The concept of percentages

The concept of percentages

Percentage is a number expressed as parts of 100. For example, 20 percent means 20 parts of a whole object divided into 100 equal parts which in short form is written as $\frac{20}{100}$. Percentage is denoted by a symbol % which is written on the right side of a number. For instance, 10 percent is written as 10%, which means 10 parts of 100 equal parts of a whole.

Figure consists of 25 rectangles of which 10 rectangles are shaded while 15 rectangles are unshaded.

1. What is the percentage of the shaded rectangles?
2. If there are 80 rectangles of which 40 rectangles are shaded, what is the percentage of the shaded part?

Figure: A diagram of 25 rectangles with 10 shaded parts

Solution

1. What is the percentage of the shaded rectangles?

   There are 10 shaded rectangles out of 25, which in fraction is $\frac{10}{25}$.

   In order to obtain the percentage of the shaded rectangles, convert the fraction such that the denominator becomes 100. To do this, multiply both the numerator and the denominator by 4. Thus, the numerator becomes 40 and the denominator becomes 100. The procedure is summarized as follows:

   $\frac{10}{25} = \frac{10 \times 4}{25 \times 4} = \frac{40}{100} = 40\%$

   Alternatively, multiply the fraction $\frac{10}{25}$ by 100 percent as follows:

   $\frac{10}{25} \times 100\% = 40\%$

   Therefore, the shaded rectangles is forty percent and it is written as 40%.

2. If there are 80 rectangles of which 40 rectangles are shaded, what is the percentage of the shaded part?

   Similarly, if there are 80 rectangles of which 40 of the rectangles are shaded, this is the same as 50 percent. That is, find a number which when multiplied by the denominator, which is 80, gives 100. This number is 1.25. Multiply both the numerator and the denominator by 1.25 as follows:

   $\frac{40}{80} = \frac{40 \times 1.25}{80 \times 1.25} = \frac{50}{100} = 50\%$

   Alternatively, it can be simply done by taking $\frac{40}{80} \times 100\% = 50\%$.

   Therefore, the shaded rectangles is 50 percent, that is 50%.