What are fractions and mixed numbers?
A fraction is in essence, a ‘fraction’ of a number! Unlike regular whole numbers, fractions represent a part of a whole. They can be defined as a portion of a whole and what the whole actually represents doesn’t matter – the whole can be any number or just an object (like a pie or a chocolate bar). For example, you can cut a pie into 6 slices which would mean that each part is 1/6 of the whole pizza.
How do we write these fractions? We write them with a numerator and a denominator like so (2 is the numerator, and 7 is the denominator):
How do we write these fractions? We write them with a numerator and a denominator like so (2 is the numerator, and 7 is the denominator):
Sometimes, the numerator will be equal to or greater than the denominator, and when this happens, we call these fractions improper, for example
(a proper fraction is the exact opposite). However, there is a way to convert an improper fraction to a mixed number fraction. Note a mixed number fraction is nothing but a whole number with a proper fraction, for example like so:
The way we could say this mixed number fraction is: “three and five sevenths”.
How to use this concept?
To be able to convert an improper fraction to a mixed number fraction, you can follow these easy simple steps:
1. Do long division of the numerator by the denominator.
2. Your division should have a quotient (a whole number result) and a remainder. The whole number result will be the bigger number on the left, and your remainder will be the new numerator of the mixed number fraction.
3. The denominator of the mixed number fraction will remain the same as the previous denominator.
Essentially, we see how many whole number times of the denominator can we fit in the numerator. If we continue with say
2. Your division should have a quotient (a whole number result) and a remainder. The whole number result will be the bigger number on the left, and your remainder will be the new numerator of the mixed number fraction.
3. The denominator of the mixed number fraction will remain the same as the previous denominator.
Essentially, we see how many whole number times of the denominator can we fit in the numerator. If we continue with say
we see that we can fit two 7’s in 18 (7 x 2 = 14 and the next multiple 7 x 3 = 21 is greater than 18 so we stick with 14). Note that the remainder (18 – 14 = 4) is 4. So we know it takes two whole 7’s and 4/7 extra to get to
. Thus, we can rewrite as a mixed number fraction:
Sample Math Problems
1. Convert this improper fraction,
to a mixed number fraction.
Solution:
