Question

The sum of three fractions is 6.if 18/7 and5/6 are two of the fractionsfind the third fraction

Answer 1

What is a fraction?

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

First, we need to solve for a common denominator.

What is a common denominator?

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

To get the common denominator between
`(18)/(7)` and
`(5)/(6)`, we multiply their denominators.

• 7 × 6 = 42

Now, we know the fractions would look like this:

• 
  `(?)/(42) (?)/(42)`

To solve for the numerators, we can use these equations:

• 18 × 6 = 108

• 5 × 7 = 35

Now, the fractions look like this:

• 
  `(108)/(42)` and
  `(35)/(42)`

Adding them together:

• 
  `(108)/(42) +(35)/(42) = (143)/(42)`

Now, we can convert this into a mixed number.

• 
  `(143)/(42) = 3(17)/(42)`

Now that we have this, we can subtract that from 6 to get the missing value.

• 
  `6 - 3(17)/(42)`
  `=2(25)/(42)`

Therefore, the third fraction is
`2(25)/(42)`.