What is a mixed number? What is an improper fraction? How do we convert between the two?
Table of Contents
What is a mixed number?
A mixed number is a whole number and a fraction.
“Pizza, Pie or Cake?”
A question I ask my students – which do they prefer? It is often easier to think of fractions, mixed numbers etc, in terms of things that you can divide into equal size slices, e.g. pizza, pie or cake!
I like cake best. 3 and 4/5 would be 3 whole cakes, and 4 slices of another cake that has been divided into 5 equal slices.
What is an improper fraction?
An improper fraction (sometimes called a “top-heavy” fraction) is where the numerator (the number on the top) is larger than the denominator (the number on the bottom).
“How Many Slices of Pizza, Pie or Cake?”
Using the example above, this would be 19 slices of cake, where each cake had been divided into 5 equal slices.How to change an improper fraction to a mixed number
We often to have to change an improper fraction to a mixed number, usually when we complete a question and want to “tidy it up”.
Take 19/5 – If we were to reconstruct whole cakes, by placing the slices together on plates, we would need 5 slices (5 fifths / parts make a whole) for each whole cake. We can do this 3 times (3 x 5 is 15) so we get 3 whole cakes and have 4 slices leftover – i.e. 4 fifths of a cake.
How to change a mixed number to an improper fraction
Sometimes we need to change a mixed number to an improper fraction (for example, before we do multiplying or dividing of fractions.
Let’s start with 3 and 4/5 – now we have 3 whole cakes, and 4 slices of the cake, divided into fifths. Changing it to an improper fraction could be rephrased as, “How many slices of cake, assuming divided into fifths, would get from 3 and 4/5?”
Each whole cake gives us 5 slices, so with 3 cakes that is 15 (3 x 5) slices, plus the 4 fifths (slices already cut) we have a total of 19 slices – i.e. 19 / 5.
Printable revision guide on How to Change an Improper Fraction to a Mixed Number
FREE download – Revision guide on How to Change an Improper Fraction to a Mixed Number.
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About Me
My name is Nicola Bhalerao and I am a private tutor based in Warwick. Since 2013, I have provided one-to-one tuition for children and adults. I specialise in maths tutoring, but cater for different requests, ranging from 11+ / entrance exams to various uses of maths, e.g. : interviews, job promotions, GCSE retakes, Functional Skills, nursing, teaching – any situation where confidence in maths is required.
My background is in computing, with a Computer Science degree from Warwick University. I have worked many years as a programmer, latterly in the games industry. Both my sons were tutored by me for the 11+ (they went to a local grammar school). I received training for teaching secondary school maths and I am fully CRB checked.
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"Nicola was a patient tutor, always helpful in answering any questions I had. I’d always found maths quite a scary subject, but through Nicola's tutoring I found I built confidence with the subject"
"Nicola has been very supportive by helping me to fill in the blanks left over from my high school education. This has been crucial to improving my confidence in mathematics"
"I was lacking confidence in maths. Nicola was a fantastic teacher and really helped to improve my technique and approach to maths problems. She is patient, understanding and friendly"
"She was very friendly and professional. After a few sessions I felt much more confident in my ability and passed the numerical reasoning tests. She explains things very clearly"
"Nicola was a patient tutor, always helpful in answering any questions I had. I’d always found maths quite a scary subject, but through Nicola's tutoring I found I built confidence with the subject"