
Use < , > , = to compare the two fractions 21/28

and 6/9. So there is a buch of ways to do this.

The easiest way is if they have the same

denominator, we can compare the numerators.

Unfortunately we do not have the same denominators

So we could do is we could find common denominators

for both the fractions and convert both the fractions

to have common denominators and compare the

numerators.Or even more simply we can

simplify them first and then try do it.

So 21/28 , they are both divisibley by 7.

Let us divide the numerator & denominator by 7

21 divide by 7 & 28 divide by 7.

Since we are dividing both by 7, we are not changing

the value of the fraction 21 ÷ 7 = 3

28 ÷ 7 = 4.

So 21/28 = 3/4.

Lets us do the same thing for 6/9

6 & 9 are both divisible by 3

So lets divide both 6 & 9 by 3

6 ÷ 3 = 2

9 ÷ 3 = 3

21/28 = 3/4

6/9 = 2/3

So we really can compare 3/4 & 2/3.

The real benefit of doing this, it is easy to find

common denominators for this than 28 &9

which means we need to multiply larger numbers

here we have smaller numbers.

the common denominator of 3/4 & 2/3 is the LCM

of 4 & 3.

4 & 3 does not share any prime factors with each other

so LCM of 4 & 3 is the product of the 2 numbers

3/4 = /12

2/3 = /12

I got 12 by multiplying 3 & 4 as they have no

common factors. another way to think is

prime factorization of 4 = 2x2

3 is already a prime number, so prime factorization

of 3 is 3.

The number that has all prime factors of 4 & 3 is 2,2 & 3

2x2x3 = 12.This is how we get LCM

to get from 4 to 12 ,you got to multiply 3

We multiply denominator by 3 to get 12

We need to multiply the numerator by 3

3 x 3 = 9

To get from 3 to 12, we multiply denominator by 4

We also have to multiply numerator by 4

4 x 2 = 8

21/28 = 3/4 = 9/12

6/9 = 2/3 = 8/12

Which of these is a greater fraction.

Since we have common denominator, we need to

look at the numerator. We know 9 > 8

So, 21/28 > 6/9

And we are done.

Another way to do is

we need not simply it. just do it for fun.

If we did not simplify it 21/28 & 6/9

LCM of 28 & 9

prime factorization of 28 = 2x2x7

Prime factorization of 9 = 3x3

The LCM of 28 & 9 must contain 2x2x3x3x7

which is esentially 28x9 = 252

The common denominator is going to be 252

To go from 28 to 252 we had to

multiply 28 by 9 ; 28 x 9

So we also have to multiply numerator by 9

21x9 = 189

To go from 9 to 252

we need to multiply by 28.

So we need to multiply numerator by 28

So 6x28 = 168

Now we have a common denominator here

and we can compare the numerator.

189 > 168

So 21/28 > 6/9