How do you find the smallest fraction

I need to find out quickly in about a minute the smallest of these fractions. I am not allowed to use a calculator, though a little rough calculation is allowed.

As I see the problem, without a calculator, converting these to decimal values is not an option. Moreover, since the numbers involved are fairly large, finding the least common denominator and changing each fraction to make their denominators the same as the least common denominator is again next to impossible without a calculator.

For the same reason, we can not try the method of making the numerators identical. If we try the approximate method of changing the numerators and denominators to easy numbers, we can get something like this:.

The biggest reciprocal should correspond to the smallest number. Multiplication isn't too slow. Now pick your favourite fraction, compare it against another, discarding the larger.

You need 4 comparisons to check which is smallest. Each comparison requires 2 multiplications. I understand that 7. Stacy Blackman Consulting. Prep MBA. Compare All. ARLee Consulting. August Academy. Experts' Global. Fortuna Admissions.

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Learn Spelling Spelling 1st Grade. Spelling 2nd Grade. Spelling 3rd Grade. If one cross-product is larger than the other, then the fraction next to that cross-product is also larger than the other fraction. Remember, always write the cross-product next to the fraction whose top number you used.

Understand why this works. To compare two fractions, typically you transform them to give them the same denominator, or lower part of the fraction. Secretly, this is what cross-multiplication does! Method 3. Use this for fractions with a top number equal or larger than the bottom number. If a fraction has a top number, or numerator , that is larger than the bottom number, or denominator , it is larger than one. Both of these fractions are examples of improper fractions.

This method helps these fractions make sense, however, and might be faster. Convert each improper fraction into a mixed number. Turn them into a mix of whole numbers and fractions. Sometimes, you might be able to do this in your head. Other times, use long division to find out how many times the numerator goes evenly into the denominator. The remainder in that long division problem, if any, gets "left over" as a fraction.

Sort the mixed numbers by whole number. Now that there are no improper fractions, you have a better idea of how large each number is. If necessary, compare the fractions in each group. You can use any of the methods in the other sections to do this. Use your results to sort your whole list of mixed numbers.

Convert the mixed numbers back to their original fractions. David Jia Academic Tutor. David Jia. Look for a common denominator between the fractions, then multiply the numerators and denominators by the same value.

Then you can see which fraction is greater just by the numerator. Not Helpful 2 Helpful 5. Jasmine Tipping. Not Helpful 44 Helpful Yes you can, the order will be the same. Just make sure to convert back to fractions for your final answer if the original numbers are given as fractions. Not Helpful 30 Helpful How do I order fractions from least to greatest if the denominators are different?

Make them the same by multiplying both the numerator and the denominator of the smallest fraction, and if necessary, the largest one as well. Not Helpful 29 Helpful