2. Multiplication and Division of Integers
Step-by-step solutions to Practice Sets 8 and 9. Maharashtra State Board (Balbharati), Grade Seven Mathematics.
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Practice Set 8
- (i) (−5) × (−7) = (5 × 7) = 35
negative × negative = positive - (ii) (−9) × 6 = −(9 × 6) = −54
negative × positive = negative - (iii) 9 × (−4) = −(9 × 4) = −36
positive × negative = negative - (iv) 8 × (−7) = −(8 × 7) = −56
positive × negative = negative - (v) (−124) × (−1) = (124 × 1) = 124
negative × negative = positive - (vi) (−12) × (−7) = (12 × 7) = 84
negative × negative = positive - (vii) (−63) × (−7) = (63 × 7) = 441
negative × negative = positive - (viii) (−7) × 15 = −(7 × 15) = −105
negative × positive = negative
Sign rule: multiply the numbers without their signs first. If the two signs are the same, the product is positive; if they are different, the product is negative.
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Practice Set 9
(i) (−96) ÷ 16 = −9616 = −6 × 161 × 16 = −6
(ii) 98 ÷ (−28) = 98−28 = −7 × 142 × 14 = −72
(iii) (−51) ÷ 68 = −5168 = −3 × 174 × 17 = −34
(iv) 38 ÷ (−57) = 38−57 = −2 × 193 × 19 = −23
(v) (−85) ÷ 20 = −8520 = −17 × 54 × 5 = −174
(vi) (−150) ÷ (−25) = −150−25 = 6 × 251 × 25 = 6
(vii) 100 ÷ 60 = 10060 = 5 × 203 × 20 = 53
(viii) 9 ÷ (−54) = 9−54 = −1 × 96 × 9 = −16
(ix) 78 ÷ 65 = 7865 = 6 × 135 × 13 = 65
(x) (−5) ÷ (−315) = −5−315 = 1 × 563 × 5 = 163
Cancel the common factor (the HCF of the two numbers) and fix the sign: same signs give a positive quotient, different signs give a negative quotient. The negative sign is written with the numerator, so the denominator stays positive.
(1) 24 ÷ 5 = 245 = 245
(2) (−24) ÷ (−5) = −24−5 = 245
(3) 48 ÷ 10 = 4810 = 245
Any division where the numerator and denominator are both multiplied by the same non-zero integer gives the same fraction, e.g. (−72) ÷ (−15) also equals 245.
(1) (−5) ÷ 7 = −57 = −57
(2) 5 ÷ (−7) = 5−7 = −57
(3) (−10) ÷ 14 = −1014 = −57
Other correct answers include 15 ÷ (−21) and (−20) ÷ 28. The two numbers must have different signs so that the quotient is negative.
Numbers on the fish: −13, −27, −24, +9, −15, +41, +12, +13, −18, −8, −28, −37.
Four multiplications (sample answer):
(−27) × 9 = −243
41 × (−8) = −328
12 × 13 = 156
(−18) × (−28) = 504
Four divisions with other pairs (sample answer):
(−24) ÷ 12 = −2412 = −2
9 ÷ (−15) = 9−15 = −35
(−28) ÷ (−8) = −28−8 = 72
13 ÷ (−37) = 13−37 = −1337
Any pairs of fish may be chosen, so answers will differ from student to student. Check each answer with the sign rules: same signs → positive, different signs → negative.