How to Tackle Difficult Percentages Mentally
mental math series, part 11
By the end of this article you’ll have the tools to calculate percentages mentally. So leave that calculator at home and take the challenge! But first we need to add another technique to our arsenal.
The 1% Trick
To calculate 1% of a number, move the decimal point two positions left.
Here are some illustrative examples:
Let’s quickly look at why the 1% Trick works by taking 1% of 250 long-hand.
Begin by rewriting 1 percent as 1/100 and performing the multiplication.
Whenever we divide by 100, we move the decimal point two places left.
Therefore, you can always move the decimal point two places left to find 1 percent.
Alright, you’re set! Now let’s try some problems.
I grew up in Washington state and our sales tax was about 8.5%. Let’s say I am purchasing an item that costs $39.95 and would like to know how much sales tax I’ll be paying.
Let’s begin by taking 10% of $39.95. Using the 10% Trick from last lesson, simply move the decimal point one position left.
At this point I know that the tax on my item will be less than $4. Suppose I want a more exact estimate. I could utilize the 1% Trick to get closer to 8.5%.
Now take 1% of $39.95.
If I subtract the 1% value from the 10% value, I will have 9% of $39.95.
That’s a pretty good estimation, but I can get even closer. I now know that 1% of $39.95 is 40 cents, if I cut this in half I can determine what 0.5% of $39.95 is.
Lastly I will subtract 20 cents from $3.60 to obtain exactly 8.5% of $39.95.
So 8.5% of $39.95 is exactly $3.40.
Pretty nifty isn’t it? With practice you’ll be surprised by how much you can do mentally!
Suppose you invest $12,000 in a Certificate of Deposit that has an interest rate of 2.5% and plan to leave it for 5 years. Let’s calculate how much money you would earn on your investment.
For our purpose this investment is collecting simple interest. Although in real life, interest is usually compounded.
Compounding is the process of adding the amount you earn (or are charged) back into the principal (the amount you invested or borrowed) before the next time interest is calculated. This requires a more advanced formula than we’re ready for, so we’ll stick to simple interest today.
To compute simple interest, multiply the principal, interest rate and time in years together.
- the principal = $12,000
- the interest rate = 2.5%
- the time = 5 years
We could enter this in a calculator, but that wouldn’t be practicing our mental math skills. So instead, begin by taking 2.5% of $12,000 mentally.
Step one: Find 1% of 12,000. Using the 1% Trick move the decimal point two digits left to yield $120.
Step two: Since 2% is twice that amount of 1%, double our previous answer.
Step three: To find 2.5% we need to find what half a percent is and add it to 2%. To obtain 0.5% divide the value for 1% by two.
After adding together the values for 2% and 0.5%, we have calculated that 2.5% of 12,000 is 300.
Step four: Now that we have 2.5% of 12,000 all that is left is to multiply by the number of years, which is five.
To do this mentally, split 300 into 3 x 100. Then multiply 5 x 3 together first, followed by 100.
Your investment will earn $1,500 in its lifetime.
And you could calculate it mentally while talking to your banker! How fancy!
Next Lesson: Understanding Common Core Number Bonds for Parents
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