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Basic Math/comparing fractions


The new Common Core Standards are requiring student to find the common numerator now. I am unfamiliar with this since I was only taught to find the common denominator. Third graders are supposed to be comparing fractions by finding a common numerator. How do I teach this to my students?

Hello, Avery.

If two fractions have common numerators, then the bigger fraction will have the larger numerator. 9/4 is a larger fraction than 9/7, because, as you know, 4 can divide into 9 more times than 7 can divide into 9.

So, it's easy to compare fractions by numerators if they already have the same numerator, as shown in the above example.

If the numerators are not the same, then you need to make them the same. If you have, say, 9/2 and 3/5, then the easiest thing to do is multiply the 3 in 3/5 by 3, giving you 9/15 (obviously you must also multiply the denominator by 3).

Now, you have 9/2 and 9/15, so you can compare numerators. 9/2, of course, will yield a higher number than 9/15.

(Essentially, when comparing fractions with common numerators, the fraction with the lower (positive) denominator will be greater; when comparing fractions with common denominators, the fraction with the larger numerator will be greater.)

Hope this helps.


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John Zalewski


I can help you solve problems involving fractions, decimals, ratios, and algebra. I can teach you how to do math faster, and even in your head. I can teach math definitions, and help you study, if necessary. Please do not ask any graphing, trigonometry, or calculus questions. Try to work through homework questions before asking for assistance.


I routinely process numbers of all kinds in my head, without need of a calculator.

I was an A math student while in high school.

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