Question

5/7 + 6/9 + 2/3 + 5/4 + 9/5
Find the sum.

Answer 1

Note that:

• Given expression:
  `(5)/(7) + (6)/(9) + (2)/(3) + (5)/(4) + (9)/(5)`

Finding the LCM of 7, 9, 3, 4 and 5:

Refer to table uploaded

• LCM = 1260

Multiplying the numerators and the denominators:

• 
  `(5(180))/(7(180)) + (6(140))/(9(140)) + (2(420))/(3(420)) + (5(315))/(4(315)) + (9(252))/(5(252))`
• ⇒
  `(900)/(1260) + (840)/(1260) + (840)/(1260) + (1575)/(1260) + (2268)/(1260)`
• ⇒
  `(900)/(1260) + (840)/(1260) + (840)/(1260) + (1575)/(1260) + (2268)/(1260)`
• ⇒
  `(6423)/(1260)`

Simplifying the fraction:

• ⇒
  `(6423)/(1260)` =
  `(2121)/(420)`

The sum of the fractions is
`(2121)/(420)`.

Answer 2

`\sf{5(41)/(420)`

Explanation:

• 
  `\sf{(5)/(7)\:+\:(6)/(9)\:+\:(2)/(3)\:+\:(5)/(4)\:+\:(9)/(5)`

adjust the fractions:

• 
  `\sf(300)/(420)+(560)/(420)+(525)/(420)+(756)/(420)`

least common multiple of 7, 9, 3, 4, 5 is 420

• 
  `\sf(300+560+525+756)/(420)`

join fractions together:

• 
  `\sf{(2141)/(420)`

final answer in mixed fraction:

• 
  `\sf{5(41)/(420)`