Question

Compare using >, <, or =
a. 5 thirds + 2 ninths _____ 1 9/8

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.

The equation for this problem is this:

• 
  `(5)/(3) + (2)/(9)` (> < =)
  `1(9)/(8)`

First, we need to find a common denominator between
`(5)/(3)` and
`(2)/(9)`.

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 find the common denominator, we can multiply the denominators, 3 and 9.

• 3 × 9 = 27

Now we know that the two new fractions are going to have a denominator of 27.

• 
  `(?)/(27) (?)/(27)`

Now, we can use these equations to solve for the numerator.

• 9 × 5 = 45

• 3 × 2 = 6

Now, the fractions look like this:

• 
  `(45)/(27) (6)/(27)`

To add them together, we can use this equation:

• 
  `(45)/(27)+ (6)/(27) = (51)/(27)`

Now, we need to convert
`1 (9)/(8)` into an improper fraction.

What is an improper fraction?

An improper fraction is a fraction that has a numerator that is greater than the denominator. For example,
`(3)/(2)` is a improper fraction.

• 
  `1(9)/(8)` =
  `(17)/(8)`

To convert
`(51)/(27)` and
`(17)/(8)` into common denominators, we need to multiply the denominators, like we did above.

• 8 × 27 = 216

The new fractions will look like this:

• 
  `(?)/(216) (?)/(216)`

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

• 17 × 27 = 459

• 8 × 51 = 408

The fractions now look like this:

• 
  `(408)/(216) (459)/(216)`

Now, convert them to mixed numbers.

• 
  `(408)/(216) = (17)/(9)`

• 
  `(459)/(216) = (17)/(8)`

Therefore, 5 thirds + 2 ninths < 1 9/8.