Fractions help?

[christina.b]

I have just started doing KS3 maths, I am very far behind due to being taken out of school at the start of year 9 and haven't really done any maths since for personal reasons.

I haven't had any problems until now, where I have started fractions and the books I am using haven't explained how to solve these questions. I have tried really hard to understand, but it doesn't make any sense to me.

It says: "For each fraction pair, put them both over a common denominator to see which is bigger. Write out the original fraction pair using the "greater than" sign > :"
a) 3/4 , 4/5
b) 2/3 , 5/8
c) 1/3 , 2/5
d) 13/20 , 7/10

I now understand what a common denominator is and how to find one (I had to search it), although the book didn't even mention them until this. I just don't understand how to "put" the fractions over the common denominators. How do I write this?
I have tried 3/20 and 4/20, but that seemed way too simple and almost pointless.
Please help.

 

[stapel]

"For each fraction pair, put them both over a common denominator to see which is bigger. Write out the original fraction pair using the "greater than" sign > :"
a) 3/4 , 4/5
b) 2/3 , 5/8
c) 1/3 , 2/5
d) 13/20 , 7/10

I now understand what a common denominator is and how to find one (I had to search it).... I just don't understand how to "put" the fractions over the common denominators.

1) Find the common denominator.
2) Note what you multiplied each "bottom" by to get that common denominator.
3) Multiply each "top" by the same value.
4) Compare the new "tops" to see which is bigger.

 

[Ishuda]

To make two fractions have a common denominator means to change the numbers in the fraction so that the bottom number is the same for both fractions AND the two numbers still have the same value. First we note that we can multiply the numerator and denominator by the same number and not change the value of the fraction. For example
\(\displaystyle \frac{3}{4} = \frac{5*3}{5*4} = \frac{15}{20}\)

So, to start with let's look at problem a. We want to find two numbers which are not the same so that when we multiply the numerator and denominator of 3/4 by the first number and multiple numerator and denominator of 4/5 by the second number both of the results have the same denominator. An easy way to do this is to use the denominator of second number for our first number to multiple by and the denominator of first number for our second number. In our case that would be use 5 (the denominator of 4/5) for our first number to multiple numerator and denominator of 3/4 (our first number) by. We did that in our example above. Now use 4 (the denominator of 3/4) for our second number so that we have
\(\displaystyle \frac{4}{5} = \frac{4*4}{4*5} = \frac{16}{20}\)

Since both fractions have the same denominator, the one with the largest numerator is the larger number. Thus
\(\displaystyle \frac{4}{5} > \frac{3}{4}\)