# Percents

18.01.2019

Episode #3 of the course Everyday math by Jenn Schilling

Welcome to Day 3 of Everyday Math! Today, we will be learning about percents, the math behind them, and how they are used in everyday life.

The Math

A percent is actually a special type of ratio that tells us a quantity per (or out of) 100. The word percent has its roots in the Latin phrase, per centum, which means, “by the hundred,” so the word literally tells us the definition.

When finding the percent of a quantity—for example, 50% of 10—you multiply the quantity by the percent, represented either as a fraction or a decimal. To turn a percent into a fraction, the percent (e.g., 50) becomes the numerator and the denominator is always 100. So, 50% is 50/100. To turn a percent into a decimal, you basically divide the percent (e.g., 50) by 100, which means the decimal point needs to be moved to the left two times. So, 50% becomes 0.50 because the percent can be written as 50.00, and then the decimal point moves twice to the left to create 0.50. Now that we have represented our percent as a fraction or a decimal, we can multiply the quantity and the percent together. So, 50% of 10 is 10 × 0.5 = 5. This means that 50% of 10 is 5.

A useful rule to simplify percent calculations is that the percent and the quantity can be flipped and result in equivalent answers. For example, 4% of 50 is equivalent to 50% of 4. The first percent would be more challenging to calculate, but 50% of 4 is simpler because we can solve it by multiplying 4 and 0.50. We could also notice that 50% is equivalent to 1/2, and 1/2 of a number is quite simple to calculate: We just divide by 2. So, either by multiplying 4 by 0.50 or by dividing 4 by 2, we can find that 50% of 4 is 2, which means that 4% of 50 is also 2.

Everyday Applications

Percents are seen frequently in our everyday lives. First, percents are used in any kind of tax rate: sales tax, income tax, estate tax, etc. To calculate the sales tax on an item, you simply multiply the cost of the item and the decimal or fraction representation of the sales tax percent. For instance, the sales tax in Maryland is 6%, so for a purchase of \$20, the sales tax can be found by finding 6% of 20 or 20% of 6 (based on the useful rule above). To find 20% of 6, you would multiply 0.20 and 6, which would give you \$1.20. So, the sales tax would be \$1.20.

Percents are also seen in discounts and sales. Frequently, retailers offer a certain percent off coupons or sales. To find the discounted price, you compute the percentage discount and then subtract it from the original price. For example, suppose you have a coupon for 30% off your purchase, and you are going to spend \$50. The discount will be 30% of \$50, which we can calculate easily by taking 50% of \$30, so the discount will be \$15 (0.50 × 30 = 15). The total cost of the purchase will then be \$50 – \$15 = 35, because we subtract the discount from the original cost. To find a discount percent, you can divide the discounted price by the original price and then subtract that answer from 1. For example, 35 ÷ 50 = 0.7 and 1 – 0.7 = 0.3, or 30%.

Another place in which percents are used frequently is in personal finance and banking: the rate of return on investments, interest rates, etc. Interest rate calculations can become rather complex, depending on how interest is accrued and whether it is compounded. However, the percent portion of interest rates is treated exactly the same as in the previous examples, and an understanding of how percents can be calculated is immensely useful when diving into the more complex world of interest rates.

Tomorrow’s lesson will explore a topic we have already touched on a few times: fractions! Fractions are useful in all kinds of applications, including time, money, and cooking. Until then!

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