Percentage

Out of a hundred

Cut a whole square into 100 equal small squares, and color 40 of them. The colored part is 40 out of 100, the fraction $\frac{40}{100}$40/100.

A part out of a hundred has its own name. The word percent means out of a hundred, and it is written with the sign %. So $\frac{40}{100}$40/100 is written 40%, and it is read as forty percent.

40 of the 100 small squares are colored: $\frac{40}{100}$40/100, which is 40%.

Each small square is 1 of the 100, which is 1%. A quarter of the square is 25 small squares: $\frac{25}{100}$25/100, which is 25%.

Count the hundredths

The same 40% can be drawn on a bar. Cut the bar into 10 big parts, and cut each big part into 10 small pieces. That makes 10 × 10 = 100 small pieces.

Color 4 of the big parts. That is 4 × 10 = 40 small pieces out of 100, so the colored part is 40%. It is not 4%: a percent counts the small pieces out of 100, not the big parts out of 10.

4 of the 10 big parts are colored, and each big part holds 10 small pieces: 40 pieces out of 100, which is 40%.

The part that is left

The pieces that are not colored are a percentage of the whole too. 100 − 40 = 60 pieces are left white, so 60% is not colored.

The colored part and the white part together are all 100 pieces: 40% + 60% = 100%. 100% is the whole thing.

Halves and quarters as percentages

Half of 100 small squares is 50 squares, so one half is 50%. A quarter of 100 is 25, so one quarter is 25%. Three quarters is 75%.

Half of the square is colored: 50 of the 100 small squares, which is 50%.

Comparing percentages

Every percentage is out of the same number, 100, so percentages are easy to compare. 65% is more than 60%, because 65 hundredths is more than 60 hundredths. A score of 72 out of 100 on a test is 72%.