Numbers Worksheets

Practice and master numbers with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

How to convert a fraction to a mixed number

By Vighnesh Hemnani

Here at Thinkster Math, you’ll learn what a fraction is, what a mixed number is and how they are related. More importantly, this will also go through a simple and easy way to convert between the two forms of decimals.

Why is this concept useful?

This concept is useful in many ways but the key way it is used is in terms of measurements. Most of the buildings and tools and things we use every day are done with great precision and sometimes this precision takes many forms. It could be a decimal/fractional measurement of a bridge which could be represented as a mixed number for an easier way to understand. A mixed number fraction would convert all the whole parts of the improper fraction into whole numbers, which make it an easier to understand measurement for some people. For example, saying 10 ½ inches is better than saying 10.5.

Where does this concept fit into the curriculum?

Grade 5

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):

27\frac{2}{7}

Sometimes, the numerator will be equal to or greater than the denominator, and when this happens, we call these fractions improper, for example

107\frac{10}{7}

(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:

3573\frac{5}{7}

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

187\frac{18}{7}

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

187\frac{18}{7}

. Thus, we can rewrite as a mixed number fraction:

2472\frac{4}{7}





Sample Math Problems

1. Convert this improper fraction,

212\frac{21}{2}

to a mixed number fraction.

Solution:

101210\frac{1}{2}

is the mixed number fraction

212\frac{21}{2}

If you divide 21 by 2, you will get a quotient of 10 and a remainder of 1, so by the steps outlined above, the mixed number fraction would be

101210\frac{1}{2}

2. Convert this improper fraction,

5610\frac{56}{10}

, to a mixed number fraction.

Solution:

56105\frac{6}{10}

is the mixed number fraction

5610\frac{56}{10}

If you divide 56 by 10, you will get a quotient of 5 and a remainder of 6, so by the steps outlined above, the mixed number fraction would be

56105\frac{6}{10}

3. Convert this improper fraction,

173\frac{17}{3}

, to a mixed number fraction.

Solution:

5235\frac{2}{3}

is the mixed number fraction

173\frac{17}{3}

. If you divide 17 by 3, you will get a quotient of 5 and a remainder of 2, so by the steps outlined above, the mixed number fraction would be

5235\frac{2}{3}

4. Convert this improper fraction,

458\frac{45}{8}

, to a mixed number fraction.

Solution:

5585\frac{5}{8}

is the mixed number fraction

458\frac{45}{8}

If you divide 45 by 8, you will get a quotient of 5 and a remainder of 5, so by the steps outlined above, the mixed number fraction would be

5585\frac{5}{8}

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Practice Math Problems

1. Convert this improper fraction,

458\frac{45}{8}

, to a mixed number fraction.

2. Convert this improper fraction,

232\frac{23}{2}

, to an improper fraction.

3. Convert this improper fraction,

563\frac{56}{3}

, to a mixed number fraction.

4. Convert this improper fraction,

2112\frac{21}{12}

, to a mixed number fraction.

Related Topics

By Puja Varude

Normal Distribution

By Patricia Martin

Tossing a Coin

By Mandi Elam

Properties of Exponents

By Debi DalPezzo

Solve for x

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?

A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.

Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.

Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!

Start 7-Day Free Trial