What an interesting thought, isn't it? How do you use multiplication to simplify addition of several numbers? Let's take a look at some practical examples that will clarify why it is beneficial to multiply while adding.
Suppose you are given the following numbers to add:
7 + 5 + 4 + 7 + 6 + 7. There is certainly nothing wrong with adding all 6 numbers in the order that were listed. On the other hand, if we multiply 3 x 7 = 21, we have quickly added half of the list of numbers that were given. To add the remaining numbers, 5 + 4 + 6 = 15. We know that 21 + 15 = 36.
Here's a practical example to consider.
Betty bought 20 pairs of socks for her grandchildren, and they were on sale for $2 per pair. How much did she spend?
Solution: Is it easier to add $2 twenty times, or use multiplication? Let's use multiplication! We quickly know that 20 x 2 = 40. Betty spent $40 (before tax) on her purchase today.
As we can see, there is more than one way to add a list of numbers. Use this great tip to simplify your life, and remember to share it with a friend!
Thursday, March 31, 2016
Wednesday, March 30, 2016
Adding a series of sequential numbers...the easy way!
Have you ever had to add a series of sequential numbers? For example, if you need to add the numbers 1 through 10. Can you do it? Can you do it without adding 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9?
Let's solve this one with today's tip.
Step 1: Add the first and last number in the sequence. 1 + 9 = 10.
Step 2: Divide that total of Step 1 by 2. 10/2 = 5.
Step 3: Multiply the answer in Step 2 times the number of numbers in the sequence. In this example, it is 9. 9 x 5 = 45.
You solved it! The total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Here's another one to try.
What is the total of the sequence of numbers from 10 to 14?
Step 1: Add the first and last number in the sequence. 10 + 14 = 24.
Step 2: Divide the total of Step 1 by 2. 24/2 = 12.
Step 3: Multiply the answer in Step 2 times the number of number in the sequence. 12 x 5 = 60.
You're right! The total of 10 + 11 + 12 + 13+ 14 = 60!
This practical tip works every time, and will simplify your life, especially if you have a long list of sequential numbers to add. Try it, and share this with a friend!
Let's solve this one with today's tip.
Step 1: Add the first and last number in the sequence. 1 + 9 = 10.
Step 2: Divide that total of Step 1 by 2. 10/2 = 5.
Step 3: Multiply the answer in Step 2 times the number of numbers in the sequence. In this example, it is 9. 9 x 5 = 45.
You solved it! The total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Here's another one to try.
What is the total of the sequence of numbers from 10 to 14?
Step 1: Add the first and last number in the sequence. 10 + 14 = 24.
Step 2: Divide the total of Step 1 by 2. 24/2 = 12.
Step 3: Multiply the answer in Step 2 times the number of number in the sequence. 12 x 5 = 60.
You're right! The total of 10 + 11 + 12 + 13+ 14 = 60!
This practical tip works every time, and will simplify your life, especially if you have a long list of sequential numbers to add. Try it, and share this with a friend!
Tuesday, March 29, 2016
Adding numbers? Regroup them for quicker calculations
Have you ever been given several numbers to add and didn't know where to begin? Did you think there must be a tip or other shortcut, but somehow in the busyness of life you have somehow forgotten it? For some of us, we struggle with adding numbers without a calculator, and especially without using paper and a pencil.
Here is a practical tip that just may simplify your life at the perfect time!
When adding numbers, group them so they can be quickly added to other numbers in your list.
Here's an example of grouping numbers.
You are given the following numbers to add, and have only 3 to 5 seconds to add them.
Find the sum of 34 + 63 + 16 + 27.
Solution: Group two pairs of numbers (34 + 16) and (63 + 27).
34 + 16 = 50 and 63 + 27 = 90.
Add the sum of both groups, and you have quickly concluded the solution is 140.
Let's try another one.
Find the sum of 12 + 91 + 9.
In this scenario, there is only one group that needs to be formed, which is (91 + 9). You can see very quickly that 100 + 12 = 112.
I know you will find this tip to be practical, and can find many ways to simplify your life by utilizing this short-cut. Please remember to share this with a co-worker or friend!
Here is a practical tip that just may simplify your life at the perfect time!
When adding numbers, group them so they can be quickly added to other numbers in your list.
Here's an example of grouping numbers.
You are given the following numbers to add, and have only 3 to 5 seconds to add them.
Find the sum of 34 + 63 + 16 + 27.
Solution: Group two pairs of numbers (34 + 16) and (63 + 27).
34 + 16 = 50 and 63 + 27 = 90.
Add the sum of both groups, and you have quickly concluded the solution is 140.
Let's try another one.
Find the sum of 12 + 91 + 9.
In this scenario, there is only one group that needs to be formed, which is (91 + 9). You can see very quickly that 100 + 12 = 112.
I know you will find this tip to be practical, and can find many ways to simplify your life by utilizing this short-cut. Please remember to share this with a co-worker or friend!
Monday, March 28, 2016
Shall I multiply or divide?
Being a full-time teacher, I instruct my students to become better problem solvers. When offering assistance, my question to them always inquires whether they need to add, subtract, multiply, or divide. Given a choice to multiply or divide, which one will you choose?
Let's take a look at a couple examples, then you decide.
Mr. Johnson is cutting a 48 inch board into 4 equal pieces. How long will each board be when he is done?
Solution: Your choices are to multiply or divide. To solve it using division, setup the problem as 48/4 = 12. You can also multiply 48 x 1/4, which is also 12. Which math operation do you prefer to use?
Here's another example.
There are 150 students who are attending a field trip today to the local zoo. There are 3 buses taking the students. How many students can ride on each bus?
Solution: Using division, the solution is 150/3 = 50. To solve the problem using multiplication, you can multiply 150 x 1/3, which equals 50.
Math often allows flexibility to solve problems. Sometimes you may prefer to multiply, other times you may divide.
Don't forget to share today's tip with a friend!
Let's take a look at a couple examples, then you decide.
Mr. Johnson is cutting a 48 inch board into 4 equal pieces. How long will each board be when he is done?
Solution: Your choices are to multiply or divide. To solve it using division, setup the problem as 48/4 = 12. You can also multiply 48 x 1/4, which is also 12. Which math operation do you prefer to use?
Here's another example.
There are 150 students who are attending a field trip today to the local zoo. There are 3 buses taking the students. How many students can ride on each bus?
Solution: Using division, the solution is 150/3 = 50. To solve the problem using multiplication, you can multiply 150 x 1/3, which equals 50.
Math often allows flexibility to solve problems. Sometimes you may prefer to multiply, other times you may divide.
Don't forget to share today's tip with a friend!
Saturday, March 26, 2016
Multiplication of two numbers made easy
Have you been at the market, or home improvement center, or perhaps were in the process of purchasing tickets for the upcoming big game, and you were confronted with another dreaded multiplication problem? You have no calculator nearby, and now you must make a quick decision whether or not to make the purchase. Relax, take a deep breath, and learn a new tip today that will simplify your life and increase your confidence!
Here is a scenario for our consideration. The cost of each concert ticket is $28 and you need to purchase 5 tickets to take your family on Friday evening. What is the total cost before taxes and other fees?
Reduce $28 to $14, but at the same time, we must double the 5 to make it 10. Instead of multiplying 5 x 28 in our head, we can work with 10 x 14. Given both scenarios, we can choose the 2nd alternative instead of guessing and hoping we are correct, or perhaps not performing the calculation, and ultimately not having enough money to make the purchase. We conclude that 28 x 5 = 10 x 14, which is 140.
Let's try another one. To paint your new office, you need to purchase 12 gallons that are $15 per gallon on sale. What is the total cost of the paint before sales tax?
Some of us may already know that 12 x 15 = 180. For the rest of us, let us reduce 12 to 6, which is cutting it in half, and also doubling 15 to 30. We now have the choice to multiply 12 x 15, or 6 x 30. We all know that 6 x 3 = 18, therefore 6 x 30 = 180.
Try this new tip today and share this great information with a friend! They will certainly appreciate you!
Here is a scenario for our consideration. The cost of each concert ticket is $28 and you need to purchase 5 tickets to take your family on Friday evening. What is the total cost before taxes and other fees?
Reduce $28 to $14, but at the same time, we must double the 5 to make it 10. Instead of multiplying 5 x 28 in our head, we can work with 10 x 14. Given both scenarios, we can choose the 2nd alternative instead of guessing and hoping we are correct, or perhaps not performing the calculation, and ultimately not having enough money to make the purchase. We conclude that 28 x 5 = 10 x 14, which is 140.
Let's try another one. To paint your new office, you need to purchase 12 gallons that are $15 per gallon on sale. What is the total cost of the paint before sales tax?
Some of us may already know that 12 x 15 = 180. For the rest of us, let us reduce 12 to 6, which is cutting it in half, and also doubling 15 to 30. We now have the choice to multiply 12 x 15, or 6 x 30. We all know that 6 x 3 = 18, therefore 6 x 30 = 180.
Try this new tip today and share this great information with a friend! They will certainly appreciate you!
Friday, March 25, 2016
Simplifying numbers for easy subtraction calculations
Have you needed to add or subtract two numbers very quickly, and didn't have a calculator nearby, or felt too tired to compute the sum or difference in your head? There are many techniques that can be used that are especially helpful for those who need a helping hand!
Let's work a couple examples.
What is the solution of 147 - 93? There are a few people that can quickly compute this within a second or two. The easiest way to simplify this calculation is to add 7 to 93, which bumps it to 100. If we add 7 to the one number, we must add 7 to the other number, increasing it from 147 to 154.
Now, what is the difference of 154 + 100? That's right! It is 54! What is 147 - 93? It is also 54, because we have maintained the same relationship between both numbers by adding the same number!
Here's another one to try. What is 83 - 36? You can increase 36 to 40 by adding 4, and also increase 83 by 4, which is 87. The difference is 47.
Many of us refrain from subtracting 2-digit numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake when we can see it in writing.
Practice this tip a few times, and don't forget to show this to a friend or co-worker.
Let's work a couple examples.
What is the solution of 147 - 93? There are a few people that can quickly compute this within a second or two. The easiest way to simplify this calculation is to add 7 to 93, which bumps it to 100. If we add 7 to the one number, we must add 7 to the other number, increasing it from 147 to 154.
Now, what is the difference of 154 + 100? That's right! It is 54! What is 147 - 93? It is also 54, because we have maintained the same relationship between both numbers by adding the same number!
Here's another one to try. What is 83 - 36? You can increase 36 to 40 by adding 4, and also increase 83 by 4, which is 87. The difference is 47.
Many of us refrain from subtracting 2-digit numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake when we can see it in writing.
Practice this tip a few times, and don't forget to show this to a friend or co-worker.
Thursday, March 24, 2016
Simplifying numbers for easy addition calculations
Have you needed to add or subtract two numbers very quickly, and didn't have a calculator nearby, or felt too tired to compute the sum or difference in your head? There are many techniques that can be used that are especially helpful for those who need a helping hand!
Let's work a couple examples.
What is the sum of 121 + 98? There are a few people that can quickly compute this within a second or two. The easiest way to simplify this calculation is to add 2 to 98, which bumps it to 100. If we add 2 to the one number, we must subtract 2 from the other number, decreasing it from 121 to 119.
Now, what is the sum of 119 + 100? That's right! It is 219.
Here's another one to try. What is the sum of 77 + 36? You can increase 77 to 80 by adding 3, and also decrease 36 by 3, which is 33. The sum is 113.
We could have easily adjusted the 36 to 40 by adding 4, and decreasing 77 by 4 to 73. 40 + 73 = 113.
Many of us refrain from adding numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake.
This is just one of many tips and shortcuts that I will share with you as you continue in your quest to love math!
Let's work a couple examples.
What is the sum of 121 + 98? There are a few people that can quickly compute this within a second or two. The easiest way to simplify this calculation is to add 2 to 98, which bumps it to 100. If we add 2 to the one number, we must subtract 2 from the other number, decreasing it from 121 to 119.
Now, what is the sum of 119 + 100? That's right! It is 219.
Here's another one to try. What is the sum of 77 + 36? You can increase 77 to 80 by adding 3, and also decrease 36 by 3, which is 33. The sum is 113.
We could have easily adjusted the 36 to 40 by adding 4, and decreasing 77 by 4 to 73. 40 + 73 = 113.
Many of us refrain from adding numbers in our head, because we don't have experience, or we prefer to write it on paper where we can see it, but also feel more confident that we won't make a mistake.
This is just one of many tips and shortcuts that I will share with you as you continue in your quest to love math!
Saturday, March 19, 2016
How do you square 2-digit numbers that end with a 0?
Of all the 2-digit numbers that you may need to square, this is certainly the easiest!
Let's try one! How quickly can you square 40?
To multiply 40 x 40, multiply 4 x 4, then place 2 zeros after the product of 4 x 4. Very simply, 40 x 40 = 1600.
Here is another one. What is 70 x 70? 7 x 7 = 49. Insert both zeros after 49. 70 x 70 = 4900.
The squaring of 2-digit numbers that end in 0 may be a calculation that you will use more often than squaring other numbers.
Use this tip often, and remember to share this with a friend!
Let's try one! How quickly can you square 40?
To multiply 40 x 40, multiply 4 x 4, then place 2 zeros after the product of 4 x 4. Very simply, 40 x 40 = 1600.
Here is another one. What is 70 x 70? 7 x 7 = 49. Insert both zeros after 49. 70 x 70 = 4900.
The squaring of 2-digit numbers that end in 0 may be a calculation that you will use more often than squaring other numbers.
Use this tip often, and remember to share this with a friend!
Friday, March 18, 2016
How do you square 2-digit numbers that end with a 1?
For the next several days, we will see how to square 2-digit numbers ending in 1 to 9, using quick, easy tips and tricks. How do you square a number that ends with a 1? As a quick review of vocabulary, to square a number simply means to multiply a number by itself. Squaring 21 means to multiply 21 x 21, and squaring 61 is multiplying 61 x 61.
What is the quickest way to square 2 numbers that end with a 1? Let's try 31 x 31.
Step 1, reduce the number to the nearest 10, which means that we will subtract 1 from 31 to make it 30.
Step 2, multiply 30 x 30, which is 900.
Step 3, add 30 + 30 to 900, which is 960.
Step 4, add 1, which is 961.
Done!
Let's try another one! What is the square of 51?
Step 1, reduce 51 to 50.
Step 2, multiply 50 x 50, which is 2500.
Step 3, add 50 + 50 to 2500, which is 2600.
Step 4, add 1, which is 2601.
That's it! 😃
It is a very simple process, and I know you will gain much confidence as you practice a few of these. Don't forget to share this tip with a friend!
What is the quickest way to square 2 numbers that end with a 1? Let's try 31 x 31.
Step 1, reduce the number to the nearest 10, which means that we will subtract 1 from 31 to make it 30.
Step 2, multiply 30 x 30, which is 900.
Step 3, add 30 + 30 to 900, which is 960.
Step 4, add 1, which is 961.
Done!
Let's try another one! What is the square of 51?
Step 1, reduce 51 to 50.
Step 2, multiply 50 x 50, which is 2500.
Step 3, add 50 + 50 to 2500, which is 2600.
Step 4, add 1, which is 2601.
That's it! 😃
It is a very simple process, and I know you will gain much confidence as you practice a few of these. Don't forget to share this tip with a friend!
Thursday, March 17, 2016
Squaring 2-digit numbers--Why is this important?
What is the importance of knowing how to square two numbers? Unless you are a full-time student, or an educator, you may be wondering why it is beneficial to know this information. Certainly anyone working in landscaping, engineering, and construction-related fields knows the value of computing numbers quickly. If you are a do-it-yourself type of person and own a home, there are many practical applications around the home, such as painting, flooring, and other remodeling jobs where quick calculations can save you time and money.
If you are installing ceramic tiles or hardwood flooring in your newly-remodeled kitchen or bathroom, and you know the dimensions of the room, you can purchase the right amount of supplies on your first trip to the home improvement store. How unfortunate it would be if you miscalculated and purchased the wrong amount of a certain tile that was on clearance, and when you completed your job a few weeks later, you were unable to find additional matching tiles.
Follow my blog each day as we continue to add tips and tricks to use Math in a practical way. Don't forget to share with a friend!
Wednesday, March 16, 2016
What is the sale price?
How often do you shop in a retail store and see sale signs everywhere, but have no idea how 30% off equates to dollars and cents?
There is more than one way to determine the net amount you will pay after the savings are deducted from the original price. Savings of 30%, simply means that you are paying 70% of the retail price.
Think about it for a moment. 100% - 30% = 70%. Instead of calculating the savings, then deducting that amount from the retail price, you can multiply the retail price by 70%, and you will quickly know the sale price.
One more thing you need to know is 70% has the same value as 0.70, or 0.7 in simplest decimal form. We know this, because 70% is 70/100, which is 0.70.
Let's try one. A shirt has a retail price of $29.99 and it is on sale for 30% off. How much is the sale price? Prior to doing the calculation, you should round up the price from $29.99 to $30 to simplify the calculation. Very simply, $30 x 70% = 30 x .70 = $21.
Try another one. The hat is $20 and is on sale for 25% off. What is the sale price? Converting 25% to a decimal = 0.25, which is also 1/4. Because we readily know that 1/4 of $20 = $5, we can subtract $5 from $20, which is $15. For many of us, it may have been easier to calculate the savings, then deduct the amount instead of multiplying $20 x .75 like we did in the first example.
Enjoy the savings, but more importantly, enjoy these new tips and share them with someone you love!
There is more than one way to determine the net amount you will pay after the savings are deducted from the original price. Savings of 30%, simply means that you are paying 70% of the retail price.
Think about it for a moment. 100% - 30% = 70%. Instead of calculating the savings, then deducting that amount from the retail price, you can multiply the retail price by 70%, and you will quickly know the sale price.
One more thing you need to know is 70% has the same value as 0.70, or 0.7 in simplest decimal form. We know this, because 70% is 70/100, which is 0.70.
Let's try one. A shirt has a retail price of $29.99 and it is on sale for 30% off. How much is the sale price? Prior to doing the calculation, you should round up the price from $29.99 to $30 to simplify the calculation. Very simply, $30 x 70% = 30 x .70 = $21.
Try another one. The hat is $20 and is on sale for 25% off. What is the sale price? Converting 25% to a decimal = 0.25, which is also 1/4. Because we readily know that 1/4 of $20 = $5, we can subtract $5 from $20, which is $15. For many of us, it may have been easier to calculate the savings, then deduct the amount instead of multiplying $20 x .75 like we did in the first example.
Enjoy the savings, but more importantly, enjoy these new tips and share them with someone you love!
Tuesday, March 15, 2016
How do you know if a number is divisible by 9?
Do you ever wonder if a number is divisible by other numbers? How do you know if a number is divisible by 9? Like the Divisibility Rule for 3 that we learned earlier this week, simply add the digits of a number, and if the sum of those digits is divisible by 9, the number is divisible by 9 as well.
Is 792 divisible by 9? The sum of the digits 7 + 9 + 2 = 18. 18 is divisible by 9, and you can conclude that 792 is also divisible by 9.
Let's try another one that you know is divisible by 9. Is 99 divisible by 9? The sum of the digits 9 + 9 = 18, and 18 is divisible by 9, therefore 99 is divisible by 9.
Another neat fact about the Divisibility of 9, you can accurately conclude that when a number is divisible by 9, it is also divisible by 3, because 3 is a factor of 9. Try this simple rule each and every time you need to divide a number by three or nine, and it works like magic!
Practice a few more examples on your own, and share this tip with a friend!
Is 792 divisible by 9? The sum of the digits 7 + 9 + 2 = 18. 18 is divisible by 9, and you can conclude that 792 is also divisible by 9.
Let's try another one that you know is divisible by 9. Is 99 divisible by 9? The sum of the digits 9 + 9 = 18, and 18 is divisible by 9, therefore 99 is divisible by 9.
Another neat fact about the Divisibility of 9, you can accurately conclude that when a number is divisible by 9, it is also divisible by 3, because 3 is a factor of 9. Try this simple rule each and every time you need to divide a number by three or nine, and it works like magic!
Practice a few more examples on your own, and share this tip with a friend!
Monday, March 14, 2016
Subtraction of numbers made easy!
Have you ever wondered if it is possible to subtract a number without the messy borrowing and regrouping of values? We all know that traditional methods of subtraction can be complicated, and therefore lead to possible mistakes.
70^0
Let's try this again, but using a simple trick. Reduce both numbers by 1 before applying the operation of subtraction.
Here is a quick glimpse of the traditional method of subtraction. Notice that you must borrow a 1 from 70, making the 0 a 10, which then allows you to subtract 6 from 10, resulting in a 4. The next step requires no regrouping, and most of us know fairly quickly that 69-53=16. We conclude that 700-536=164, which is correct.
69 1
-53 6
164
Let's try this again, but using a simple trick. Reduce both numbers by 1 before applying the operation of subtraction.
699
-535
164
Notice that no borrowing nor regrouping of numbers was required to perform the operation, yet we have the same answer! By reducing both numbers by 1, we didn't change the relationship between those numbers, and our answer is the same.
Time for one more?
303
-169
?
To solve this problem with great ease, reduce both numbers by 4.
299
-165
134
Try this trick, and share it with others!
Sunday, March 13, 2016
How do you know if a number is divisible by 3?
Do you ever wonder if a number is divisible by other numbers? How do you know if a number is divisible by 3? Simply add the digits of a number, and if the sum of those digits is divisible by 3, the number is divisible by 3 as well.
Is 891 divisible by 3? The sum of the digits 8 + 9 + 1 = 18. 18 is divisible by 3, and you can conclude that 891 is divisible by 3.
Let's try another one that you know is divisible by 3. Is 66 divisible by 3? The sum of the digits 6 + 6 = 12, and 12 is divisible by 3, therefore 66 is divisible by 3.
Try this simple rule each and every time you need to divide a number by three, and it works like magic!
Is 891 divisible by 3? The sum of the digits 8 + 9 + 1 = 18. 18 is divisible by 3, and you can conclude that 891 is divisible by 3.
Let's try another one that you know is divisible by 3. Is 66 divisible by 3? The sum of the digits 6 + 6 = 12, and 12 is divisible by 3, therefore 66 is divisible by 3.
Try this simple rule each and every time you need to divide a number by three, and it works like magic!
Saturday, March 12, 2016
How to square 2-digit numbers ending in a 5
Looking for a quick, easy way to multiply 2 identical 2-digit numbers that end with a 5?
How do you multiply 25 x 25? Very simply, multiply 2 x (2+1), then place a 25 on the end. Solution = 2 x 3= 6, then place 25 after the 6. 25 x 25 = 625.
Let's try one more. What is 65 x 65? Multiply 6 x (6+1), then place a 25 on the end. 65 x 65 = 4,225.
This tip works well squaring all 2-digit numbers ending in a 5 from 15 x 15 to 95 x 95.
Practice a few, then you'll be one step closer to enjoying Math!
Share this tip with someone today!
How do you multiply 25 x 25? Very simply, multiply 2 x (2+1), then place a 25 on the end. Solution = 2 x 3= 6, then place 25 after the 6. 25 x 25 = 625.
Let's try one more. What is 65 x 65? Multiply 6 x (6+1), then place a 25 on the end. 65 x 65 = 4,225.
This tip works well squaring all 2-digit numbers ending in a 5 from 15 x 15 to 95 x 95.
Practice a few, then you'll be one step closer to enjoying Math!
Share this tip with someone today!
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Welcome to I Want to Love Math! I will share daily tips, tricks, and ideas to entice you to love Math.
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