Question

Could someone teach me how to work with fractions.

Answer 1

I was recently asked to add, multiply, subtract and divide fractions. One of the questions was 4/7 - 12/4
I would like for you to elucidate.

Answer 2

So what I was saying is... you need to find a number that can act as a common denominator for both fractions. These numbers are often chosen to be common multiples of the denominators. Let me explain:

The number, 28, for example, is a common multiple of 4 and 7, which, in its essence, means only that it is a multiple of both 4 and 7. (Try checking why!)

Answer 3

because 4 * 7

Answer 4

Yes, pretty obvious. Now convert both fractions so that both have denominator = 28.

Answer 5

so 4/28 - 12/28?

Answer 6

That's not exactly how it works though.

Draw a picture of a cake in your mind. The number 1 represents the whole cake. The number 1/2 represents, well, half of the cake. But thinking about it, if you divide the halves into halves again (which you call quarters) then eating two quarters of the cake will be the same as eating half of the cake!

Therefore, 1/2 can be converted to denominator 4 by writing it as 2/4.

Answer 7

So then the meaning of converting fractions is this:

4/7 = 16/28 - why is this true? Because if you divided the cake into seven parts and ate four of them, then that'd be the same as dividing it into 28 parts and eating 16 of them.

Answer 8

But how do I figure that out in my head? Think about it like this: I want to eat the same amount of cake as I decided. Now if someone doubles the number of pieces of the cake, what I do is I simply double the amount of pieces I decided on eating to keep the same amount of cake.

Answer 9

So what I am saying is this: if someone multiplies the number of total pieces by some number, I will multiply the number of pieces I want to eat by that same number. Makes sense?

Answer 10

Now there's a seven-piece cake of which I want to eat four pieces. But now it's been cut into 28 pieces. In other words, they multiplied the total number of pieces by 4. But that's OK, I can multiply the number of pieces I want to eat by 4 too, but I can't say that in the new cake, 4 pieces will be the same as in the original cake (because now, a piece is 4 times smaller!)

Answer 11

In math language: if you're multiplying the denominator by some number to convert it to an equivalent fraction, multiply the numerator by that same number.

Answer 12

4/7 ----> ???/28

In doing so, I multiplied the denominator by 4, so I will multiply the numerator (4) by 4 too.

So 4/7 ---> 4*4/28 ---> 16/28

Can you do something similar for the other fraction??

Answer 13

hmm
multiply by 12?

Answer 14

12/4 ---> ???/28 right? Our topmost priority is switching to a denominator of 28.

Answer 15

hmm

Answer 16

Parth I appreciate the help
But someone just messaged me in the meantime and taught me all about this fraction business. :o

Answer 17

So thank you, but I no longer require assistance.

Also I'm tired of putting on this facade.

Answer 18

Farewell for now.

Answer 19

Ah, great to hear that. Good luck.