Page 57 - classs 6 a_Neat

EXAMPLE 20: (i) 4 × (-7) = -28 (ii) 7 × (-4) = - 28
RULE To subtract one integer from another, we take the additive inverse of the integer to be (iii) (-9) × 4 = -36 (iv) (-3) × 7 = - 21
subtracted and add it to the other integer.
Thus, if a and bare two integers then a -b =a+ (-b). RULE 2:To find the product of two integers with the same sign, we find the product of their values regard
less of their signs and give a plus sign to the product.
SOLVED EXAMPLES
EXAMPLE 21: (i) 4 × 13 = 52 (ii) (-4) × (-13) = 52
EXAMPLE 17: Subtract (iii) (-7) × (-9) = 63 (iv) (-18) × (-10) = 180
(i) 7 from 2 (ii) -8from 5 (iii) 4from -9 (iv)-7 from -5
EXAMPLE 22: Find each of the following products:
SOLUTION: (i) 2 - 7 = 2 + (negative of 7) = 2 + (-7) = -5. (i) 36 × (-17) (ii) (-81) × 15
(ii) 5 - (- 8) = 5 + (negative of -8) = 5 + 8 = 13. (iii) (-23) × (-18) (iv) (-60) × (-21)
. (iii) - 9 - 4 = - 9 + (negative of 4) = (-9) + (-4) = -13.
(iv) - 5 -(-7) = (-5) + (negative of -7) = (-5) + 7 = 2. SOLUTION: (i) 36 × (-17) = -(36 × 17) = -612.
(ii) (-81) × 15 = -(81 × 15) = -1215.
EXAMPLE 18: Subtract (iii) (-23) × (-18) = 23 × 18 = 414.
(i) - 2459 from 5128 (ii) -1040 from - 687 (iv) (-60) × (-21) = 60 × 21 = 1260.
(iii) 347 from - 58 (iv) -728 from 0
SOLUTION: We have: PROPERTIES OF MULTIPLICATION ON INTEGERS
(i) 5128 - (-2459) = 5128 + 2459 = 7587 [negative of -2459 is 2459)
(ii) -687 - (-1040) = - 687 + 1040 = 353 [negative of -1040 is 1040] (ii) COMMUTATIVE LAW FOR MULTIPLICATION For any two integers a and b, we have a × b =b × a.
(iii) -58 - (347) = (-58) + (-347) = - 405 [negative of 347 is -347]
(iv) 0 - (-728) = 0 + 728 = 728 [negative of -728 is 728] EXAMPLE 24: (i) 3 × (-7) = - 21, and (-7) × 3 = - 21.

EXAMPLE 19: The sum of two integers is -27. if one of them is 260,flnd the other. :. 3 × (-7) = (-7) × 3.

SOLUTION: Let the other number be x . Then, (ii) (-5) × (-8) = 40, and (-8) × (-5) = 40.

260 + × = (-27) :. (-5) × (-8) = (-8) × (-5).
= × = (-27) - 260 = (-27) + (-260) = - 287.
Hence, the other number is -287. (iii) ASSOCIATIVE LAW FOR MULTIPLICATION if a, b, c are any three integers then
(a × b) × c = a × (b × c).
PROPERTIES OF SUBTRACTION ON INTEGERS
EXAMPLE 25: Consider three integers (-7), (-5) and (- 8).
(i) CLOSURE PROPERTY if a and b are integers then (a - b) is also an integer. We have: 1(-7) × (-5)) × (-8) = 35 × (-8) = - 280.
(ii) If a is any integer then (a - 0) = a. And, (-7) × 1(-5) × (-8)) = (-7) × 40 = - 280.
(iii) If a, b, care integers and a > b then (a - c) > (b - c). :. [(-7) × (-5)) × (-8) = (-7) × [(-5) × (-8)).

EXAMPLE 26: Consider three integers 3, (-5) and (-7).
MULTIPLICATION OF INTEGERS We have: [3 × (-5)) x (-7) = (-15) × (-7) = 105.
And, 3 × [(-5) × (-7)) = 3 × 35 = 105.
RULE 1 To find the product of two integers with unlike signs, we find the product of their values regardless of 13 × (-5) × (-7) = 3 × [(-5) × (-7)].
their signs and give a minus sign to the product.
(iv) DISTRIBUTIVE LAW if a, b, c be any three integers then a × (b + c) = a × b + a × c.
(i) 4 × (-7) = - 28 (ii) 7 × (-4) = - 28
(iii) (-9) × 4 = -36 (iv) (-3) × 7 = - 21 EXAMPLE 27: Consider the integers 4, (-5) and (-6).
We have: 4 × 1(-5) + (-6) = 4 × (-11) = - 44.
RULE 2 To find the product of two integers with the same sign, we find the product of their values regard And, 4 × (-5) + 4 x (-6) = (-20) + (-24) = - 44.
less of their signs and give a plus sign to the product. 4 × 1(-5) + (-6)) = 4 × (-5) + 4 × (-6).