Percentage Trick - Solve precentages mentally - percentages made easy with the cool math trick!

tecmath
15 Feb 201310:41

TLDRIn this Tech Math video, the host teaches viewers how to calculate percentages mentally using simple math tricks. The tutorial focuses on percentages that are multiples of five and ten, such as 15%, 25%, 50%, 75%, and 95%. The method involves understanding the relationship between percentages and their decimal equivalents, and then mentally adding or subtracting these values from the whole number. The video provides step-by-step examples, encouraging viewers to practice these techniques to improve their mental math skills.

Takeaways

  • 😀 Understanding percentages: A percentage is a number out of 100, where 'per' means 'out of' and 'cent' means 'hundred'.
  • 🧠 Mental math for percentages: Learn to calculate percentages mentally by breaking them down into simpler parts like 10%, 5%, and 50%.
  • 🔢 100% of a number: This is the actual number itself, e.g., 100% of 80 is 80.
  • 📉 50% of a number: This is half of the number, e.g., 50% of 80 is 40.
  • 📈 10% of a number: This is one-tenth of the number, calculated by dividing the number by 10, e.g., 10% of 80 is 8.
  • 📌 5% of a number: This is half of 10%, e.g., 5% of 80 is 4.
  • ➕ Adding percentage parts: To find a percentage like 15%, add the 10% part to the 5% part of the number.
  • 🔄 Subtracting for higher percentages: For percentages over 100%, like 95%, subtract the smaller percentage (5% in this case) from the whole (100%).
  • 💡 Practice with mental math: The video encourages practicing these calculations mentally to improve speed and accuracy.
  • 🚀 Advanced techniques: The video hints at future content that will cover more complex percentages, like 22% or 53%, moving beyond easily divisible numbers by five.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is a mental math trick for solving percentages quickly in your head.

  • What does the word 'percentage' mean?

    -The word 'percentage' means a number out of 100, where 'per' means out of and 'cent' means 100.

  • How do you calculate 15% of a number using the mental math trick?

    -You calculate 15% of a number by first determining 10% of the number and then adding half of that amount to account for the additional 5%.

  • What is the 10% of a number in terms of the decimal place?

    -The 10% of a number is found by moving the decimal place one position to the left.

  • How do you determine 50% of a number?

    -50% of a number is half of the number, which can be calculated by dividing the number by 2.

  • What is the mental math trick for finding 5% of a number?

    -5% of a number is half of 10%, so you take half the amount you would calculate for 10%.

  • Can you give an example of how to calculate 60% of 42 using the mental math trick?

    -60% of 42 is calculated by taking 50% (which is half of 42, so 21) and then adding 10% of 42 (which is 4.2) to get a total of 25.2.

  • What is the approach to calculate 95% of a number, like 720, using the mental math trick?

    -For 95% of a number, you first consider 100% of the number and then subtract 5%. For 720, 10% is 72, and half of that is 36, so you subtract 36 from 720 to get 694.

  • How can you practice the mental math trick for percentages?

    -You can practice by trying to calculate percentages of numbers mentally, then checking your answers on paper, and repeating the process to improve.

  • What is the next step after mastering the percentages with fives and tens?

    -After mastering percentages with fives and tens, the next step is to practice with more complex percentages that are not divisible by five, such as 22%, 53%, or 87%.

Outlines

00:00

🧮 Introduction to Quick Percentage Calculations

The video begins by introducing the concept of calculating simple percentages mentally, focusing on percentages like 15%, 25%, 50%, and 75%. It explains the foundational concept of percentages, breaking down the meaning of 'percent' as 'out of 100'. The host provides an example of calculating 15% of 80, encouraging viewers to try it in their heads, and explains the importance of knowing how to quickly calculate 100%, 50%, 10%, and 5% of a number. These smaller parts will be used in later steps to solve percentages faster.

05:05

📊 Using Simple Percentages to Calculate 15% and 60%

This section builds on the earlier concepts by showing how to calculate 15% of 80 using 10% and 5%. The host walks through the process of first calculating 10% of 80 (which is 8) and then finding 5% by halving the 10% value (which is 4), then adding them together to get 12. Another example calculates 60% of 42 by combining 50% (half of 42) and 10% (moving the decimal of 42 to get 4.2), adding the two to get 25.2.

10:07

📉 Subtracting Percentages and Solving Complex Problems

The video progresses to more challenging problems, like finding 95% of 720. The host explains that you can start by finding 100% (720) and subtracting 5% (half of 10%, which is 36), resulting in 720 - 36 = 684. This method of subtraction is useful for working out percentages like 95%, 85%, or 75%. The host encourages viewers to practice the method for efficiency.

🧠 Practice Problems for 55%, 25%, and 85%

The host presents three practice problems: 55% of 360, 25% of 860, and 85% of 620. He breaks them down step by step, starting with 55% of 360 by adding 50% (180) and 5% (18), resulting in 198. For 25% of 860, he uses the method of dividing by four to find a quarter (215). For 85% of 620, he subtracts 10% (62) and 5% (31) from 620 to arrive at 527.

📐 Wrapping Up and Preparing for Complex Percentages

The video concludes by acknowledging that working out percentages like 85% can be more difficult than simpler numbers like 15%. The host emphasizes that with practice, solving these mentally becomes faster. In the next video, he plans to cover percentages that are not divisible by 5, like 22% or 53%, expanding the skills learned in this video to more complex percentages.

Mindmap

Keywords

💡Percentage

A percentage is a way of expressing a number as a fraction of 100. In the video, the host explains that 'per' means out of, and 'cent' means 100, which means a percentage is a number out of 100. This forms the basis for understanding how to quickly calculate percentages mentally.

💡100% of a number

100% of a number is simply the number itself, as it represents the whole. For example, 100% of 80 is 80. The video uses this concept to establish a foundation for calculating percentages of numbers.

💡50% of a number

50% of a number is half of that number, as 50% represents half of the whole. In the video, this is exemplified by calculating 50% of 80, which is 40. This basic percentage is used to build more complex calculations.

💡10% of a number

10% of a number is found by dividing the number by 10. For instance, 10% of 80 is 8. This concept is emphasized in the video as a simple and essential building block for mental percentage calculations.

💡5% of a number

5% of a number is half of 10% of that number. For example, 5% of 80 is 4, which is half of 10% of 80 (which is 8). This technique is often used in the video to quickly calculate small percentages mentally.

💡Adding percentages

Adding percentages means breaking down a percentage into smaller, easily calculable parts, like 10% and 5%, and then adding the results. In the video, the example of calculating 15% of 80 is shown by adding 10% (8) and 5% (4) to get 12.

💡Dividing by 10

Dividing by 10 is a key mathematical operation used to calculate 10% of a number. In the video, moving the decimal point to the left by one place is illustrated as a simple way to divide numbers by 10 mentally.

💡Taking away percentages

Taking away percentages refers to subtracting a percentage from a whole number. For example, in the video, 95% of 720 is calculated by taking 5% away from 720. First, 5% of 720 is calculated as 36, then subtracted from 720 to get 684.

💡Mental math

Mental math is the practice of performing calculations in your head, without the use of calculators or paper. The video demonstrates techniques for quickly calculating percentages mentally by breaking numbers down into simpler components.

💡Practice

Practice is emphasized in the video as crucial for improving one's ability to calculate percentages mentally. The host encourages viewers to work through examples and try solving percentages both on paper and mentally to become more proficient.

Highlights

Introduction to solving percentages mentally with simple tricks.

Explanation of what percentage means: 'per' means out of, and 'cent' means 100.

Step-by-step method to solve percentages involving 5s and 10s, such as 15%, 25%, 50%, and 75%.

Breakdown of percentage calculations: 100% is the full number, 50% is half, 10% is the number divided by 10, and 5% is half of 10%.

Example of calculating 15% of 80: 10% of 80 is 8, and 5% of 80 is 4. Adding them gives 12.

Working through percentage calculations mentally by combining smaller percentages, such as 50% and 10%.

Example of calculating 60% of 42: 50% of 42 is 21, and 10% of 42 is 4.2. Adding these gives 25.2.

Method for calculating 95% of a number: subtract 5% from 100%, as in 720 - 36 = 684.

Practice problem: 55% of 360 calculated as 50% (180) + 5% (18) = 198.

Simplified method for calculating 25% of a number: divide by 4. Example: 25% of 860 = 215.

Using 10% and 5% to solve 85% of 620: 620 - 62 (10%) - 31 (5%) = 527.

Encouragement to practice mental math to improve speed and accuracy in percentage calculations.

Upcoming video will cover more complex percentages, such as 22%, 53%, and 87%.

Importance of mastering smaller percentage values like 5%, 10%, and 50% for faster calculations.

The trick works well for percentages ending in 5 and 0, and makes solving them easy.

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