Anyone know 55% as a fraction?

[beenonthemath]

I know from mentors it's 11/20

Because 55% is 55 over 100.

I get the numerator part because 5 goes into 55 a total of 11 times

However, why is the denominator 20?

11x5 is 55 and 20 x 5 is 100

I get that. But I am confused because I got the numerator by doing 5x11

11 goes into 55 a total of 5 times. So why isn't it 5 over 20 (because 5 goes into 100 20 times)

I am going an adult functional skills course, promise I'm not a school kid posting on his/her break

First sentence should say memory, not mentors

5 goes into 55 11 time and into 100 20 times

So 11/20

You divide both numerator and denominator by 5.

55% means 55 over 100.

With any fraction if you divide the top and bottom by the same number you will get different numbers but the same amount.

55 divided by 5 is 11
100 divided by 5 is 20

What you do to the top, you have to do to the bottom...

Think about fractions you know like 2/4 is the same as 1/2... both numerator and denominator have been divided by 2.

So the numerator and the denominator are like your children: you must treat them equally.

55/100 is the fraction

So 55 divided by 5 is 11
Treat the 100 the same as it's sibling.
100/5 is 20

5 doesnt go into 11, though: so 55 divided by 5 is 11, and 100 divided by 5 is 20.
The rule is what you do to the top you have to do to the bottom. So you've divided both top and bottom by 5.

Do you have 100 lego blocks? It may help to put the blocks together in groups of five to visual that 55 is 11 blocks of 5 and 100 is 20 blocks of 5.

55/100 is a proper fraction in its own right but it can be simplified - reducing it to its lowest terms. So 2/4 is the sane as 1/2 but 1/2 is its lowest terms. You cannot reduce the numbers anymore.

to simplify you simply divide both the top and bottom by the highest number that can divide into both. To do this you look at the factors - a number that divides into a number leaving a whole number.

the factors of 55 are 1, 5, 11 and 55 I.e. 1x55=55 and 5x11=55. You then look and see what are also factors of the bottom number. Here the highest number that divides into both are 5.

then you divide both by 5 so 55/5=11 and 100/5=20 making the answer 11/20.

you know it cannot be simplified further as 11 is a prime number

Because it needs to be a whole number and 5 is the highest number that divided into both 55 and 100 to leave whole numbers

100 / 11 wouldn’t work

Because 5 over 20 would be 1/4.

Okay, so you understand that you got 55 by using the numerator 5.

You need to use the same numerator (5) on the top and the bottom number of a fraction.

So 5 into 100 = 20.

You need twenty 5p coins to make a pound (£1). So one twentieth of 100p is 5p.

To make 50% (half, "50 out of 100") of £1, you'd need to get 50p in 5p coins, which is ten of them. 5p x 10 = 50p.
To go up to 55% you'd need to bring in one more 5p - so you'd have eleven 5p coins in all, in your "55% pile". 11x 5p = 55p (and you'd also the other nine 5p coins in a "45% pile" leftover because 100%-55%=45% and to check, 5p x 9 = 45p.)

So if eleven 5p coins make 55%, and there are twenty 5p coins in the whole pound, then you have 11 out of 20 of them - 11 twentieths of a pound, or 11/20.

you know it cannot be simplified further as 11 is a prime number

Another reason to remember my prime numbers! Didn't think of this trick

Thank you all

It is 11/20 because you only show them as whole numbers and in the smallest common denominator. 11 is a prime number so cannot be divided any further.

So any fraction you see with 11 as a numerator, can just be left as you cannot simplify 11 because it's a prime number?

i don't really understand your query.
i do not have a simple formula for working these out, sorry.
so perhaps you picked those figures as an easy example ?
i just know that there are 20 lots of 5 in 100.
to check it i say there are 10 lots of 10 in 100, so there must be 20 lots of 5 in a 100.
50 is just over half of 100.
so there are half of 20 lots of 5s, which is 10, plus one more 5, to make up to 55, which is 11.
that is 11 out of 20, so 11 over 20 written as a fraction.
now you can all laugh at me.
but i can reckon money.
in my head.
and did pass O level maths, middle grade, some years after leaving school.

The biggest number that divides into both is 5. 11 times into 55 and 20 times into 100. There isn't a whole number that divides into 11 and 20 so you're done simplifying. As pp have said, if your numerator or denominator is prime, you're done anyway.

No. It's the 55 you divided, to get to 11.

You're focusing on the 11. You need to think of the number 5.

To reduce a fraction you divide the top and the bottom by the same number.

You divide the 55 by 5 to get to 11.

You therefore divide the 100 by 5 also, to get to 20.

But you're right that you can't divide 11 any further as it's a prime number.

Unless the denominator can be divided by 11 eg 11/110 =1/10, or 11/220 = 1/20

You can possibly cancel further if the numerator is prime.
For example, 11/22 can be simplified.

Any prime number numerator cannot be further simplified.

2 even numbers always can until you get a odd number that doesn’t share factors or is a prime number.

same for denominater

This

@SnowsFalling

You are correct, I should have stated that you can further simplify if the numerator is a divisor of the denominator - op needs to recognise highest common factor. <hangs head in shame>