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Given two fractions we can compare which is larger if we express them using a common denominator.


Which fraction is larger?

2/3or 5/7

To determine this, let us write these fractions using a common denominator. We use 3*7=21 . Thus

2/3 = (2*7)/(3*7)=14/215/7=(5*3)/(7*3)=15/21

14/21 < 15/21,  hence,  2/3 < 5/7.

More Examples

We can see this clearly on a number line.

a positive number line

Just as for the whole numbers, is greater than means is to the right on the number line. Similarly , is less than means is to the left on the number line. Notice that 22/7 is greater than 2 1/4 because it is to the right on the number line. 4/5 is less than 7/4 and is to the left on the number line.


Choose which inequality or equality sign makes the statement true:



If a, d are both positive, there is an alternative method of solving these problems that does not involve computing a common denominator.

 a/b < c/d if and only if  a*d < b*c.

For example, 2/3 < 5/7, as 2*7 < 3*5.

Similarly,  a/b > c/d if and only if  a*d > b*c, and, as mentioned under Equivalent Fractions, a/b = c/d if and only if  a*d = b*c.


Using this method try some more exercises.



Look again at the number line, including negative fractions.

number line

When negative and positive fractions are compared, the situation is easy. Any positive number is greater than a negative number. This applies to fractions as well as integers. Positive numbers are always on the right on a number line and negative numbers on the left. For example ½ > −2¼.

When two negative fractions are compared using the common denominator method, the smaller numerator belongs to the greater fraction . For example −¼ > −¾ or −1/2 > −4/5 because −1/2 = -5/10 whereas −4/5 = -8/10. The same thing applies to negative mixed numbers. for example −1¼ > −3¾.


Now try some exercises where the fractions may be of either sign.




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