CBSE Class 7 Mathematics Integers Assignment Set 04

Question. Simplify using the Distributive Law
(i) \( 4 \times (-5 + (-6)) \)
(ii) \( 2 \times (3 + (-4)) \)
Answer:
(i) \( 4 \times (-5 + (-6)) = 4 \times (-5) + 4 \times (-6) = -20 + (-24) = -44 \)
(ii) \( 2 \times (3 + (-4)) = 2 \times 3 + 2 \times (-4) = 6 + (-8) = -2 \)

Question. Give the opposite of
(i) \( -(-5) \)
(ii) \( +(-5) \)
(iii) \( (-4) \)
Answer:
(i) \( -5 \)
(ii) \( +5 \)
(iii) \( +4 \)

Question. Simplify in two ways
(i) \( 4 \times (-4 - 5 + 6 - 7) \)
(ii) \( (-4) \times (1 - 2 + 3 - 4) \)
Answer:
(i) Method 1: \( 4 \times (-4 - 5 + 6 - 7) = 4 \times (-10) = -40 \)
Method 2: \( 4 \times (-4) - 4 \times 5 + 4 \times 6 - 4 \times 7 = -16 - 20 + 24 - 28 = -40 \)
(ii) Method 1: \( (-4) \times (1 - 2 + 3 - 4) = (-4) \times (-2) = 8 \)
Method 2: \( (-4) \times 1 - (-4) \times 2 + (-4) \times 3 - (-4) \times 4 = -4 + 8 - 12 + 16 = 8 \)

Question. Using convenient grouping simplify
(i) \( 18 \times (-25) \times 30 \)
(ii) \( (-51) \times (-10) \times 45 \)
Answer:
(i) \( (18 \times 30) \times (-25) = 540 \times (-25) = -13500 \)
(ii) \( [(-51) \times 45] \times (-10) = -2295 \times (-10) = 22950 \)

Question. Simplify in short way
(i) \( 30 \times (-23) + 30 \times (-7) \)
(ii) \( (-15) \times (-14) + (-15) \times (-16) \)
Answer:
(i) \( 30 \times [(-23) + (-7)] = 30 \times (-30) = -900 \)
(ii) \( (-15) \times [(-14) + (-16)] = (-15) \times (-30) = 450 \)

Question. Divide
(i) \( (-81) \) by \( (-9) \)
(ii) \( (-324) \) by \( 18 \)
Answer:
(i) \( (-81) \div (-9) = 9 \)
(ii) \( (-324) \div 18 = -18 \)

Question. Fill the blanks
(i) \( 77 \div \dots\dots = -7 \)
(ii) \( 84 \div \dots\dots = -12 \)
(iii) \( 121 \div \dots\dots = -11 \)
(iv) \( (-16) \div (-8) = \dots\dots \)
Answer:
(i) \( -11 \)
(ii) \( -7 \)
(iii) \( -11 \)
(iv) \( 2 \)

Question. By means of an example show "Is every integer divided by itself equal to 1"
Answer: Yes, for example, \( \frac{10}{10} = 1 \).

Question. Verify the following:
\( (-21) \times [(-4) + (-6)] = (-21) \times (-4) + (-21) \times (-6) \)
Answer:
LHS = \( (-21) \times [(-4) + (-6)] = (-21) \times (-10) = 210 \)
RHS = \( (-21) \times (-4) + (-21) \times (-6) = 84 + 126 = 210 \)
Since LHS = RHS, the relation is verified.

Question. \( x \) and \( y \) are two integers such that \( x \) is the predecessor of \( y \). Find the value of \( (x - y) \)
Answer: \( -1 \) (Since \( x \) is the predecessor of \( y \), we have \( x = y - 1 \). Therefore, \( x - y = -1 \).)

Question. Write True (T) or False (F)
(i) \( 0 \div 5 = 0 \)
(ii) \( 18 \div 0 = 0 \)
(iii) \( 0 \div 0 = 0 \)
(iv) \( -8 \div 8 = 1 \)
Answer:
(i) T
(ii) F
(iii) F
(iv) F

Question. To get admission in class VII, a test was given containing 10 questions. 5 marks are awarded for every correct ans. (-2) for every wrong ans. Zero for not attempting.
(i) Anil gets 4 correct and 5 incorrect ans. Find his score.
(ii) Arun gets 6 correct and 3 incorrect ans. Find his score.
(iii) Sita gets 3 correct and 6 incorrect ans. What is her score?
Answer:
(i) Anil's score = \( 4 \times 5 + 5 \times (-2) = 20 - 10 = 10 \) marks
(ii) Arun's score = \( 6 \times 5 + 3 \times (-2) = 30 - 6 = 24 \) marks
(iii) Sita's score = \( 3 \times 5 + 6 \times (-2) = 15 - 12 = 3 \) marks