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
d. compare your answer to problem 1c to the answer in the example.

Explanation:

Step1: Convert percentage to fraction

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

Step2: Convert percentage to decimal

To convert a percentage to a decimal, divide the percentage value by 100. \(25\%=\frac{25}{100}=0.25\)

Step3: Write and evaluate the multiplication expression

We can use either the fraction form or the decimal form of the percentage.

• Using the fraction form: \(25\%\text{ of }500=\frac{1}{4}\times500=\frac{500}{4} = 125\)
• Using the decimal form: \(25\%\text{ of }500=0.25\times500=(0.2\times500)+(0.05\times500)=100 + 25=125\)

Step4: Compare the answers

In the example, it is shown that \(25\%\text{ of }500 = 125\). In part (c), when we calculate using the fraction \(\frac{1}{4}\times500\) or the decimal \(0.25\times500\), we also get 125. So, the answer in part (c) is the same as the answer in the example.

Answer:

a. \(\frac{1}{4}\)
b. \(0.25\)
c. Using the fraction: \(\frac{1}{4}\times500 = 125\); Using the decimal: \(0.25\times500=125\)
d. The answer in part (c) is the same as the answer in the example.