Summary

The web content provides a comprehensive guide on mastering mental math for calculating percentages, particularly focusing on everyday applications such as tipping and shopping discounts.

Abstract

The article emphasizes the importance of mental math skills, specifically in handling percentages, which are commonly encountered in daily activities. It introduces a simple trick for calculating 10% of any number by moving the decimal point one position to the left. Building on this, the author explains how to calculate tips mentally for common percentages like 10%, 15%, and 20% using the base 10% value. Additionally, the article covers the application of mental math in calculating discounts while shopping, demonstrating how to estimate percentages like 10%, 25%, 30%, and 50% off items. The author, who learned these skills from their mother, advocates for the reader to achieve confidence and proficiency in mental calculations without relying on a calculator.

Opinions

The author is proud and enthusiastic about the mental math skills they have acquired and is eager to share these techniques with others.
There is a strong emphasis on the practicality and everyday utility of mental math, particularly for financial transactions.
The author believes that mastery of these mental math skills can lead to increased confidence in everyday situations, such as dining out or shopping.
The article suggests that these skills are not only useful but also teachable and accessible to anyone willing to learn.
The author values the ability to approximate and round numbers for practical purposes, highlighting the importance of estimation in mental math.
There is an underlying opinion that learning these skills can be enjoyable and rewarding, as evidenced by the author's personal anecdote of learning from their mother while shopping.

The Most Valuable Everyday Math Skill

mental math series, part 10

Percentages. They come up all the time, in the most casual places: shopping, dining out, grabbing a latte, checking grades, banking, taxes … that makes them the most valuable everyday math skill I can teach you.

I’m proud to say my mom taught me this trick when I was very young. We’d spend Saturdays shopping and she’d quiz me over and over, having me calculate the discounts mentally.

I cannot stress enough how much I want you to master this! The next time you’re out dining, I want you to fill in the tip on your receipt with confidence and gusto and without even one glance at your phone calculator. How’s that sound?

A Little Trick

A percent represents the portion per 100. So 15% means fifteen per one-hundred. Of course most of the time we are not taking a percentage of 100, but of a different value like 10% of 250.

The 10% Trick

To calculate 10% of a number, move the decimal point one position left.

Here are some examples to illustrate:

Note the decimal point is always immediately after the one’s place, even if not shown.

Why does this work?

Suppose we were calculating 10% of 250 long-hand. I would begin by rewriting 10% as 10/100 and multiplying.

Then I’d reduce 10/100 by canceling out factors of 10.

In Lesson Thirteen we learned that when dividing by 10 we move the decimal point one place to the left. So 10% of 250 is 25.

Calculating Restaurant Tips

Using the trick we can calculate common tip percentages of 10%, 15% and 20% mentally. Suppose your dinner bill comes to $48.50.

10% Tip Mentally

To find 10%, use the 10% trick.

15% Tip Mentally

To calculate 15% combine 10% and 5% of $48.50. Five percent is half of ten percent, so 5% of $48.50 will be half of 10% of $48.50.

Note I rounded $2.425 to the nearest penny, $2.43

For practical purposes you can approximate the tip, so feel free to round up to $2.50. Finally combine the 10 and 5 percent approximations.

This is only 22 cents away from the exact value of 15% of $48.50!

20% Tip Mentally

To find 20% double the 10 percent value.

Again we may wish to approximate instead.

Approximately 20% of $48.50 is $10.

Calculating Discounts

Another everyday scenario where you might encounter percents is while shopping. For example, suppose we have a sub-total of $168.75. Let’s calculate a variety of possible discounts.

10% off

First take 10 percent of $168.75.

Note we rounded $16.875 to the nearest penny, which is $16.88

Since it is 10% off, subtract $16.88 from $168.75. An estimate will suit our purposes so round $168.75 and $16.88 to the nearest dollar and subtract.

Our estimation is very close, only 13 cents over the exact answer.

25% off

Now let’s try 25% off. We have two options for finding 25% mentally:

25% is one-fourth of 100 percent, so we may divide our total by 4.
we may compose 25% by adding two 10%’s and one 5%.

Option One:

Since an estimate is suitable begin by rounding $168.75 to $170 and then use strategic division to divide $170 mentally.

Note: If you struggle to perform those divisions mentally, you may wish to split them into pieces and divide individually. For example, 170 = 160 + 10.

Likewise, $85 ÷ 2 can be split apart and divided individually by 2 to yield $42.50. Hence the total after discount is approximately $127.50.

Option Two:

Using this method we’ll compose 25% from 10% and 5%. First, approximate 10%.

Secondly, find 5% by dividing 10% in half.

Then combine two 17’s and 8.5 to obtain an approximation for 25%.

30% off

To calculate 30% add together three 10%’s. We’ve already approximated 10% of 168.75 as 17, so add three 17’s together.

Notice I added 17 in stages to make it easier to sum mentally

Therefore 30% off is $51 off and the total after discount is about $119.

Mentally, I subtract $51 by first subtracting the tens and then the ones

50% off

Fifty percent is half off. All we need to do is divide 170 by 2. Therefore the total after discount is $85.

That’s a great start! These techniques will aid you in most percentages you’ll experience day-to-day. In the next lesson, we’ll take a look at how to mentally calculate percentages to the exact percent.

Next Lesson: How to Tackle Difficult Percentages Mentally

Thanks for reading!

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