Question

example
there are 500 students who participate in an after - school sports program. of these students, 25% play field hockey. how many students play field hockey?
you can use a model to find 25% of 500.
the model shows 500 divided into 4 groups of 125. each group of 125 represents 25% of 500. this means that 25% of 500 is 125.
there are 125 students who play field hockey.
1 a. what is 25% written as a fraction?
b. what is 25% written as a decimal?
c. write and evaluate a multiplication expression that represents 25% of 500.

Explanation:

a.

Step1: Convert percentage to fraction

Percent means "per hundred". So \(25\%=\frac{25}{100}\). Then simplify the fraction by dividing both numerator and denominator by their greatest - common divisor (GCD). The GCD of 25 and 100 is 25. \(\frac{25\div25}{100\div25}=\frac{1}{4}\)

b.

Step1: Convert percentage to decimal

To convert a percentage to a decimal, divide the percentage value by 100. For \(25\%\), we have \(25\div100 = 0.25\)

c.

Step1: Write the multiplication expression

Since "of" in percentage problems means multiplication. If we want to find \(25\%\) of 500, and using the fraction form of \(25\%\) (\(\frac{1}{4}\)), the expression is \(\frac{1}{4}\times500\). Using the decimal form of \(25\%\) (0.25), the expression is \(0.25\times500\)

Step2: Evaluate the expression

Using the fraction: \(\frac{1}{4}\times500=\frac{500}{4}=125\)
Using the decimal: \(0.25\times500=( \frac{25}{100})\times500=\frac{25\times500}{100}=\frac{12500}{100}=125\)

Answer:

a. \(25\%=\frac{1}{4}\)
b. \(25\% = 0.25\)
c. The multiplication expressions are \(\frac{1}{4}\times500\) or \(0.25\times500\), and their values are \(125\)