rewrite 11/25 and 9/20 then use <,=,>to order11/25 and9/20
common denonminator for 11/25 and9/20
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First, we need to find the least common multiple (LCM) of the two denominators, 25 and 20. The LCM is the smallest integer that both numbers divide into evenly (i.e. without any remainder). For 25 and 20, the LCM is 100.
11/25 = 44/100 (multiply the numerator and denominator by 4).
9/20 = 45/100 (multiply the numerator and denominator by 5).
Since 45/100 > 44/100, then:
9/20 > 11/25.
In order to figure out the order of fractions in this problem, the common denominator will be 100. So 11/25 equals 44/100 while 9/20 equals 45/100. So the order is 11/25 < 9/20. I hope this helps. The thing to remember with common demoninators is that you need to think about a number that goes into both denominators. Let us know if there is anything else we can do.
you want the least common denominator or the least common multiple(LCM)
to be a multiple of 25, the LCM must contain all of 25's factors (the two 5's)
so far we have LCM=5*5, but we are not done yet
the LCM must be a multiple of 20 also, so the LCM must contain all of 20's factors
the LCM must contain two 2's and a 5(20's factors)
But we only use the factors from 20 that we need, not the ones that we already have
we already have the 5 from 25, so we don't use the 5 from 20
however, we don't have the two 2's from 20
so we put in the two 2's as factors in the LCM: LCM=5*5*2*2=100
by the way, how do we know this is the LCM ?(least common multiple)
if we divide 100 by 20 we get 5 and if we divide 100 by 25 we get 4; 5 and 4 have no common factors except the number 1
11/25=44/100 and 9/20=45/100
45/100>44/100, so 9/20>11/25
by the way, if you ever get stuck for a common denominator you can always multiply the two denominators together but you will not necessarily get the LCM(you will get the LCM this way if the two numbers have no common factors !)
so if you multiply 25 and 20 you get 500
but now you are working with much larger numbers and therefore there is more chance of making an arithmetic mistake, so the best thing to do is find the LCM, but if you get stuck you can do this and at least solve the problem !!
1) Find least common multiple of 25 and 20.
25=5*5; 20=2*2*5; So they have 5 as a common factor, then 4 and 5 are co-factors, which are unique to those numbers. Least common multiple is 100, that is 25 times 4, co-factor for 20. Multiply both numerator and denominator of 11/25 by a co-factor for 20, that is 4. Do the same with 9/20, but use co-factor for 25, that is 5. You will obtain:
2) Compare two fractions. Obviously, 45/100 > 44/100, since 45>45 and denominators are the same.