Question

Find the sum of 5/17, 2/3 and 15 /7.

explain how to?

Answer 1

Given :  5/17, 2/3 and 15/7​

To Find : Sum

Solution:

5/17, 2/3 and 15/7​

Sum

= 5/17   + 2/3  +  15/7

To add these we will have all term with same denominator

Denominator would be LCM of 17 , 3 , 7

as all are prime numbers Hence

LCM =  3x 7 x 17

5/17    = (5/17  ) ((3x 7 x 17 )/  (3x 7 x 17) )  = (5 x 3x 7 )/  (3x 7 x 17) )

= 105/357

2/3     = (2/3   ) ((3x 7 x 17 )/  (3x 7 x 17) )  = (2 x 7x 17 )/  (3x 7 x 17) )

= 238/357

15/7    = (15/7  ) ((3x 7 x 17 )/  (3x 7 x 17) )  = (15 x 3x 17 )/  (3x 7 x 17) )

= 765/357

105/358  + 238/357 + 765/357

= (105 + 238 + 765 )/357

= 1108/357

5/17   + 2/3  +  15/7  = 1108/357

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Answer 2

Question :-

• Find the sum of $\sf \dfrac{5}{17} \: + \: \dfrac{2}{3} \: + \: \dfrac{15}{7}$

Solution :-

To add all the Terms , first we have to make the Bases ( denominator ) same by taking the LCM of denominators.

$\longmapsto\boxed{ \bf{LCM \: = \: 357}}$

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First Fraction :-

$\quad \longmapsto \sf \dfrac{5 \: \times \: 3 \: \times \: 7}{17 \: \times \: 3 \: \times \: 7 } \: = \: \bf{ \dfrac{105}{357}}$

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Second Fraction :-

$\quad \longmapsto\sf \dfrac{2\: \times \: 17 \: \times \: 7}{3 \: \times \: 17 \: \times \: 7 } \: = \: \bf{ \dfrac{238}{357}}$

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Third Fraction:-

$\quad \longmapsto \sf \dfrac{15\: \times \: 17 \: \times \: 3}{7 \: \times \: 17 \: \times \: 3} \: = \: \bf{ \dfrac{765}{357}}$

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Now , Bases are same so we can add them.

${:} \longrightarrow\sf \dfrac{105\: + \: 238 \: + \: 756}{357} \:$

${:} \longrightarrow \bf \dfrac{1108}{357}$

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So , the Solution is the Fraction is 1108/357.

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More For Knowledge :-

Steps to Solve these types of questions :-

• Step 1 :- Obtain the rational number and see whether their denominator are positive or not if the denominator of one ( or both ) of the number is negative , rewrite it so that the denominator becomes positive.
• Step 2 :- Obtain the denominators of the rational number in step 1.
• Step 3 :- Find the LCM of the denominators obtained in step 2.
• Step 4 :- Express each one of the rational number in step 1 so that LCM obtained in step 3 becomes their common denominator.
• Step 5 :- Write a rational number whose numerator is equal to the sum of the numerator of rational numbers obtained in step 4 and denominator as the LCM obtained in step 3.
• Step 6 :- The rational number obtained in step 5 is required sum.

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