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How to solve fraction questions using fractions classroom resources

Like percentages, fractions really scare a lot of people. This is probably because of nightmare maths lessons when studying for SATS preparation or during K-12. Being given endless fraction of amount worksheets and being asked to endlessly find fractions of a number. Usually you find a trick when multiplying fractions with whole numbers and then that does you. Unfortunately, you rarely get to understand what a fraction really is.

It is this basic question of ‘What is a fraction?’ that Grade 5 or Grade 6 (Year 5 or Year 6 in the UK) don’t get.

how to divide by thirds

how to divide by thirds

How to solve fraction questions using fractions classroom resources

Like percentages, fractions really scare a lot of people. This is probably because of nightmare maths lessons when studying for SATS preparation or during K-12. Being given endless fraction of amount worksheets and being asked to endlessly find fractions of a number however excellent are the fractions classroom resources. Usually, you find a trick when multiplying fractions with whole numbers and then that’s enough. Unfortunately, you rarely get to understand what a fraction really is.

It is this basic question of ‘What is a fraction?’ that Grade 5 or Grade 6 (Year 5 or Year 6 in the UK) don’t get.

fractions and division explanation math animated gif

There are three facts that will help you to understand fractions:

Fact 1

In maths ‘of’ means times (x)

Fact 2

The slash through the middle of the fraction means ‘out of.’ It also means divide. (That’s where the division symbol comes from -surely).

Fact 3

A student will be asked to take 4 and divide it by 9. They look confused and can’t get that 4÷9 is 49

In other words, fractions are one number divided by (or ‘out of’) another.

fractions and division explanation math animated gif

There are three facts that will help you to understand fractions:

Fact 1

In maths ‘of’ means times (x)

Fact 2

The slash through the middle of the fraction means ‘out of.’ It also means divide. (That’s where the division symbol comes from -surely).

Fact 3

A student will be asked to take 4 and divide it by 9. They look confused and can’t get that 4÷9 is 49

In other words, fractions are one number divided by (or ‘out of’) another.

Now some ‘methods’

Down below, there are 3 simple methods to solve fraction problems and then if you want to use or print out the free worksheets or use the fractions classroom resources above you can try some yourself. They are designed for people of all abilities so you can set your own level of challenge.

What is 49 of 36?

There are a couple of ways to solve a question such as what is 49 of 36: one with a calculator, and one without.

Using a calculator (method 1)

If you have a calculator there are two quick methods. The answer (unless you have set up a scientific calculator to do otherwise) could be a decimal. This can be a problem. A simple fraction like 27 will look like this: 0.28571428571

So:

49 of 36

Just ‘decode’ it. The slash means divide and ‘of’ means times.

So it’s 4 ÷  9 x 36

Type in:

solve fraction questions using a calculator

Using a calculator (method 2)

This is a bit weird, but some people like to do it the other way ie. backwards. It gives you the same answer, and it’s a bit like the written method that we are going to learn next.

49 of 36

solve fraction questions using a calculator

…same answer (hopefully).

Why don’t we just always use a calculator?

It’s the same(-ish) answer as for any math problems. Even though nearly everyone has access to a calculator all of the time these days, they can be banned from some maths tests.

Primarily the real reason to learn to learn to find a find a fraction of a quantity without a calculator is that it really teaches you to understand what fractions are, and consequently how to use them properly. It’s really important to understand what you are typing into calculators, else sometimes you just write down all sorts of weird answers to simple fraction questions, because you just pressed the wrong buttons.

Also, if you want fraction answers to fraction questions, pen and paper or mental methods are the best. They also give you a headstart when you start doing division in algebra.

Anyway…

How to multiply fractions with whole numbers without a calculator
or
Whole number times fraction problems without a calculator
or
How to find a fraction of a number without a calculator

(It’s all the same thing)

First:

Learn a fact about unit fractions

what are fractions explanation

In other words, if you see something that asks you to multiply a number by 19, it’s the same as saying divide it by 9.

Similarly, if you see something that asks you to multiply a number by 110 , it’s the same as saying divide it by 10.

Therefore, if you need to know 15 of 20, you just do 20 ÷ 5.

Ps. There is an option on the fractions classroom resources  above (press chooser) to turn it into a unit fraction worksheet, so you can practise unit fractions.

Now we’re ready to go…

Best method to solve percentage problems without a calculator

It’s not the quickest, but I like it, because you get to understand how fractions really work. After a bit, you can then develop your own shortcuts to speed things up.

Let’s try three examples…

how to solve fraction questions

In conclusion

I know that there are many different methods to learn to work with simple fractions and learn what to do when multiplying fractions with whole numbers, but this one works and hopefully gives you some help to understand fractions.

Once you have understood these, all of those fractions of amounts worksheets or fractions classroom resources that teachers print out for their students should be whole lot easier, as should any problems multiplying fractions with whole numbers.

The best way from here is to improve your maths by practising the maths fraction drills above and whether you are a student, teacher, tutor or homeschool educator, I hope the free printable fraction worksheets and fractions classroom resources can be useful for you. It’s a great classroom or homework resource to help people with their maths and in particular fractions and get people to feel a bit more at home with fractions and math in general.

Ps. For a greater level of challenge, change the question type to mixed or inverse. This effectively means that you can practise dividing fractions as well. Enjoy!

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