Mathnasium #MathTricks: Special Percents (Advanced)

Dec 7, 2022

Welcome to Mathnasium’s Math Tricks series. Today we are finding the percentage amount of any number by breaking it apart and using special percents.

In an earlier Mathnasium Math Trick we used special percents because they represent easy-to-calculate amounts. We can use the same strategy to calculate seemingly complex percents by decomposing them into easy-to-calculate parts.

Recall these special percents:

0% means “none of it”
1% means “1 for each 100”
10% means “10 for each 100”
25% means “a quarter of it”
50% means “half of it”
33¹⁄₃% means “a third of it”
66²⁄₃% means “two-thirds of it”
75% means “three-quarters of it”
150% means “all of it and half of it”
100% means “all of it”
200% means “all of it, twice”

Use the special percents above and follow the examples below to find the percentage amounts.

Example 1: Find 126% of 836.

Step 1: Break apart the percent into manageable parts.
126% is equal to 100% + 25% + 1%.

Step 2: Find each part.
100% of 836 is all of it, which is 836.
25% of 836 is a quarter of it, which is 209.
1% of 836 is one for each hundred, which is 8.36.

Step 3: Calculate the total.
836 + 209 + 8.36 = 1,053.36

Answer: 1,053.36.

Example 2: A $30 item is on sale for 15% off. Find its sale price.

Step 1: Break apart the percent into manageable parts.
15% off means the sale price will be 85% of the original price.
85% is equal to 100% - 10% - 5%.

Step 2: Find each part.
100% of 30 is all of it, which is 30.
10% of 30 is ten for each hundred, which is 3.
5% of 30 is one half of 10% of 30, which is 1.5.

Step 3: Calculate the total.
30 - 3 - 1.5 = 25.5

Answer: $25.50.

Now, with this strategy, you are ready to use this Mathnasium Math Trick to find the percent of any number by breaking apart the percent and using your knowledge of special percents. Click here for more practice problems, then check your answers here.

If you missed this, or any of our other Math Tricks videos, check them out on our YouTube channel!