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Converting Mixed and Improper Fractions

November 12, 2024•2 min read

This week a couple of people have asked about doing mixed and improper fractions. Because fractions seem to be something that so many people struggle with, I thought I'd create this post with the hope that it will help someone.

Mixed to Improper Fractions

These are the fractions where you have a whole number, then a fraction sat next to it. So, for example 1 ½ would work as an example.

To swap this into an improper fraction (where the number at the top of the fraction is bigger, the three steps are simply:

1. Multiply the number at the bottom of the fraction (the denominator) by the whole number.

2. Add the number at the top of the fraction (the numerator) to your answer to step 1.

3. Write the answer to step 2 above the 2 (the original number at the bottom of the fraction.

So, if you were changing 1 ½ into an improper fraction:

2x1 =2

2+1 =3

Answer: 3/2

To go the other way and change an improper fraction to a mixed fraction using 3/2 as an example:

1. Ask how many times the numerator (bottom number) would go into the top number (denominator) (how many 3’s in 2)

2. This becomes the whole number (Big number or for the official term integer) that sits to the left of the fraction.

3. Write your remainder over the top of the 2 (the original bottom number in the fraction)

Giving you the answer 1 ½

That’s it. The number at the bottom of the fraction never changes (unless they ask you to simplify it but that’s something different but if you want me to explain, please do say).

Each week we send out emails to parents with hints and support on maths, English, and revision (up to the end of GCSE). If you think it would be of help to you or your child and you'd like to receive the emails let me know, and I will happily make sure you receive them as well: info@clarajamestutoring.co.uk

fractionsmathsimproper fractionmixed fractionsGCSE mathsmaths revision

Dawn Strachan

For the past 20+ years I have been a firm believer that learning should be an enjoyable experience. I appreciate that traditionally education has revolved around worksheets, textbooks, listening to teachers. But a grounding in early years and working with children who had a variety of learning styles from I learned that it is an individual activity that is personal to all of us. We don’t all learn in the same way. Our influences, our experiences, our capabilities all influence how we retain information. But through it all, I believe that if we can make it enjoyable and engaging, they will want to participate. With participation comes practice which in turn boosts skill and confidence. With an increase in skill and confidence comes a willingness to have a go. This in turn leads to more practice which leads to a positive spiral of success. The moral, we need to make learning fun, engaging, use a range of techniques.

Back to Blog

Morning,

I hope the week is going well.

So many people seem to be doing D of E and work experience
at the moment, good luck if that’s you and if you’re at Marlow Camp next
fingers crossed for good weather!

I’ve just finished a lesson on division. It seems to be
something that messes with the brains of so many people.

I found it got easier when I stopped thinking about it as
division and instead thought about it as multiplication. So, if for example I
had the question 396 divided by 3, I would look at it as 3x what = 3. My answer
would be 1. How many times would I need to multiply 3 to get to 9, (my answer
would be 3). Then 3x something = 6. My answer would be 2. Giving me the overall
answer of 132.

I know that’s a really simple example but hopefully it explains
my point.

Thankfully in schools they don’t often seem to need to do
long division, but I’ve worked with a couple of adults (generally nurses for
some reason) who have needed it.

I think I’ll explain this one in a video, as it will be too
complicated to explain it with words as bits get put all over the place. I hope
this makes sense though:

https://youtu.be/cxkN_C5Ecwc

Enjoy the rest of the week and speak soon,

Dawn