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Mathematics · Fractions and decimals

Comparing and ordering fractions

Which is bigger, 3/5 or 2/3? Learn to compare and order fractions by making the denominators equal, by using unit fractions and one half as benchmarks, or by converting to decimals.

  • 20 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

On the school's running day, Zeynep ran 35\dfrac{3}{5} of the course and Kerem ran 23\dfrac{2}{3}. When the teacher blew the whistle, who was further ahead? Looking at the digits, Zeynep's numbers seem bigger. But with fractions, do bigger digits always mean a bigger amount?

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Ordering

Order the fractions

Put the cards in order by dragging them or by swapping them with the arrows, then press Check.

Prediction

Predict first

Do you think the largest of these fractions will be the one with the biggest numerator?

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Frequently asked

5 questions

The digits of 3/5 are bigger than those of 2/3, so why is 3/5 smaller?

The size of a fraction depends on how the numerator relates to the denominator, not on how big the digits are. With the common denominator 15, 3/5 = 9/15 and 2/3 = 10/15. Since 10/15 is bigger, 2/3 > 3/5.

If the numerators are equal, why is the fraction with the smaller denominator bigger?

With equal numerators you take the same number of parts in both fractions, but the parts are bigger when the denominator is smaller. Comparing 3/5 and 3/8, three fifths are more than three eighths.

Both 5/6 and 7/8 are one part short of a whole. Aren't they equal?

No, the missing parts are not the same size. 5/6 is 1/6 short of a whole, 7/8 is 1/8 short, and 1/8 is smaller. So 7/8, which is missing less, is bigger. Check: 5/6 = 20/24 and 7/8 = 21/24.

Can I estimate quickly without finding a common denominator?

Yes, use one half as a benchmark. 3/8 is less than a half and 5/8 is more than a half, so 3/8 < 5/8 without any calculation. Turning fractions into decimals also helps: 2/5 = 0.4 and 1/2 = 0.5.

Is a decimal with more digits always bigger?

No. Line up the place values and compare from the left. For 0.75 and 0.7, write 0.7 as 0.70; the tenths are equal and 5 > 0 in the hundredths, so 0.75 is bigger. But for 0.8 and 0.75, 8 > 7 in the tenths, so 0.8 is bigger.