Percentages are probably one of the most widely used mathematical concepts in everyday life. You will see percentages almost everywhere. Tax on a purchase, tip in a restaurant, discount in a store – are all percentages. Interest rates are also usually expressed as percentages, be it on a loan, a credit card, an investment, or a mortgage. Although percentages are important for understanding the financial aspects of everyday life, many people perceive them as hard and rely on technology to calculate them.
The word “percent” is a Latin word that means “out of one hundred”. This means that we are talking of a whole-to-part ratio with 100 being the whole. Ratios are a generalization of fractions, and if you know how to calculate a fraction of a number, you can calculate a percentage of a number as well.
In one episode of JUMP Math’s new, Mighton Math Minute video series, JUMP Math Founder, Dr. John Mighton explains how to understand interest rates through learning about percentages and fractions. In the video, he offers some fun examples of how to find fractions and percentages of numbers, using the idea of sharing cookies on plates, he explains how to find one-fifth of 20.
Let’s see how you can find 1/100 of a number. We divide the number by 100. That is 1% of the number. How do you find 13% of the number? Divide by 100 and multiply the result by 13.
Now let’s apply the procedure to other examples of everyday life:
Sales Tax (like Goods and Services Tax, GST)
When you go shopping for any goods, you pay a percentage towards tax. Let’s calculate the tax on a pair of sandals that cost $70 with the following steps:
Step 1. Calculate 1% of $70: 70 ÷ 100 = 0.70. (You can shift the decimal point two places to the left to divide by 100. Why? We will explain it in one of the later posts.)
Step 2. Calculate 13% of $70 by multiplying the previous result by 13. How? 13 = 10 + 3, so to multiply by 13, you multiply the number by 10 and multiply the number by 3, then add the results:
10+ 3
0.70 x 10 + 0.7 x 3
13
$0.70 × 13 = $0.70 × 10 + $0.70 × 3
= $7 + $2.10
= $9.10.
So, with the sales tax, your sandals are going to cost $70 +$9.10 = $79.09
Restaurant Tipping
Another common example of calculating percentage is giving a tip at a restaurant. Let’s say you want to give 20% tip on a meal that cost $35. Percentages that are multiples of 10 are even easier to calculate that regular percentages. This time, you want to calculate 10%, or 10/100. Since 10/100 is equivalent to 1/10 (divide the numerator and the denominator by the same number, 10, to make the equivalent fraction), you need to divide the original number by 10. So:
10% of $35 = 1/10 of $35 = $35 ÷ 10 = $3.50
20% of $35 = 2 × 10% = 2 × $3.50 = $7.00
Therefore, your tip is $7, and you can leave a fiver and a toonie as your tip.
Discounts
When you go shopping, you see a lot of stores having seasonal sales. Sales and discounts are percentages too. Let’s say you have a 30% discount on a notebook that usually costs $499. Well, if there is a 30% discount, this means that you are paying 70% of the price. Again, first calculate 10% (meaning, $499 ÷ 10 = $49.90) and multiply it by 7. You can do it in your head by multiplying $50 × 7 and adjusting:
$49.90 = $50 – $0.10,
7 × $49.90 = 7 × $50 + 7 × $0.10
= $350 – $0.70
= $349.30
In this case, you most likely are also going to pay tax on the $349.30, so we are back to the initial calculation:
1% of $349.90 is about 1% of $350 = $3.50
13% of $350 = 13 × $3.50
= 10 × $3.50 + 3 × $3.50
= $35.00 + $10.50
= $40.50.
You would need to adjust for the rounding up by 70 cents, which is about $0.10, so the tax you are paying will be $40.40, and the total cost of the notebook is $349.30 + $40.40 = $389.70
As you can see, percentages are used in many different aspects of our daily lives. By understanding how to calculate percentages, we can make better decisions, solve problems more effectively, and communicate information more accurately.
JUMP Math offers a curriculum-aligned student Assessment & Practice resource that is backed by research on how children learn best. Check out our student resources:https://jumpmath.org/ca/shop
You can understand interest rates through learning about more about percentages. Watch this episode of the Mighton Math Minute video series to learn more: Episode 4 – Being Financially Literate Matters.
