Decimals and Fractions Practice Test 4

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Question : 26 of 40

Marks: +1, -0

The simplified value of

{1/3 . 1/3 . 1/3+1/4 . 1/4 . 1/4+1/5 . 1/5 . 1/5-3 1/3 . 1/4 . 1/5}/{1/3 . 1/3+1/4 . 1/4 +1/5 . 1/5-(1/3 . 1/4+ 1/4 . 1/5+1/5 . 1/3) }

is:

$51 /60$
$47 /60$
$13 /60$
$49/ 60$

Solution:

we know that

{a^3+b^3+c^3-3abc}/{a^2+b^2+c^2-(ab+bc+ca)}

={(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}/{a^2+b^2+c^2-(ab+bc+ca)}

=a+b+c

Here

a=1/3,b=1/4,c=1/5

∴{1/3 . 1/3 . 1/3+1/4 . 1/4 . 1/4+1/5 . 1/5 . 1/5-3 1/3 . 1/4 . 1/5}/{1/3 . 1/3+1/4 . 1/4 +1/5 . 1/5-(1/3 . 1/4+ 1/4 . 1/5+1/5 . 1/3) }

=1/3+1/4+1/5=47/60

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