How to determine which fraction is greater than the other

This topic can be a tiny challenging, so stop walk with it one action at a time. We’re talking around relationships in between numbers.

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The very first thing we"ll deal with is how to identify which of two fractions is greater than the other. If 2 fractions have actually the very same denominator, the fraction with the better numerator is the greater one.


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For example, the denominators of ???2/7??? and also ???5/7??? space equal, and also the molecule ???5??? is greater than the numerator ???2???, for this reason ???5/7??? is better than ???2/7???.

If the denominators of two fractions room different, us can"t compare them directly; we an initial have to uncover a usual denominator. For example, consider ???5/8??? and also ???2/3???. Because that a common denominator, we"ll usage the least common multiple the the denominators ???8??? and also ???3???, which is ???24???. So

???frac58=frac58left(frac33 ight)=frac5 imes38 imes3=frac1524???

???frac23=frac23left(frac88 ight)=frac2 imes83 imes8=frac1624???

The fountain ???15/24??? and ???16/24??? are identical to ???5/8??? and ???2/3???, respectively. Since they have actually the very same denominator ???24???, thefraction v the better numerator is higher than the portion with the lessernumerator. Therefore, ???16/24??? is greater than ???15/24???, which means that???2/3??? is higher than ???5/8???, or we can say ???5/8??? is much less than ???2/3???.

Now stop talk around the relationship in between two integers - in particular, how we can discover the number it is a portion of the distance (along the number line) from the smaller integer come the bigger one. Let’s say we’re thinking around the integers ???3??? and ???8???. We understand that ???3??? is 5 units to the left the ???8???, or the ???8??? is five units come the right of ???3???. In other words, they’re five units apart, because ???8-3=5???.

Now what if ns asked friend what number is two-fifths the the way from ???3??? come ???8???? What I’m questioning is, “If I division the distance in between ???3??? and ???8??? into 5 equal pieces, and then I begin from ???3??? and move toward ???8??? by 2 of those five equal pieces, where carry out I end up?”

Here’s just how we number that out. An initial we discover the distance in between ???3??? and ???8??? by individually the smaller sized number from the bigger number.

???8-3=5???

The distance in between ???3??? and ???8??? is ???5???. Now, because we’re looking to walk two-fifths of that distance, we desire to first divide the distance ???5??? into five equal piece (each of i m sorry is one-fifth of the distance), i m sorry we do by separating ???5??? through ???5???.

???frac55=1???

So one-fifth that the ???5??? units of distance in between ???3??? and also ???8??? is ???1??? unit. Since I desire two-fifths of the distance between ???3??? and ???8???, I should multiply ???1??? unit by ???2???, and also I get ???2??? units, so two-fifths the the distance in between ???3??? and also ???8??? is ???2???. This way that if we want to walk two-fifths of the means from ???3??? come ???8???, we start at ???3???, and add ???2???, and also we end up at

???3+2=5???

So the number it is two-fifths that the way from ???3??? to ???8??? is ???5???.

In general, once we have some portion “of” an additional number, it way we must multiply the portion by the various other number. Because that example, ???2/3???of ???6??? is

???frac23cdot6=frac23cdotfrac61=frac2cdot63cdot1=frac123=4???

Therefore, us say that ???2/3??? of ???6??? is ???4???, or that two-thirds that ???6??? is ???4???.

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Now we can also do this through fractions. The procedure is exactly the same; we’re just dealing with fractions instead of integers.