Fractions

Compare Fractions

Decide which is larger: 3/5 or 7/10. Find the LCD of 5 and 10, convert 3/5 to 6/10, then compare 6/10 and 7/10 directly. Because 6 < 7, we get 3/5 < 7/10.

Example

Compare 3/5 and 7/10 by rewriting with a common denominator.

highlighted = computed this step

Step 1 — Set up

Set up the fraction expression.

35710\frac{3}{5} \quad \frac{7}{10}
Start with the two fractions3/57/10

Step 2 — Find LCD

Find a common denominator: LCD(5, 10) = 10.

LCD(5,10)=10\mathrm{LCD}( 5 , 10 )= \hl{10}
Use common denominator 103/57/10

Step 3 — Convert left fraction

Convert the left fraction by multiplying by 2 over 2.

35×22=610\frac{3}{5} \times \frac{2}{2} = \hlmath{\frac{6}{10}}
Convert 3/5 to 6/106/107/10

Step 4 — Convert right fraction

Convert the right fraction by multiplying by 1 over 1.

710×11=710\frac{7}{10} \times \frac{1}{1} = \hlmath{\frac{7}{10}}
Convert 7/10 to 7/106/107/10

Step 5 — Compare numerators

Compare the numerators: 6 and 7.

610<710\hlmath{\frac{6}{10}} < \hlmath{\frac{7}{10}}
Compare shaded parts out of 106/107/106 < 7, so left is smaller

Step 6 — Result

Read the final result.

35<710\frac{3}{5} < \frac{7}{10}
3/5 is less than 7/106/107/106 < 7, so left is smaller
common-denominator Two fractions can be compared only when they have the same denominator. Convert one or both fractions to equivalent ones using the LCD, then compare numerators. The fraction with the larger numerator is greater.