How would you give £30 as a percentage of £90?

30/90=0.333

×100 = 33.3%

Hi Carolyn,

The steps are in order to find £30 as a percentage of £90 you need to

1. 30 divided by 90 = 1/3
2. Now you multiply 1/3 times 100 = 33.33%( The answer will be a recurring one so you need to keep it up to 2 or 3 decimal places.

1/3 (simplified) or 30/90

(30/90) × 100 = 0.333333333 x 100 = approximately 33.3%

It is approximately 33.3% as 30/90 =1/3 which as a decimal is 0.3 recurring.

Evaluate:

Here are the steps we take to express one number as a percentage of another.

1. First, look at the two numbers carefully, and decide which is the whole and which is its part.
2. Then write the two numbers in a fraction, part/whole.
3. Then evaluate the fraction as a decimal.
4. Finally, multiply the decimal by 100.

1. Our whole or total is $90. Our part of that is $30.
2. 30 out of 90 is written as 30/90.
3. 30/90 as a decimal is 0.333 recurring.
4. Our percentage is (0.333) X 100 % = 33.3%

Before and after this practice, we would explore simpler concrete examples and level check students' understanding with learning points like below (not in any particular order)

Explore:

A percentage is a special kind of fraction. It tells us how many parts of a whole of one hundred parts that there are.

10% is 10 parts in a hundred. We can write this as a fraction - 10/100.

What about 80%? That's right, 80 parts in one hundred. Or 80/100.

So if I need to change a fraction like 80/100 into percentage points, I should multiply by 100.

(80/100) X 100 = 80%.

In this problem, which is our whole? 30 pounds or 90 pounds? Yes. 90 pounds is our whole, and 30 pounds is the part of the whole. Our whole is not 100 pounds, but 90 pounds.

30 pounds in 90 pounds. Can you express this as a fraction?

Right. 30/90.

Explain:

So we need to show how many hundredths of the total 90 pounds 30 pounds is.

We saw above that we can multiply by 100 to do this.

Our percentage is (30/90) X 100.

We can use a calculator to get the decimal value of 30/90. The answer is: 0.3333 recurring

(30/90) X 100 = 0.333 X100 = 33.3%

So we have discovered a general rule for expressing two numbers as a percentage.

1. First, look at the two numbers carefully, and decide which is the whole and which is its part.
2. Then write the two numbers in a fraction, part/whole.
3. Then evaluate the fraction as a decimal.
4. Finally, multiply the decimal by 100.

Have you got it?

Let's see. What percentage is $20 out of $50?

a) 0.4 b) 40% c) 20%

What did you choose? The answer is b) 40%.

Let's go through our steps.

Our whole is $50. We want to find out what percentage $20 is of this whole.

$20 out of $50 is written as 20/50 as a fraction.

20/50 is 0.4 as a fraction.

Our percentage is (0.4) X 100% = 40%.

Extension:

But what if we have no calculator?

What is 30/90 as a decimal?

Looking at this big fraction, it's difficult to say , right?

That's why we need to use one of our Maths superpowers, simplifying fractions.

Do you remember how to do that? We need to look for common factors for the top and bottom of the fraction, and divide by it.

For example, 2/4 can be simplified. @ and 4 both can be divided by 2. That makes 2 their common factor. When we divide top and bottom by 2, what doe sthe fraction become.

That's right. 2/4 is the same as 1/2.

Back to our question:

30 and 90 both have 10 as a common factor.

So 30 divided by 10 is 3, and 90 divided by 10 is 9.

Our fraction is now 3/9. I still don't know what that is a sa decimal.

Are there any more factors? Look closely.

Right! 3 and 9 have 3 as a common factor.

3 divided by 3 is 1, and 9 divided by 3 is 3.

So we now know our fraction is 1/3. You probably know that 1/3 is 0.3333 as a decimal.

Pre-teach according to student level:

Do you know what the word 'percentage' means?

Interesting fact: It comes from the Latin word, 'cent'. That's the Latin word for 100.

So if I had $100, and gave you 50%, how much money would I give you?

That's right, $50. Generous, aren't I? :)

And if I gave you 1%, I'd only part with $1.

That's because 'percentage' means how many parts in one hundred.

When we use a percentage like this, we are saying how many hundredths of the whole make up our share.

Imagine your mum has baked a giant cake. A really giant cake. That's the whole.

Now the cake is so big, you can easily cut it into 100 identical slices. Each of these counts a one percentage point.

So if I were to eat 10% of that giant cake (which would make me greedy), how many slices would I take?

Correct. 10 slices.

We have looked at taking parts of a whole before. One half, one quarter, two thirds. What do we call these numbers? Right. Fractions. So a percentage is really just a special kind of fraction.

For example, we can write the percentage 60% as 60/100.

How would the percentage 37% be written as as a fraction? Yes. 37/100.

Going the other way, can you express 1/2 as a percentage? The answer is 50%. Can you say why?

To express one value as a percentage of another, you divide that value by the original and multiply by 100.

so ...

30 / 90 = 0.33333 ....

0.33333 .... x 100 = 33.3 %

In order to express any value as a percentage of another, you must divide that value by the original and multiply by 100.

In this case, the value is 30 and the original is 90.

So,

30 / 90 = 0.333333...

0.333333... x 100 = 33.3%

Therefore £30 as a percentage of £90 is 33.3%

First turn into fraction

30/90 —> 3/9 —> 1/3

then into decimal or straight into percentage

1/3 is commonly known as 0.33 or 33.3%

33 percent, or a one third of the total.

The answer is 33.3%. As 30/90= 3/9= 1/3. So this equals to 33% as a percentage.

Thirty three point three recurring

Divide 30 by 90 and simplify to give 1/3 . Then multiply that by 100 and it will give 33.3% which is the answer.

£30 is a third of £90 therefore it is 33.333333%

£30 as a percentage of £90 can also be written as 30/90. This changes to 10/30 if divided by ten and 1/3 when divided by 3. 1/3 as a percentage is 33%

Hi Carolyn,

Firstly, we would put 30 as a numerator in a fraction and 90 as the denominator so it would become 30/90. Then we would simplify by dividing both the top and bottom by the common factor of 30 which would leave us with 1/3, finally we know that a third as a percentage is 33.3 %