Download Tips And Secrets for Mental Math Mastery and more Cheat Sheet Mathematics in PDF only on Docsity!
01 - Mental Math Secrets! - Rapidly Multiply by 11s!
Cool Mental Math Multiplication Trick
Multiplying a Double-Digit Number by 11
Multiplying a double-digit number by 11 is quite easy. Here's the technique: Take the two digits of the number you're multiplying by (e.g., for 42, take 4 and 2). Add these two digits together (4 + 2 = 6). Sandwich the sum between the two digits of the original number ( becomes 462). Let's practice this technique with some examples: Example 1: 31 times 11 Take 3 and 1, add them together (3 + 1 = 4), and sandwich 4 between 3 and 1. The answer is 341. Example 2: 63 times 11 Take 6 and 3, add them together (6 + 3 = 9), and sandwich 9 between 6 and 3. The answer is 693. Example 3: 72 times 11 Take 7 and 2, add them together (7 + 2 = 9), and sandwich 9 between 7 and 2. The answer is 792. Example 4: 38 times 11 Take 3 and 8, add them together (3 + 8 = 11), and carry the 1 over to the next column. The answer is 418. Example 5: 88 times 11
Take 8 and 8, add them together (8 + 8 = 16), and carry the 1 over to the next column. The answer is 968. Example 6: 49 times 11 Take 4 and 9, add them together (4 + 9 = 13), and carry the 1 over to the next column. The answer is 539.
Multiplying Larger Numbers by 11
Can we use the same technique for larger numbers? Let's find out. Example 7: 127 times 11 First, add the first two digits (1 + 2 = 3) and separately add the second two digits (2 + 7 = 9). Sandwich the results between the first and last digits. The answer is 1397. Example 8: 342 times 11 Add the first two digits (3 + 4 = 7) and the second two digits (4 + 2 = 6). Sandwich the results between the first and last digits. The answer is 3762.
Practice
Now, let's practice what we've learned. Try to solve the following problems: Problem 1: 17 times 11 Answer: 187 Problem 2: 25 times 11 Answer: 275 Problem 3: 39 times 11 Answer: 429
Calculating a 20% Tip
If you want to give a 20% tip, you can calculate it by first calculating a 10% tip and then doubling it. For example, if your bill is $10, a 10% tip would be $1, and doubling that would give you a 20% tip of $2.
Calculating a 15% Tip
To calculate a 15% tip, you can take a 10% tip and add half of it. For example, if your bill is $20, a 10% tip would be $2, and half of that is $1. So a 15% tip on a $20 bill would be $3. Similarly, if your bill is $30, a 10% tip would be $3, and half of that is $1.50. So a 15% tip on a $30 bill would be $4.50.
Calculating Tips
When calculating a tip, it can be helpful to break it down into smaller percentages. For example, if you want to calculate a 15% tip, you can first calculate a 10% tip and then add half of that to get the final amount. Let's take a look at an example: Bill amount: $ 10% tip: $4.60 (move the decimal point one spot) 5% tip: $2.30 (half of the 10% tip) 15% tip: $4.60 + $2.30 = $6. So, the 15% tip for a $46 bill is $6.90. You can do this calculation in your head by breaking it down into smaller percentages and adding them together. What if the bill amount is larger, like $160? Let's calculate the 15% tip for that: 10% tip: $16 (move the decimal point one spot) 5% tip: $8 (half of the 10% tip)
15% tip: $16 + $8 = $ So, the 15% tip for a $160 bill is $24. If the bill amount has cents, you can round it up or down to the nearest dollar and still get a close estimate in your head.
03 - Mental Math Secrets! - The Secret to Mental
Addition - Math Tricks for Fast Calculations!
Do you know the most important secret to mental addition? Keep reading to find out what it is. Today we're going to learn the most important secret to being able to do mental addition and subtraction. It's something that you already know, but we're going to practice it here so that you get really good at it. And that is knowing your compliments. In the context of what we're talking about, a compliment is just the number that, when added to another number, gives you ten. For example, the complement of the number two is the number eight. The complement of the number three is seven. The complement of the number four is six, and so on. Knowing these complements will give you a huge advantage in mental math. Here's a quick drill to practice your compliments. I'll write a number, and you yell out its complement as fast as you can. The compliment of six is four. The compliment of three is seven. The compliment of four is six, and so on. Play this part of the video again if you need to practice more. Now, let's twist it a little. I'll write a number, and you yell out how far away it is from a given number, like twenty. For example, the number sixteen is four units away from twenty because six and four are complements. Practice this exercise to improve your mental subtraction skills. Remember, every step on a journey to getting good at something begins with practice. If you understand these complements and can quickly recall them, it will make mental addition and subtraction much easier for you.
knowledge of regular complements. Practice this technique and become comfortable with it to improve your mental math skills. Knowing how far away a number is from 100 will also be helpful in dealing with money, as currency is based on the decimal system. Mastering this skill will give you a solid foundation for future math lessons.
04 - Mental Math Secrets! - Rapid Single Column
Addition
Do you know the fastest way to add two plus five plus eight plus seven plus four plus three plus five in your head? Keep watching to find out how. we're going to begin our quest in getting really good at mental arithmetic. We're going to learn to crawl before we walk, and we're going to do that by really working and practicing with single-column addition. Now, in order to do this and speed it up so that you can get good at it in your mind, there are two things that you need to remember:
- You're going to add the numbers as usual, so we're not going to use any fancy tricks to actually add 7 plus 4 together. You're going to have to get good at it and have it on the tip of your tongue.
- We're going to look for our compliments, which we've learned how to do in the last section. You're going to see here in just a second how that's going to really speed up the process. Here's a pretty easy arithmetic problem: 3 plus 4 plus 7. Most people would start at the top and work their way to the bottom. But instead, I want you to look for compliments. Notice we have three and seven in this problem, and we know that 3 and 7 are complements. So, we can add those together to make 10. Then, 10 plus 4 is 14. This is faster than doing 3 plus 4 equals 7, 7 plus 4 equals 14. Let's look at another example: 2 plus 9 plus 8. Most people would start at the top and add up through the bottom. But if we look for compliments,
we notice that 2 is a complement with 8, so that immediately sums to 10. Then, 10 plus 9 is 19. We can use the same process no matter how long the list of numbers is. Look for more pairs of numbers that make complements. For example, 1 plus 4 plus 5 plus 6. We notice we have a 6 and a 4, so that sums to 10. Then, we have 10 plus 5 equals 15, and 15 plus 1 equals 16. Another example: 2 plus 9 plus 8 plus 1. We notice that 2 and 8 are complements, so that makes 10. Also, 9 and 1 are complements, so that makes 10. The answer is 20. When the list of numbers gets really long, you can still apply this method. For example, 4 plus 7 plus 1. We don't have a pure complement, but we notice that 7 and 3 make 10. So, we have 10 plus 1 plus 1, which gives us
Lastly, 6 plus 2 plus 2 plus 5 plus 9. We notice that 6 and 4 are complements, so all of that together makes 10. Then, we have 10 plus 9 equals 19, and 19 plus 5 equals 24. By looking for compliments, you can save a lot of computation time and make mental arithmetic faster and easier.
Study Hack: Mental Math Made Easy
When it comes to adding multiple numbers together, there's a simple trick that can make the process much faster and easier. By identifying complements, or pairs of numbers that add up to 10, you can quickly find the sum without needing to perform each individual addition. Identifying Complements Let's take a look at an example: 7 + 3 = 10 4 + 6 = 10
05 - Mental Math Secrets! - Rapid Two Column
Addition
Math and Science
Adding Numbers Mentally: A Rapid
Approach
Hello! In this article, we will explore a rapid approach to mentally adding numbers. Traditionally, when adding numbers, we start from the right- hand column and carry digits as we go along. However, this can be challenging to do mentally. So, let's throw that method out the window and learn a more efficient way to add numbers mentally.
An Example: 15 + 34
Let's start with a simple example: 15 + 34. Instead of starting from the right-hand column, we will start from the left-hand column and move to the right. This approach makes it easier to keep track of the numbers in your head. Think of the numbers as their individual values. For example, 15 is actually 10 + 5, and 34 is 30 + 4. Now, let's add them mentally. Start with the leftmost column: 10 + 30 = 40 Move to the next column: 40 + 5 = 45 Finally, add the remaining number: 45 + 4 = 49 So, the answer to 15 + 34 is 49. By practicing this method, you will be able to add numbers mentally much faster.
Practice Makes Perfect
Now, let's try a few more examples: 38 + 53 = 91 44 + 67 = 111
Remember to start from the leftmost column and move to the right. Keep practicing, and you'll be able to add large numbers mentally with ease. So, that's how you add numbers mentally using a rapid approach. Say goodbye to carrying digits and start impressing others with your mental math skills! In general, you can add as many numbers together as you want using two- column addition. With practice, you will become faster and more comfortable with this method. Here are some tips to improve your mental math abilities: Grab a piece of paper and write down some numbers to practice adding together. Get used to the process and you will find that it becomes much faster. Consistently practice to improve your speed and ability to add more digits mentally. By building your mental math skills, you will be able to impress your friends and perform better on tests and exams. Keep practicing and enjoy the benefits of improved math abilities!
Placing the Decimal Point
After adding the numbers, you simply place the decimal point two places from the end to indicate the cents. This will give you the final answer in dollars and cents.
Practice Makes Perfect
By practicing these techniques, you can become more comfortable with adding money mentally. Start with simple problems and gradually work your way up to larger numbers and longer lists of numbers. With enough practice and patience, anyone can master this skill.
07 - Mental Math Secrets! - Rapidly Multiply 2-Digit
Numbers! Fast Mental Calculation Tricks
Mental Math Secrets: Multiplying Two-Digit
Numbers
we will learn a powerful technique for multiplying two-digit numbers in your head. This method can be applied to any two-digit multiplication problem. It's called the Crisscross Method of Multiplication, and it's incredibly useful for quick mental calculations. The Crisscross Method Let's start by focusing on the rightmost column. Multiply the two digits in this column to get the rightmost digit of the answer. For example, 4 times 1 equals 4. To find the middle digit, we use the crisscross technique. Imagine an "x" superimposed over the digits. Multiply 4 by 1 and 1 by 5, then add these products together. For example, 4 times 1 equals 4, and 1 times 5 equals 5. Adding 4 and 5 gives us 9, which is the middle digit. Finally, multiply the leading digits together to get the leftmost digit. For example, 4 times 5 equals 20. So the final answer is 2091.
This method can also be applied to three and four-digit numbers, but we'll cover that later. Example Problems Let's practice with a few examples: 41 times 51: Rightmost digit: 1 times 1 equals 1 Middle digit: 4 times 1 plus 1 times 5 equals 9 Leftmost digit: 4 times 5 equals 20 Final answer: 2091 13 times 12: Rightmost digit: 3 times 2 equals 6 Middle digit: 1 times 2 plus 3 times 1 equals 5 Leftmost digit: 1 times 1 equals 1 Final answer: 156 22 times 12: Rightmost digit: 2 times 2 equals 4 Middle digit: 2 times 2 plus 2 times 1 equals 6 Leftmost digit: 2 times 1 equals 2 Final answer: 264 More Challenging Problems: XXX XXX XXX By using the Crisscross Method, you can quickly and accurately multiply two-digit numbers in your head. With practice, you'll become faster and
With practice, this technique can help you solve multiplication problems more easily. 9 times 3 is 27 plus 3 gives us 30,3094. Now we have 47 times 45. In the right-hand column, 7 times 5 is 35. We can't write 35 down, so we write 5 and carry a floating 3. Next, we work on the middle digit. We have 4 times 5 which gives us 20 plus 28 gives us 48. So we have 48 with a crisscross plus the 3 gives us 51. We can't write 51 here, so we write a 1 and carry the 5. Then we work on the leading digit. 4 times 4 is 16 plus the floating 5 that we just carried, which gives us 21. So the answer is 2115. Our final problem is 19 times 53. Proceed as usual. In the right-hand column, 9 times 3 is 27. We write a 7 and carry the 2. Now we work on the crisscross. We have 3 plus 9 times 5, which is 45. So 3 plus 45 gives us 48. We have 48 from the crisscross plus 2, which gives us 50. We can't write 50, so we put a 0 and carry the 5. Then we work on the left-hand column. 1 times 5 is 5 plus 5 gives us 10. So the answer is 1007. This is a good introduction to what I call crisscross multiplication. It's very powerful and easy to pick up, especially with smaller numbers. It doesn't involve carrying, which makes it useful for numbers like 10 times 12 or 11 times 14. With practice, you can even multiply larger numbers in your head or with minimal math on paper. It's not intended to replace traditional multiplication, but it can be a faster method that saves time on exams and tests.
08 - Mental Math Secrets! - Rapidly Multiply Numbers
Ending in 5
Fast Way to Square Numbers Ending in 5 In this lesson, we will learn a quick and useful mathematical technique to square any number that ends in 5. This technique can be very helpful when you need to do calculations quickly, such as on standardized tests like the SAT or GRE.
Squaring a Number When we square a number, it means we multiply the number by itself. For example, if we square 15, we are multiplying 15 by 15. The Fast Technique When squaring a number that ends in 5, we can use a fast technique. Here's how it works: Step 1: Look at the first digit of the number. Multiply that digit by the next higher digit. Step 2: Take the result from Step 1 and append "25" to the end. Let's apply this technique to some examples: Example 1: 15 squared To square 15, we take the first digit (1) and multiply it by the next higher digit (2). The result is 2. Then we append "25" to the end. So, 15 squared is
Example 2: 45 squared For a number like 45, we take the first digit (4) and multiply it by the next higher digit (5). The result is 20. Then we append "25" to the end. So, 45 squared is 2025. Example 3: 85 squared For a larger number like 85, we take the first digit (8) and multiply it by the next higher digit (9). The result is 72. Then we append "25" to the end. So, 85 squared is 7225. Example 4: 105 squared For a number greater than 100, like 105, we take the digits other than 5 (10) and multiply it by the next higher digit (11). The result is 110. Then we append "25" to the end. So, 105 squared is 11025. Example 5: 115 squared For another example with a 3-digit number, like 115, we take the digits other than 5 (11) and multiply it by the next higher digit (12). The result is
- Then we append "25" to the end. So, 115 squared is 13225.
- Square the second digit, which is 4. 4 squared is 16.
- Combine the results: 29 + 16 = 2916. Therefore, 54 squared is 2916. Now, let's try another example. We'll calculate 57 squared:
- Add 25 to the second digit, which is 7. 25 + 7 = 32.
- Square the second digit, which is 7. 7 squared is 49.
- Combine the results: 32 + 49 = 3249. Therefore, 57 squared is 3249. As you can see, this trick works for larger numbers as well. Let's calculate 59 squared:
- Add 25 to the second digit, which is 9. 25 + 9 = 34.
- Square the second digit, which is 9. 9 squared is 81.
- Combine the results: 34 + 81 = 3481. Therefore, 59 squared is 3481. Lastly, let's square the number 52:
- Add 25 to the second digit, which is 2. 25 + 2 = 27.
- Square the second digit, which is 2. 2 squared is 4.
- Combine the results: 27 + 04 = 2704. Therefore, 52 squared is 2704. Remember that if the second digit squared results in a single-digit number, you need to write it as a two-digit number. For example, if the second digit squared is 4, write it as 04. Practice this trick and you'll find it incredibly easy to calculate the square of numbers in the 50s. It's a valuable tool to have for exams and tests. Good luck!
10 - Mental Math Secrets! - Square Numbers Close to
Math and Science
Squaring Numbers near 100
When squaring numbers near 100, there is a simple process that can be used to find the answer quickly. Let's go through some examples to demonstrate this process. Example 1: 95 squared We are 5 units away from 100, but going down, so we subtract 5 from 95 to get 90. We square the difference (5 squared) to get 25. The answer is obtained by putting the two results together: 9025. Example 2: 91 squared We are 9 units away from 100, but going down, so we subtract 9 from 91 to get 82. We square the difference (9 squared) to get 81. The answer is obtained by putting the two results together: 8281. Example 3: 112 squared We are 12 units away from 100, so we add 12 to 112 to get 124. We square the difference (12 squared) to get 144. The answer is obtained by putting the two results together: 124144. Example 4: 110 squared We are 10 units away from 100, so we add 10 to 110 to get 120.
