What is the simplified value of 1/7 + 3/14 + 2/3 + 2/5 + 5/6 ?

1 Answer
Shwetank Mauria
Apr 29, 2016

1/7+3/14+2/3+2/5+5/6=2 27/105

Explanation:

To add 1/7+3/14+2/3+2/5+5/6, firs convert all denominators to Lease Common Denominator (LCD), which is nothing but Least common multiple of 7, 14, 3, 5 and 6.

LCD of 7, 14, 3, 5 and 6 is

14xx6xx5=420 (as 7 is a factor of 14 and 3 is a factor of 5).

Hence, converting each denominator of 1/7+3/14+2/3+2/5+5/6 to 420,

1/7+3/14+2/3+2/5+5/6

= (1xx60)/(7xx60)+(3xx30)/(14xx30)+(2xx140)/(3xx140)+(2xx84)/(5xx84)+(5xx70)/(6xx70)

= 60/420+90/420+280/420+168/420+350/420

= (60+90+280+168+350)/420

= 948/420=(237cancel948)/(105cancel420)=237/105=2 27/105

(We have divided 948 and 420 by 4 here to simplify.)

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