If a is an integer other than 1 and -1, match the following:
Column I Column II
(a) a ÷ (-1) (i) a
(b) 1 ÷ (a) (ii) 1
(c) (-a) ÷ (-a) (iii) Not an integer
(d) a ÷ (+1) (iv) -a
Solution:
Here we will use the rules of integers closed under addition and subtraction.
We have four individual options in column I that can be matched with column II option, let us solve the pairs individually for different values of a to get the correct match. While solving the pairs we will use the rule of integers, (+) × (-) = - and (-) × (-) = +.
Option (a) in column I matches with option (iv) in column II. On solving the expression we have a ÷ (-1) = -a
Option (b) in column I matches with option (iii) in column II. On solving the expression we have 1 ÷ (a) = Not an integer.
Option (c) in column I matches with option (ii) in column II. On solving the expression we have (-a) ÷ (-a) = 1
Option (d) in column I matches with option (i) in column II. On solving the expression we have
a ÷ (+1) = a
✦ Try This: If the value of a = -7, find the value of a + a - a + 3a × a
The above given problem can be solved by using integer rules and by substituting the value of a = -7 in a + a - a + 3a × a.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1
NCERT Exemplar Class 7 Maths Chapter 1 Solved Ex 11
If a is an integer other than 1 and -1, match the following: Column I Column II (a) a ÷ (-1) (i) a (b) 1 ÷ (a) (ii) 1 (c) (-a) ÷ (-a) (iii) Not an integer (d) a ÷ (+1) (iv) -a
Summary:
On solving the given pairs individually using the addition and subtraction rules of integers provided the given condition that if a is an integer other than 1 and -1, the pairs that exactly matches are (a) ↔ (iv) (b) ↔ (iii) (c) ↔ (ii) (d) ↔ (i)
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