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How to Add Fractions (and Multiply and Divide Fractions)

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8th August, 2022

How to Add Multiply and Divide Fractions

When I teach how to add and subtract fractions, I start with explanations of equivalent fractions and how to simplify them.

Moving on from that, I look at multiplying and dividing fractions – which is easier than adding and subtracting!

Equivalent Fractions and Simplifying Fractions

Equivalent Fractions

 

If you multiply or divide the numerator and denominator by the same number you have an equivalent fraction.

“Whatever you do to the top, you do to the bottom”

Equivalent Fractions Example

Simplifying Fractions

 

If you can divide the top and bottom by the same number, you can simplify the fraction.

Simplifying Fractions Example

How to Multiply Fractions

Multiply Fractions

Multiplying Fractions Example

Multiply Fractions – Multiply tops and bottoms

First multiply the numerators together then do the same for the denominators.
Multiplying Fractions Example - Step 1

Multiply Fractions – Simplify Fraction

If needed, reduce the fraction to its lowest form: divide the numerator and the denominator by the same number.
Multiplying Fractions Example - Step 2

How to Divide Fractions

Divide Fractions – change to a multiply question

To divide fractions, we change it to a multiply question, using “K.F.C.” – Keep, Flip, Change.

  • Keep the first fraction
  • Flip the numbers on the second fraction
  • Change the question to a multiplication
Dividing Fractions Example

Divide Fractions – Multiply

Now that we have changed the question to a multiplication, do as before for multiplying. Multiply the numerators together then do the same for the denominators.
Dividing Fractions Example - Step 1

Divide Fractions – Simplify Fraction

If needed, reduce the fraction to its lowest form: divide the numerator and the denominator by the same number.
Dividing Fractions Example - Step 2

How to Add and Subtract Fractions

How to Add and Subtract Fractions – when the denominators are the same

The denominators remain the same, simply add or subtract the numerators to find the sum of the fractions.

Adding and Subtracting Fractions - same denominator

How to Add and Subtract Fractions – when the denominators are different

Change to equivalent fractions with common denominators, then add or subtract.

And what’s the best common denominator to use? The one that is the lowest common multiple of the two denominators.

e.g. the lowest common multiple of 3 and 4 is 12. The lowest common multiple of 2 and 5 is 10.

Adding and Subtracting Fractions - different denominators

Printable revision guides on How to Simplify Fractions, How to Add / Subtract Fractions, How to Multiply Fractions and How to Divide Fractions

FREE downloads –

Revision guide on How to Simplify Fractions.

Revision guide on How to Multiply Fractions.

Revision guide on How to Divide Fractions.

Revision guide on How to Add / Subtract Fractions.

Equivalent and Simplifying Fractions - resource
Multiplying Fractions - resource
Dividing Fractions - resource
Adding and Subtracting Fractions - resource

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Nicola Bhalerao - Warwick Tutor

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+ to various computing skills, including website training.

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.

I am a WordPress expert, having spent many years creating numerous websites with my other business, Smiling Panda Web Design. Although I no longer actively work on websites for others, I offer help with understanding / updating / creating your own WordPress website.

Read here for more information on tuition for your child or tuition for yourself or another adult.

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"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"

"My daughter has gained a lot of confidence, especially with her mental maths. Her progress has been shown in her school work. Nicola has shown great empathy towards her"

"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"

"Any work we did at home would typically end up with us both becoming frustrated. He had been reluctant to put his hand up and ask in school. In a short time he has gained a lot more confidence"

"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"

"Already I have noticed a big difference in his attitude and approach to his school homework; he has gained a willingness to give it a go and not just assume he can't do it!"

"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"

"We have been impressed with her professionalism, patience and teaching. She worked at a level and pace that suited our children. Both have gone on to receive 11+ results we are very proud of."