Exercise: 1-A
Q1: Evaluate
i. 427 × 8 + 2 × 427
Step 1: Identify the common factor
427 × 8 + 2 × 427
= (427 × 8) + (427 × 2) [Rewriting terms]
Step 2: Apply distributive property:
= 427 × (8 + 2) [a × b + a × c = a × (b + c)]
= 427 × 10
Step 3: Multiply:
= 4270
ii. 394 × 12 + 394 × (-2)
Step 1: Identify the common factor
= (394 × 12) + (394 × -2)
Step 2: Apply distributive property:
= 394 × (12 + (-2))
= 394 × 10
Step 3: Multiply:
= 3940
iii. 558 × 27 + 3 × 558
Step 1: Rewriting:
= (558 × 27) + (558 × 3)
Step 2: Apply distributive property:
= 558 × (27 + 3)
= 558 × 30
Step 3: Multiply:
= 16740
Q2: Evaluate
i. 673 × 9 + 673
= 673 × 9 + 673 × 1
= 673 × (9 + 1)
= 673 × 10
= 6730
ii. 1925 × 101 – 1925
= 1925 × 101 – 1925 × 1
= 1925 × (101 – 1)
= 1925 × 100
= 192500
Q3: Verify
i. 37 × {8 + (-3)} = 37 × 8 + 37 × (-3)
LHS = 37 × (8 – 3) = 37 × 5 = 185
RHS = 296 + (-111) = 185
Verified
ii. (-82) × {(-4) + 19} = (-82) × (-4) + (-82) × 19
LHS = (-82) × 15 = -1230
RHS = 328 + (-1558) = -1230
Verified
iii. {7 – (-7)} × 7 = 7 × 7 – (-7) × 7
LHS = (7 + 7) × 7 = 14 × 7 = 98
RHS = 49 – (-49) = 49 + 49 = 98
Verified
iv. {(-15) – 8} × (-6) = (-15) × (-6) – 8 × (-6)
LHS = (-23) × (-6) = 138
RHS = 90 + 48 = 138
Verified
Q4: Evaluate
i. 15 × 8 = 120
ii. 15 × (-8) = -120
iii. (-15) × 8 = -120
iv. (-15) × (-8) = 120
Q5: Evaluate
i. 4 × 6 × 8 = 192
ii. 4 × 6 × (-8) = -192
iii. 4 × (-6) × 8 = -192
iv. (-4) × 6 × 8 = -192
v. 4 × (-6) × (-8) = 192
vi. (-4) × (-6) × 8 = 192
vii. (-4) × 6 × (-8) = 192
viii. (-4) × (-6) × (-8) = -192
Q6: Evaluate
i. 2 × 4 × 6 × 8 = 384
ii. 2 × (-4) × 6 × 8 = -384
iii. (-2) × 4 × (-6) × 8 = 384
iv. (-2) × (-4) × 6 × (-8) = -384
v. (-2) × (-4) × (-6) × (-8) = 384
Q7: Determine the integer whose product with ‘-1” is:
i. -47 → 47
ii. 63 → -63
iii. -1 → 1
iv. 0 → 0
Q8: Eighteen integers are multiplied together. What will be the sign of their product, if :
i. 15 of them are negative and 3 are positive?
→ Odd negatives → Negative
ii. 12 of them are negative and 6 are positive?
→ Even negatives → Positive
iii. 9 of them are positive and the remaining are negative?
→ Odd negatives → Negative
iv. all are negative?
→ Even negatives → Positive
Q9: Find which is greater?
i. (8+10)×15 = 18×15 = 270
8 + 10×15 = 8 + 150 = 158
→ (8+10)×15 is greater
ii. 12×(6-8) = 12×(-2) = -24
12×6 – 8 = 72 – 8 = 64
→ 12×6 – 8 is greater
iii. {(-3)-4}×(-5) = (-7)×(-5) = 35
(-3) – 4×(-5) = -3 – (-20) = -3 + 20 = 17
→ {(-3)-4}×(-5) is greater
Q10: State true or false
i. Product of two different integers can be zero → True
ii. Product of 120 negative and 121 positive integers is negative → True
iii. a × (b + c) = a × b + c → False
iv. (b – c) × a = b – c × a → False
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