Question

Which statement is true?
12/13 < 36/30
13/17>24/28

Answer 1

The first one: 12/13 > 36/30

Explanation:

The first one would be correct as 12/13 is less than 36/30.

To explain why 13/17 is actually less than 24/28, see below:

So when comparing fractions, we must follow steps.

Step One: convert mixed numbers to a fraction, if there are any

There are not mixed numbers to compare, so we can move to the next step.

Step Two: find the least common denominator of the two fractions

Least common denominator = 476

Check out our least common denominator calculator for help on finding this.

Step Three: rewrite each fraction to an equivalent fraction using the denominator 476

To do this, start by dividing 476 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 476. Repeat this for the second fraction

364/476 408/476

Step Four: compare the numerators

At this point, to compare the fractions, we can simply compare the numerators to see which is larger

364<408

Step Five: rewrite each fraction as the original fraction

13/17<24/28

Therefore, the first statement (12/13 > 36/30) is true.

Answer 2

12/13 < 36/30

Explanation:

There are many ways to compare numbers. One way is to compare them to some value that lies between. Another is to consider their difference from a value that does not lie between.

12/13 vs 36/30

In the first fraction, 12 < 13, so the value of the fraction is less than 1:

12/13 < 1

In the second fraction, 36 > 30, so the value of the fraction is greater than 1:

1 < 36/30

Then the order of the fractions is ...

12/13 < 1 < 36/30

12/13 < 36/30 . . . . . the given order is True

13/17 vs 24/28

We notice the difference between numerator and denominator is 4 in each case, so we can write each fraction as a difference from 1:

(13/17) vs (24/28)

= (1 - 4/17) vs (1 -4/28) . . . . . fractions rewritten

= -4/17 vs -4/28 . . . . . . . . . subtract 1 from both

The first fraction, 4/17, has a smaller-value denominator, so its magnitude is larger than that of the fraction 4/28. In other words, the ordering of these fractions is ...

-4/17 < -4/28

1 -4/17 < 1 -4/28 . . . . . . add 1 to both sides

13/17 < 24/28 . . . . . the given order is False

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Additional comment

One sort of "no brainer" way to compare the fractions is to multiply them by the product of their denominators. This looks like "cross multiplication" where each numerator is multiplied by the opposite denominator. As long as you keep the numerators in the same relative places, the comparison symbol will be the correct one for the fractions.

12/13 vs 36/30 ⇒ (12·30) vs (13·36) ⇒ 360 < 468

The left fraction is smaller than the right fraction.

Similarly, ...

13/17 vs 24/28 ⇒ (13·28) vs (17·24) ⇒ 364 < 408

The left fraction is smaller than the right fraction.

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Here, we have used the fractions "as is." In each case, the fraction on the right could be reduced, possibly making the comparison easier.