CBSE Class 7 Mathematics Integers Assignment Set 07

Question. Write True (T) or False (F) against the following statements:
(i) The smallest integer is zero
(ii) Zero is not an integer
(iii) The opposite of zero is zero
(iv) The absolute value of an integer is always greater than the integer.
(v) Every negative integer is less than every natural number.
Answer:
(i) False
(ii) False
(iii) True
(iv) False
(v) True

Question. Fill the gap so that the statement becomes True:
(i) Natural numbers are called \(\_\_\_\_\_\) integer.
(ii) \(-10\) can be read as \(\_\_\_\_\_\) or \(\_\_\_\_\_\) ten.
(iii) The smallest integer is \(\_\_\_\_\_\).
(iv) The successor of \(-260\) is \(\_\_\_\_\_\).
(v) The predecessor of \(-251\) is \(\_\_\_\_\_\).
Answer:
(i) positive integers
(ii) minus or negative
(iii) does not exist
(iv) \(-259\)
(v) \(-252\)

Question. (i) An elevator descends into a mine shaft at the rate of \(5\) metres per minutes. What will be its position after \(1\text{ hr}\).
(ii) If it begins to descend from \(15\text{ m}\) above the ground, what will be its position after \(45\) minutes.
Answer:
(i) \(300\text{ m}\) below the ground level.
(ii) \(210\text{ m}\) below the ground level.

Question. Name the property used in integers. If \(a\) and \(b\) are any two integers then:
(i) \((a+b)\) is also an integer
(ii) \((a-b)\) is also an integer
(iii) \((a \times b)\) is also an integer
Answer:
(i) Closure Property for addition
(ii) Closure Property for subtraction
(iii) Closure Property for multiplication

Question. Name the following property used in the set of integers. If \(a\) and \(b\) are any two integers then:
(i) \(a + b = b + a\)
(ii) \(a \times b = b \times a\)
Answer:
(i) Commutative Property for addition
(ii) Commutative Property for multiplication

Question. For any three integers \(a\), \(b\) and \(c\), name the property:
(i) \(a + (b + c) = (a + b) + c\)
(ii) \(a \times (b \times c) = (a \times b) \times c\)
Answer:
(i) Associative Property for addition
(ii) Associative Property for multiplication

Question. Name the following property in integers. For any three rational numbers \(a\), \(b\) and \(c\):
\(a \times (b + c) = (a \times b) + (a \times c)\)
Answer: Distributive Property

Question. Name the following property if \(a\) is any integer and \(0, 1\) are two integers then:
(i) \(a + 0 = 0 + a = a\)
(ii) \(a \times 1 = 1 \times a = a\)
Answer:
(i) Additive identity
(ii) Multiplicative identity

Question. Add \(+4\) and \(-10\) on the number line.
Answer: To add \(+4\) and \(-10\) on a number line:
1. Start at \(0\) and move \(4\) units to the right to reach \(+4\).
2. From \(+4\), move \(10\) units to the left.
3. You will land on \(-6\).
Therefore, \(+4 + (-10) = -6\).

Question. Add the following integers:
(i) \(137\) and \(-254\)
(ii) \(-163\) and \(-125\)
Answer:
(i) \(-117\)
(ii) \(-288\)

Question. Choose two integers in such a way that their sum is:
(i) \(-5\)
(ii) \(0\)
(iii) \(+5\)
Answer:
(i) \(-7 + 2 = -5\)
(ii) \(7 - 7 = 0\)
(iii) \(12 - 7 = +5\)
(Other answers are possible)

Question. Find the additive inverse of:
(i) \(-57\)
(ii) \(63\)
Answer:
(i) \(+57\)
(ii) \(-63\)

Question. Find the sum of \(-51, 63, -50, 97\).
Answer: \(+59\)

Question. Simplify \(1056 + (-790) + (-30) + 59\).
Answer: \(+295\)

Question. A car travelled north of Bombay by \(60\text{ km}\) and then to the south of it by \(90\text{ km}\). How far from Bombay was the car finally?
Answer: \(30\text{ km}\) South.