3. DISTRIBUTIVELAWS
3. The distributive law can also be extended to division as long as
there aren’t any denominators that end up being equal to zero. For
all real numbers a, b, and c, where a ≠0 the following equations
are valid:
a(b + c)= ab + ac
1. For all real numbers a, b, and c, the following equation holds. The
operation of multiplication is distributive with respect to addition:
2. The above statement logically implies that multiplication is
distributive with respect to subtraction, as well:
a(b – c)= ab-ac
(ab-ac)/a = ab/a - ac/a = b- c
(ab+ac)/a = ab/a + ac/a = b+ c
4. example:
a = 5, b = 2, and c = 3
1.Step workmanship:
Way 2: a (b + c) = ab + ac = ...
1. Multiply by b (ab = 10)
2. Multiply by c (ac = 15)
3. Add multiplication result ab = 10 and ac = 15 and produce 25.
1. Add first in brackets. A + b = 2 + 3 = 5
2. Multiply the number of results a + b = 5 with a=5 and the result 25
Way 1: a (b + c) = ...
Way 2: a (b-c) = ab-ac = ...
1. Multiply by b (ab = 10)
2. Multiply by c (ac = 15)
3. Subtract product ab = 10 with bc = 15 yield -5.
2. Step workmanship
Way 1: a (b-c) = ...
1.First reduce the brackets, b-c = 2-3 = -1
2.Multiply the result of deductions by 5 and yield -5.
5. B. (ab-ac) / a = ab / a - ac / a = b- c
1. Subtract the first from inside brackets. Ab-ac = -5
2. Divide the deduction with a. -5 / a = -5 / 5 = -1
3. Steps of workmanship:
example:
a = 5, b = 2, and c = 3
A. (ab + ac) / a = ab / a + ac / a = b + c
1. Count first in brackets. Ab + ac = 25
2. Divide the number by a. 25 / a = 25/5 = 5
