Verify that a x (b + c) = (a x b) + (a x c) for a=4/5 b=-6/7 c=-2/3
Answers
Step-by-step explanation:
Distributive property a×(b+c)=(a×b)+(a×c)
(1) a= -1/2 b=2/3 c=-5/6
To find:
We have to verify the distributive property for the given a,b,c values
Solution:
The given distributive property is a×(b+c) = (a×b)+(a×c)
Let us substitute the given values in above equation
(\frac{-1}{2})(2−1) × (\frac{2}{3}+ \frac{-5}{6} )(32+6−5) = (\frac{-1}{2}(2−1 × \frac{2}{3} )32) + (\frac{-1}{2}(2−1 × \frac{-5}{6} )6−5)
(\frac{-1}{2})(2−1) × (\frac{(2)(2) + (1)(-5)}{6} )(6(2)(2)+(1)(−5)) = (\frac{-2}{6} )(6−2) + (\frac{5}{12} )(125)
(\frac{-1}{2})(2−1) × (\frac{4-5}{6} )(64−5) = \frac{(2)(-2)+(1)(5)}{12}12(2)(−2)+(1)(5)
(\frac{-1}{2})(2−1) ×(\frac{-1}{6} )(6−1) = \frac{-4+5}{12}12−4+5
\frac{1}{12}121 = \frac{1}{12}121
L.H.S = R.H.S
Hence verified.
(2) a=4/7 b=1/5 ×\frac{3}{4} )43)
(\frac{4}{7})(74) ×(\frac{(4)(1)+(5)(3)}{20} )(20(4)(1)+(5)(3)) = (\frac{4}{35} )(354) + (\frac{12}{28} )(2812)
(\frac{4}{7})(74) × (\frac{19}{20} )(2019) = (\frac{(4)(4)+(5)(12)}{140})(140(4)(4)+(5)(12))
(\frac{76}{140} )(14076) = (\frac{76}{140} )(14076)
L.H.S = R.H.S
Hence verified.
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