Mastering Percentage Calculations with Ease and Speed
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Introduction to Percentages
Percentages are a common element in our daily lives, especially in financial contexts and statistical reports across various fields, including sports and politics. For instance, a glance at my screen reveals that the 'FTSE 250' index has dropped by 0.43% today.
While percentages are frequently mentioned, we often lack the context of the new value that corresponds to this change. Understanding the percentage change is vital, but knowing the new amount is also essential. This guide will illustrate how to derive the new figure from a percentage change.
In a subsequent article, I will address how to reverse-engineer the calculation to determine the percentage change itself.
Step 1: Choose Your Calculation Method
Let’s consider calculating x% of y. We can utilize a key property of percentages:
For example, determining 50% of 7 yields 3.5, and conversely, finding 7% of 50 also results in 3.5. It’s straightforward to compute 50% of 7, as it’s simply half of 7. This initial judgment of which option seems simpler is crucial.
For clarity, we will use the example of finding 26% of 188. Alternatively, we could calculate 188% of 26, but the first option appears more manageable.
Step 2: Decompose the Percentage
Originating from the term ‘cent’ meaning one hundred, a percentage signifies parts per hundred. Therefore, 50% can be viewed as 50 hundredths, or one half.
We will leverage this to our advantage. To find 26% of 188, we could divide 188 by 100 and then multiply by 26, resulting in 1.88 * 26, which can be cumbersome. Instead, we will identify simpler percentages that cumulatively add up to 26%.
What constitutes an easy percentage? It is one that can be quickly calculated through division. Here are some examples:
To determine 25% of a figure, simply divide by 4. To find 15%, you can divide by 20 and then multiply by 3. Alternatively, divide by 10, halve it, and add for the same outcome.
For example, 15% of 120 equals 12 + 6, which totals 18. Another method would be to find 120% of 15: 100% of 15 plus 20% of 15 (15 + 3 = 18).
Returning to our primary example — calculating 26% of 188 — we can break it down as follows:
26% is composed of 25% + 1%.
Calculating each:
- 25% of 188 equals 188 / 4 = 47.
- 1% of 188 equals 188 / 100 = 1.88.
Adding these results gives us: 47 + 1.88 = 48.88, meaning 26% of 188 is 48.88.
Now that you’re equipped to deconstruct percentage values, you can determine your approach in Step 1 based on ease of calculation.
For instance, if you need to find 35% of a number, you can express it as 25% + 10%. Alternatively, it can be framed as 5 multiplied by 7. Deciding whether to add a quarter and a tenth or to multiply a twentieth by seven depends on your preference.
Challenge Yourself
Challenge 1: Try calculating 34% of 250, 140% of 20, and 82% of 45.
Challenge 2: Explore why x% of y is equivalent to y% of x.
Quick Calculation Techniques
The first video, "Percentages made easy - fast shortcut trick!", offers practical tips for quick percentage calculations.
Advanced Mental Math Strategies
In the second video, "How to calculate percentages in seconds Mental Maths- 15", discover advanced techniques for mental calculations to improve your speed and accuracy.