Rule #1
When two fractions have the same denominator, the bigger fraction is the one with the bigger numerator.
Rule # 2
When comparing fractions that have the same numerator, the bigger fraction is the one with the smaller denominator.
Rule # 3
You can convert the fractions and then just put the greater than, less than or equal to sign to see what the comparison is between the fractions.
You can use the same symbols that you use to compare integers or decimals: equal, greater than, greater-than-or-equal, etc.
Cause they did
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
what the heck
You can convert them to equivalent fractions with like denominators, then simply compare the numerators.You might also convert each fraction to a decimal (divide the numerator by the denominator); then you can also compare them.
Because decimals are a form you use regularly like with money, but with fractions, its not used all the time such as a decimal is used.
When the numbers are greater than 1
In order to multiply fractions with variables, factor all numerators and denominators completely. Use the rules for multiplying and dividing fractions, cancel any common factors, and leave your final answer in factored form.
As fractions are numbers you would use the same methods as any other comparison or ordering of numbers. Largest to smallest or smallest to largest are the most likely ways
Assuming the fractions are "normalized" (the fractional part is less than 1): First compare the integer part. If the integer part is the same, you need to compare the fractions. If the denominator of the fractions is different, you have to convert to a common denominator. The simplest way to find a common denominator is to multiply both denominators (i.e., you don't need the LEAST common denominator - any common denominator will do).
If the fractions have different denominators, you need to: 1) Convert to equivalent fractions with a common denominator, 2) Compare the numerators. If the fractions already have the same denominator, there is no need for the first step - which happens to be the most difficult step. Note that as a shortcut, you don't need the LEAST common denominator, any denominator can do. Thus, you can just use the product of the two denominators as the common denominator. As a result, to compare the fractions, you simply multiply the numerator of each fraction by the denominator of the other one, and then compare. However, this is still more work than simply comparing two numbers.
You can use the same symbols that you use to compare integers or decimals: equal, greater than, greater-than-or-equal, etc.
You draw each of the fractions on the number line, and see which one is more to the right, i.e., greater. Please note that plotting the exact position of fractions this way is a bit imprecise - it is more exact to convert the fractions to a common denominator.
In a practical sense, sometimes it is better to have whole units rather than just pure fractions. it gives a better idea of "how big" is the thing. Having only fractions could be hard to compare (and thus make decisions based on those measurements)
72
You can use the same notation and ordering for fractions as you do integers. The difficulty with fractions is that in most cases you need to find eqivalent denominators to see how they rank. Ie. If I said order for smallest to largest 2/3, 1/6, 72/96 and 24/48. It would be difficult without finding some similar base (is 2/3>72/96?). Instead if you conver them into a common base... 8/12, 2/12, 9/12, 6/12. Now you can easily order and/or compare the fractions.