Comparing Fractions 2

Fractions

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Comparing Fractions 2 Comparing Fractions

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Comparing Fractions 2

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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

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