Question

3/5 greater or least 7/10. I need to use compare fractions common numerator

Answer 1

We have the following fractions

`(3)/(5)\text{ and }(7)/(10)`

We know that if the denominators of two fractions are the same then the fraction with the largest numerator is the larger fraction.

Then, we need to convert the denominator of one fraction so they both have the same denominator. For instance, if we multiply and divide by 2 the first fraction, we have an equivalent fraction, that is,

`(3)/(5)=(3)/(5)*(2)/(2)=(6)/(10)`

This means that 3/5 is equivalent to 6/10 but in the last form 6/10 and 7/10 have the same denominator, so we can compare their numerators. In other words, we need to compare

`(6)/(10)\text{ and }(7)/(10)`

Since 7 is greater than 6 then:

`(3)/(5)<(7)/(10)`

Instead of converting 3/5, we can convert the fraction 7/10. If we multiply and divide 7/10 by 1/2, we have

`(7)/(10)=((7)/(2))/((10)/(2))=(3.5)/(5)`

Now, we can compare these fractions:

`\begin{gathered} (3)/(5)\text{ and }(3.5)/(5) \\ \sin ce\text{ 3.5 is greater that 3, then} \\ (3)/(5)<(7)/(10) \end{gathered}`