# Kai calculates that he spends 75 minutes of a school day in science class. If he spends 500 minutes in school, what percent of his school day does Kai spend in science class?

May 15, 2018

15%.

#### Explanation:

The minutes in science class over total minutes gives the decimal .15. Move the decimal two places to the right to get the percentage. Thus:

75/500 = .15= 15%

May 15, 2018

15%

#### Explanation:

$\textcolor{b l u e}{\text{The teaching bit}}$

Percentage is basically a special fraction. What makes it special is that the denominator (bottom number) is always 100.

The other way of writing percentage is to use the symbol %.

This symbol behaves like a unit of measurement but one that is
worth $\times \frac{1}{100}$ including the multiplication sign.

Example: Consider say 30%. This is the same as
$30 \times \frac{1}{100} = \frac{30 \times 1}{100} = \frac{30}{100}$
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$\textcolor{b l u e}{\text{Answering the question}}$

The given fraction in the question is: $\left(\text{time in class")/("time in school}\right) \to \frac{75}{500}$

Note that the units for the bottom number is the same as the units for the top number ie minutes.

But we need the bottom number to be 100.

For multiply or divide what we do to the bottom we also do to the top if we wish to retain the proportional relationship.

$\frac{75 \div 5}{500 \div 5} = \frac{15}{100}$

15/100 = 15xx1/100 = 15%