Comparing scores using percentages

The idea

Quantities measured out of different totals are compared by converting each to a percentage of its own total, which puts them all on the common base of 100.

Who did better, and in which test?

Eesha scored 42 out of 50 in English and 70 out of 80 in Science. She lost only 8 marks in English and 10 in Science, so she says English was better. Reema says Science, as 70 is more than 42. Vishu says the totals are different, so we cannot compare.

What should we do to compare the two tests?

• Compare the marks lost: 8 and 10
• Compare the marks scored: 42 and 70
• Put both on the same total first

Put both scores on a base of 100

In Marks view the bars are as long as the totals, so they are not the same size. Switch to Out of 100 and compare. Then change the marks and find the three things in the goal.

The common base of 100

Quantities measured out of different totals are compared by converting each to a percentage of its own total, which puts them all on the common base of 100.

Eesha's scores as percentages: English: 42/50 × 100 = 84% Science: 70/80 × 100 = 87.5% The Science score is higher, so Eesha did better in Science.

The same idea works on food labels. If 99 out of 150 parts of a drink mix are sugar, the sugar share is 99/150 × 100 = 66% Percentages make two products easy to compare.

Notes

Quantities measured out of different totals are compared by converting each to a percentage of its own total, which puts them all on the common base of 100.

Check yourself

Mira scored 36 out of 40 in Maths. What is that as a percentage?

Answer: 90 %

36/40 × 100 = 90%.

Mira scored 51 out of 60 in Hindi. What is that as a percentage?

Answer: 85 %

51/60 × 100 = 85%.

Mira scored 36 out of 40 in Maths and 51 out of 60 in Hindi. In which subject did she do better?

Anu scored 30 out of 40 and Binu scored 45 out of 60. Who did better?

• Maths: 90% against 85% — correct. Yes! 36 out of 40 is 90%, and 51 out of 60 is 85%, so Maths is better.
• Hindi, because 51 is more than 36. The totals are different (40 and 60), so the marks cannot be compared directly. As percentages: Maths 90%, Hindi 85%.
• Hindi, because the total 60 is bigger. A bigger total does not mean a better score. Compare the percentages: Maths 90%, Hindi 85%.
• Neither: both scored 75% — correct. Yes! 30 out of 40 is 75%, and 45 out of 60 is 75%. The scores look different, but they are equal on the base of 100.
• Binu, because 45 is more than 30. The totals are different (60 and 40). As percentages, Anu has 75% (30 out of 40) and Binu has 75% (45 out of 60).
• Anu, because she lost only 10 marks. Binu lost 15 marks, but out of a bigger total. As percentages, both have 75%.