Difficult Fractions to Percentages

“In Henry’s orchard, 344 apples out of 3 467 were spoiled by hail. In Maria’s orchard, 4 567 out of 43 890 apples were spoiled. Whose orchard was worse affected?”

Discuss why the fractions of affected apples are 344/3467and 4567/43890. Turning both these into percentages (hundredths in effect) allows us to compare them directly. Now the issue is how to turn any fraction into a percentage.

A clever method is to recreate a division problem from which fractions might have been derived and then use the calculator:

344/ 3467 = 344 ÷ 3467 ≈ 0.0992212 and 4567/43890 = 4567 ÷ 43890 ≈  0.1040556.

The ability to round to three decimal places is now needed. Here the answers are 0.099 = 9.9% (1 dp) and 0.104 = 10.4% (1 dp). So Henry’s orchard suffers fractionally less damage.

Examples: Compare these situations by working out 1 dp percentages.

“The ACE Sweet Company makes a profit of $456,789 on sales of $4,366,888. The Triangle Lolly Company makes a profit of $45,677 on sales of $267,900. Which company is more profitable?”

“A survey of 1 461 days (4 years) shows it rains on 678 days in Circleton. A survey of 1 095 days (3 years) shows it rains on 431 days in Linetown. Which town is more rainy?”