1. Determine each of the following products: (i) 12 × 7 (ii) (-15) × 8 (iii) (-25) × (-9) (iv) 125 × (-8) Solution: (i) Given 12 × 7 Here we have to find the products of given numbers 12 ×7 = 84 Because the product of two integers of like signs is equal to the product of their absolute values. (ii) Given (-15) × 8 Here we have to find the products of given numbers (-15) ×8 = -120 Because the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values. (iii) Given (-25) × (-9) Here we have to find the products of given numbers (-25) × (-9) = + (25 ×9) = +225 Because the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values. (iv) Given 125 × (-8) Here we have to find the products of given numbers 125 × (-8) = -1000 Because the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values. 2. Find the value of: (i) 1487 × 327 + (-487) × 327 (ii) 28945 × 99 – (-28945) Solution: (i) Given 1487 × 327 + (-487) × 327 By using the rule of multiplication of integers, we have 1487 × 327 + (-487) × 327 = 486249 – 159249 Since the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values. =327000 (ii) Given 28945 × 99 – (-28945) By using the rule of multiplication of integers, we have 28945 × 99 – (-28945) = 2865555 + 28945 Since the product of two integers of like signs is equal to the product of their absolute values. =2894500 3. Divide: (i) 102 by 17 (ii) -85 by 5 (iii) -161 by -23 (iv) 76 by -19 (v) 17654 by -17654 (vi) (-729) by (-27) (vii) 21590 by -10 (viii) 0 by -135 Solution: (i) Given 102 by 17 We can write given question as 102 ÷ 17 102 ÷ 17 = |102/17| = |102|/|17| [by applying the mod] = 102/17 = 6 (ii) Given -85 by 5 We can write given question as -85 ÷ 5 -85 ÷ 5 = |-85/5| = |-85|/|5| [by applying the mod] = -85/5 = -17 (iii) Given -161 by -23 We can write given question as -161 ÷ -23 -161 ÷ -23 = |-161/-23| = |-161|/|-23| [by applying the mod] = 161/23 = 7 (iv) Given 76 by -19 We can write given question as 76 ÷ -19 76 ÷ -19 = |76/-19| = |76|/|-19| [by applying the mod] = 76/-19 = -4 (v) Given 17654 by -17654 We can write given question as 17654 ÷ -17654 17654 ÷ -17654 = |17654/-17654| = |17654|/|-17654| [by applying the mod] = 17654/-17654 = -1 (vi) Given (-729) by (-27) We can write given question as (-729) ÷ (-27) (-729) ÷ (-27) = |-729/-27| = |-729|/|-27| [by applying the mod] = 729/27 = 27 (vii) Given 21590 by -10 We can write given question as 21590 ÷ -10 21590 ÷ -10 = |21590/-10| = |21590|/|-10| [by applying the mod] = 21590/-10 = -2159 (viii) Given 0 by -135 We can write given question as 0 ÷ -135 0 ÷ -135 = 0 [because anything divided by 0 we get the result as 0] 4. Find the value of 1. 36 ÷ 6 + 3 Solution: Given 36 ÷ 6 + 3 According to BODMAS rule we have to operate division first then we have to do addition Therefore 36 ÷ 6 + 3 = 6 + 3 = 9 2. 24 + 15 ÷ 3 Solution: Given 24 + 15 ÷ 3 According to BODMAS rule we have to operate division first then we have to do addition Therefore 24 + 15 ÷ 3 = 24 + 5 = 29 3. 120 – 20 ÷ 4 Solution: Given 120 – 20 ÷ 4 According to BODMAS rule we have to operate division first then we have to do subtraction Therefore 120 – 20 ÷ 4 = 120 – 5 = 115 4. 32 – (3 × 5) + 4 Solution: Given 32 – (3 × 5) + 4 According to BODMAS rule we have to operate in brackets first then move to addition and subtraction. Therefore 32 – (3 × 5) + 4 = 32 – 15 + 4 = 32 – 11 = 21 5. 3 – (5 – 6 ÷ 3) Solution: Given 3 – (5 – 6 ÷ 3) According to BODMAS rule we have to operate in brackets first then we have move to subtraction. Therefore 3 – (5 – 6 ÷ 3) = 3 – (5 – 2) = 3 –3 = 0 6. 21 – 12 ÷ 3 × 2 Solution: Given 21 – 12 ÷ 3 × 2 According to BODMAS rule we have to perform division first then move to multiplication and subtraction. Therefore, 21 – 12 ÷ 3 × 2 = 21 – 4 × 2 = 21 – 8 = 13 7. 16 + 8 ÷ 4 – 2 × 3 Solution: Given 16 + 8 ÷ 4 – 2 × 3 According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction. Therefore, 16 + 8 ÷ 4 – 2 × 3 = 16 + 2 – 2 × 3 = 16 + 2 – 6 = 18 -6 = 12 8. 28 – 5 × 6 + 2 Solution: Given 28 – 5 × 6 + 2 According to BODMAS rule we have to perform multiplication first followed by addition and subtraction. Therefore, 28 – 5 × 6 + 2 = 28 – 30 +2 = 28 – 28 = 0 9. (-20) × (-1) + (-28) ÷ 7 Solution: Given (-20) × (-1) + (-28) ÷ 7 According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction. Therefore, (-20) × (-1) + (-28) ÷ 7 = (-20) × (-1) – 4 = 20 – 4 = 16 10. (-2) + (-8) ÷ (-4) Solution: Given (-2) + (-8) ÷ (-4) According to BODMAS rule we have to perform division first followed by addition and subtraction. Therefore, (-2) + (-8) ÷ (-4) = (-2) + 2 =0 11. (-15) + 4 ÷ (5 – 3) Solution: Given (-15) + 4 ÷ (5 – 3) According to BODMAS rule we have to perform division first followed by addition and subtraction. Therefore, (-15) + 4 ÷ (5 – 3) = (-15) + 4 ÷ 2 = -15 + 2 = -13 12. (-40) × (-1) + (-28) ÷ 7 Solution: Given (-40) × (-1) + (-28) ÷ 7 According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction. (-40) × (-1) + (-28) ÷ 7 = (-40) × (-1) – 4 = 40 – 4 = 36 13. (-3) + (-8) ÷ (-4) -2 × (-2) Solution: Given (-3) + (-8) ÷ (-4) -2 × (-2) According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction. (-3) + (-8) ÷ (-4) -2 × (-2) = -3 + 2 -2 × (-2) = -3 + 2 + 4 = 6 – 3 =3 14. (-3) × (-4) ÷ (-2) + (-1) Solution: Given (-3) × (-4) ÷ (-2) + (-1) According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction. (-3) × (-4) ÷ (-2) + (-1) = -3 × 2 -1 = – 6 – 1 = -7