}{21}, \frac{4}{7}, \frac{13}{21}.

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

7. Write four more rational numbers in each of the following.

Question (i).
\frac{-1}{5}, \frac{-2}{10}, \frac{-3}{15}, \frac{-4}{20}, \ldots
Solution:
The given rational numbers are :
\frac{-1}{5}, \frac{-2}{10}, \frac{-3}{15}, \frac{-4}{20}, \ldots
\frac {-1}{5} is the rational number in its lowest form
Now, we can write
\frac{-2}{10}=\frac{-1}{-5} \times \frac{2}{2},
\frac{-3}{15}=\frac{-1}{5} \times \frac{3}{3} and \frac{-1}{5}=\frac{-1}{5} \times \frac{4}{4}
Thus, we observe a pattern in these numbers.
The next four rational numbers would be
\frac{-1}{5} \times \frac{5}{5}=\frac{-5}{25},
\frac{-1}{5} \times \frac{6}{6}=\frac{-6}{30},
\frac{-1}{5} \times \frac{7}{7}=\frac{-7}{35}
\frac{-1}{5} \times \frac{8}{8}=\frac{-8}{40}
Hence required four more rational numbers are :
\frac{-5}{25}, \frac{-6}{30}, \frac{-7}{35}, \frac{-8}{40}

Question (ii).
\frac{-1}{7}, \frac{2}{-14}, \frac{3}{-21}, \frac{4}{-28}, \ldots
Solution:
The given rational numbers are
\frac{-1}{7}, \frac{2}{-14}, \frac{3}{-21}, \frac{4}{-28}, \ldots
\frac {-1}{7} is the rational number in its lowest form
Now, we can write
\frac{2}{-14}=\frac{-1}{7} \times \frac{-2}{-2}=\frac{2}{-14}, \frac{3}{-21}
= \frac{-1}{7} \times \frac{-3}{-3} and \frac{4}{-28}=\frac{-1}{7} \times \frac{-4}{-4}
Thus, we observe a pattern in these numbers.
The next four rational numbers would be :
-\frac{1}{7} \times \frac{-5}{-5}=\frac{5}{-35}, \frac{-1}{7} \times \frac{-6}{-6}=\frac{6}{-42},
\frac{-1}{7} \times \frac{-7}{-7}=\frac{7}{-49}, \frac{-1}{7} \times \frac{-8}{-8}=\frac{8}{-56}
Hence required four more rational numbers are :
\frac{5}{-35}, \frac{6}{-42}, \frac{7}{-49}, \frac{8}{-56}

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

8. Draw a number line and represent the following rational number on it.

Question (i).
\frac {2}{4}
Solution:
Draw a line and choose a point O on it to represent the rational number zero (0). We choose a point A to the right of 0 to represent 1.
Divide the segment OA into four equal parts. Second part from O to the right represents the rational number \frac {2}{4} as shown in the figure.
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 7

Question (ii).
\frac {-3}{4}
Solution:
Draw a line and choose a point O on it to represent the rational number zero (0). We choose a point A to the right of 0 to represent -1.
Divide the segment OA into four equal parts. Third part from O to the left represents the rational number \frac {-3}{4} as shown in the figure.
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 8

Question (iii).
\frac {5}{8}
Solution:
Draw a line and choose a point O on it to represent the rational number zero (0).
We choose a point A to the right of 0 to represent 1.
Divide the segment OA into eight equal parts. Fifth part from O to the right represents the rational number as shown in the figure.
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 9

Question (iv).
\frac {-6}{4}
Solution:
Draw a line and choose a point O on it to represent the rational number zero (0).
We choose a point A to the left of O to represent -2.
Divide the segment OA into eight equal parts. Sixth part from O to the left represents the rational number \frac {-6}{4} as shown in the figure.
PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1 10

9. Multiple Choice Questions :

Question (i).
\frac{3}{4}=\frac{?}{12} then ? =
(a) 3
(b) 6
(c) 9
(d) 12.
Answer:
(c) 9

PSEB 7th Class Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question (ii).
\frac{-4}{7}=\frac{?}{14} then ? =
(a) -4
(b) -8
(c) 4
(d) 8
Answer:
(b) -8

Question (iii).
The standard form of rational number \frac {-21}{28} is
(a) \frac {-3}{4}
(b) \frac {3}{4}
(c) \frac {3}{7}
(d) \frac {-3}{7}
Answer:
(a) \frac {-3}{4}

Question (iv).
Which of the following rational number is not equal to \frac {7}{-4} ?
(a) \frac {14}{-8}
(b) \frac {21}{-12}
(c) \frac {28}{-16}
(d) \frac {7}{-8}
Answer:
(d) \frac {7}{-8}

Question (v).
Which of the following is correct ?
(a) 0 > \frac {-4}{9}
(b) 0 < \frac {-4}{9}
(c) 0 = \frac {4}{9}
(d) None
Answer:
(a) 0 > \frac {-4}{9}

Question (vi).
Which of the following is correct ?
(a) \frac{-4}{5}<\frac{-3}{10}
(b) \frac{-4}{5}>\frac{3}{-10}
(c) \frac{-4}{5}=\frac{3}{-10}
(d) None
Answer:
(a) \frac{-4}{5}<\frac{-3}{10}

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