EXERCISE 1.3
1. Using the distributive property, evaluate the following:
(1) 251 x 38 + 251 x 2
(ii) (-464) * 56 + (-464) x 4
(iii) (-62) × 82 + (-62) × (-2)
(iv) 1526 x 337 + (-526) X 337
(v) 725 x 78 - 725 x 8
(vi) 2584 * (-886) - 584 * ( 886)
(vii) (-45) 20 + (-45) × 12 + (-45) * (-2) (viii) 265 x 99 + 265
(ix) 299 x 3567 - (-3567)
(x) 385 * (-25) + 385 (-24) - 385
2. Without actual multinlication find the following
Answers
Answer:
The simplified expressions are:
(i) 10,040
(ii) -27,840
(iii) -4,960
(iv) 337,000
(v) 50,750
(vi) -2,806,848
(vii) -1,350
(viii) 26,500
(ix) 1,070,100
(x) -19,250
Step-by-step explanation:
The distributive law of multiplication and division is another name for the distributive property.
This property explains how to approach form a(b+c) issue.
It is one of the mathematical properties that is used the most.
We can use the distributive property to simplify each expression as follows:
(i) 251 × 38 + 251 × 2 = 251 × (38 + 2) = 251 × 40 = 10,040
(ii) (-464) × 56 + (-464) × 4 = (-464) × (56 + 4) = (-464) × 60 = -27,840
(iii) (-62) × 82 + (-62) × (-2) = (-62) × (82 + (-2)) = (-62) × 80 = -4,960
(iv) 1526 × 337 + (-526) × 337 = (1526 - 526) × 337 = 1,000 × 337 = 337,000
(v) 725 × 78 - 725 × 8 = 725 × (78 - 8) = 725 × 70 = 50,750
(vi) 2584 × (-886) - 584 × 886 = (-2584) × 886 - 584 × 886 = (-2584 - 584) × 886 = (-3168) × 886 = -2,806,848
(vii) (-45) × 20 + (-45) × 12 + (-45) × (-2) = (-45) × (20 + 12 + (-2)) = (-45) × 30 = -1,350
(viii) 265 × 99 + 265 = 265 × (99 + 1) = 265 × 100 = 26,500
(ix) 299 × 3567 - (-3567) = 299 × 3567 + 3567 = (299 +1)× 3567 = 300 × 3567 = 1,070,100
(x) 385 × (-25) + 385 × (-24) - 385 = 385 × (-25 - 24) -385 = 385 × (-49) - 385 = 385 × (-49 -1) = 385 × (-50) = -19,250
Therefore, the simplified expressions are:
(i) 10,040
(ii) -27,840
(iii) -4,960
(iv) 337,000
(v) 50,750
(vi) -2,806,848
(vii) -1,350
(viii) 26,500
(ix) 1,070,100
(x) -19,250
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