How to Rename a Mixed Number

In this lesson let’s learn how to rename or rewrite a mixed number and we are going to do that by learning about an improper fraction. So a mixed number can be written number can be written as improper fraction, let’s cover that first. Well we know if I have a fraction like 2/5 the numerator is always less than the denominator. That what makes it a fraction or a part, this is called the proper fraction. If we have a numerator which is greater than a denominator this is called improper fraction.

This means I got six parts out of five which means I got more than a whole that is what a mixed number does. So let’s learn how to convert this, the problem says for us to rename 1 6/10 as a fraction in the simplest form. So first lets’ write it as a fraction, we got one and 6/10 that is a mixed number. I know that this is the same as 1 + 6/10 but how I will I add 1 and 6/10? Well before we do that, let’s actually convert one, what is one? One is the same as 10/10. 10 ÷ 10 is 1, so I can write a whole number as a fraction equivalent.

What I need to do is to take a look at this fraction part since the denominator is 10, I take the whole number and make it a equivalent fraction with the denominator of 10. So what I am left with? Well this is the same as 10/10 + 6/10; all I did was replace one with 10/10. Well this is easy since the denominator is the same it is 10 + 6 which is 16/10.

So if it is 16/10 that is a fraction, how do I write it in simplest form? Well we can divide sides, numerator and denominator by two, what do we get? 16 ÷ 2 = 8 and 10 ÷ 2 = 5, so what are we left with? A fraction which is an improper fraction the numerator is greater than the denominator but it is in the simplest form. So our mixed number can be written as a fraction by simply taking the whole number part and converting to its fraction equivalent. What we do is one can be written as 10/10 it can also be a 100/100 what we do is make it the same as the denominator. So one became 10/10, 10/10 add it to 6/10 became 16/10 which it is in simplest form I just divided the top divided by 2 to get 8/5.

Let’s try another problem, it says Scott troops ride a waterlog ride. They needed one and ¼ log cars for their trip, how many fourths is that? Well this I have to write as an improper fraction. How do we do that? Well we know 1 + ¼ is what this means. And so the 1 I can write down 4/4, one is the same as 4/4. And the reason I chose 4/4 is because in that fraction part I got four as the denominator. So what do I have 4/4 + 1/4 , how do I add this? Same denominator 4 + 1+ 5 and the denominator is copied over. So 1 ¼ is the same as the same as 5/4 and the way we did that is by converting one to its fraction equivalent. Well if it is 5/4 how many fourths is that? Five, so we need 5/4 cars for their troops so 5/4 the answer is 5.