Question

The sum of two fractions is 5 3/8 one of the numbers is 7/9 what is the other number

Answer 1

`\boxed{\mathrm\bold {4(43)/(72)}}`

Explanation:

Let the unknown fraction be x

We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9

First convert 5 3/8 to an improper fraction for easier calculation

`5 (3)/(8) = (5* 8 + 3)/(8) = (43)/(8)`

Therefore we get:

`(7)/(9) + x = 5(3)/(8)\\\\(7)/(9) + x = (43)/(8)\\\\`

Subtract
`(7)/(9)` on both sides to isolate x:

`(7)/(9) - (7)/(9) + x = (43)/(8) - (7)/(9)`

`x = (43)/(8) - (7)/(9)`

To compute the right side

• Find the LCM of 8 and 9: 8 x 9 = 72
• Adjust the fractions based on LCM so we get 72 as a common denominator:
• 
  `(43)/(8)=(43\cdot \:9)/(8\cdot \:9)=(387)/(72)\\\\\\(7)/(9)=(7\cdot \:8)/(9\cdot \:8)=(56)/(72)\\\\`
  
• Subtract the numerators and use 72 as the common denominator
  
  
  `(43)/(8) - (7)/(9) = (387)/(72) - (56)/(72)\\\\\\= (387-56)/(72)\\\\= (331)/(72)`
  
  
  `= 4(43)/(72)`