Hard Simplifying Fractions!!!?

Question

What is c/5 + 3c/10? My Year 11 brother doesn't even know this! Tell me how you did this aswell please!

Answer 1

The common denominator is 10.

c/5 + 3c/10 =

c*2/5*2 + 3c/10 =

2c/10 + 3c/10 =

5c/10

It is a little difficult to see typed out, but you need to first create a common denominator to add the fractions. In this problem the common denominator is 10.

To make the first fraction have a denominator of ten you need to multiply the fraction by 2/2.  

2/2 is the same thing as one, so you are not changing the value of the fraction why you multiply it by 2/2, just changing what it looks like. Anything times one gives you the same number back. (3 x1 =3, 4 x 1 = 4...)

Once you have the common denominator you can add the numerators and the denominator remains the 10.

Answer 2

c/5+3c/10

2c+3c=5c/10= c/2

Answer 3

When adding or subtracting fractions, you have to have them all with the same denominator (the lower part). This means that you have to find some adjustment that will make all of the denominators the same. Many times this simply involves multiplying one fraction to match the other. And that is what you do in this case.

c/5 + 3c/10

Just be looking, you can see that 5 is a multiple of 10. So, all you have to do is get the first fraction into tenths, and you'll be all set. You'll need to multiply this fraction by 2.

When multiplying a fraction by two, you will need to multiply both the top and the bottom by the number. (See below why this is true.)

c/5 times 2/2 = 2C/10

Now you can add the two fractions:

2c/10 + 3c/10 = 5c/10

You could leave it that way, but visually you can now see that 5 is a multiple of 10, and that you can divide both the top and the bottom by 5:

5c/10 divided by 5/5 = 1c/2 or just plain c/2.

The reason that you multiply or divide both the top and bottom by the same number is that you don't want to change the value of the fraction, only adjust it so that it says the same thing, only a different way.

If you only multiply the top number by two, for example, you are effectively multiplying by 2/1, or 2, and doubling the value.

If you only multiply the bottom number by 2, you are effectively multiply by 1/2, or halving the value.

ALWAYS REMEMBER, when adjusting the fraction, DON'T CHANGE THE VALUE.

Answer 4

To add fractions together, you must make a common denominator.

Your fractions are c/5 and 3c/10.  The common denominator between 5 and 10 is 10, so multiply c/5 by (2/2) which will get you your base of 10, but will really just be multiplying the fraction by 1 since (2/2) simplifies to (1/1).

(c/5)(2/2) + 3c/10

2c/10 + 3c/10

Add the two fractions together.

2c/10 + 3c/10

5c/10

Now simplify

5c/10 = c/2

Because 5 is divisible by 5 and 10 is divisible by 5, you can simplify the fraction to 1/2.  Therefore your answer is c/2.