Alright.. after a prolonged break (sorry), I am now ready to guide you into the realm of powers.
It's really quite easy, and even fun.
Powers are to multiplication, as multiplication is to addition. In other words, powers are simply the same number multiplied several times.
5x5x5 is an example, although it is generally written as 5^3...
There is no real shortcut for doing powers. So generally, you will just have use multiplication principles.
In the above formula, 5^3.. you would multiply 5 by itself 3 times... like this..
5x5=25.... 25x5=125 (this may seem a bit weird, but what you're doing is multiplying the previous multiplication by 5, which is how it is supposed to be)
Since powers are simply specific multiplication problems, it doesn't take much more to explain it..
Just remember. The number after the ^ sign.. is simply how many times you are multiplying the number.
If it helps, for the problem Y^X.. simply write down X number of Ys. Then multiply.
Now, for a little secret that will help speed up the process.
When you have a number to the power of 4 or more, it is often easier to multiply in chunks, then multiply the chunks together... like this;
4^4.. you could multiply it out 4 times.. OR you can break it down into 2 chunks of 4x4.. getting 16x16...
You can probably answer 4x4 in your head, and 16x16 is pretty easy to multiply as well. Plus, you're only doing 2 multiplications (because doing 4x4 twice doesn't require doing the math again.. you KNOW that 4x4 will always equal 4x4)
If you did it the other way, you would have to do 3 separate multiplications. 4x4... 16x4 and 64x4
To put this into formulatic terms
Y^X = Y^X/2 x Y^X/2 OR
Y^X= Y^X/3 x Y^X/3 x Y^X/3 ... etc.
OK.. this week's problems!
3^3
4^3
10^2
11^3
5^5
4^4
16^2
(note: these are all fairly easy, and you should be able to do each one within 1-2 minutes)
Mar 6, 2012
Feb 6, 2012
Multiplying.
Hello friends! Are you ready to continue with math? You are? Good.
Today we will take a look at multiplication.
Multiplying is as easy as addition. In fact, sometimes it's easier.
Ok, how does multiplication work? Well, multiplication is merely adding the same number to itself a certain number of times. For example, 7x3, is really 7+7+7. Guess what? that's a simple single-digit addition, and then another single-digit number added to a double-digit number. The answer, as you've probably already figured out, is 21. (7+7=14 14+7=21).
All single-digit multiplications are just as easy, though it is advisable to memorize the multiplication table up to at least 12. Multiplication Table
When doing double-digit multiplication.. or greater, break them down into single-digit multiplication. Almost exactly the same way you break down additions, with one important point. Every number on one side of the multiply sign MUST be multiplied by every number on the other side.
Thus, in the equation 234x567, breaking it down into single-digit multiplications, will result in;
4x7, 4x60, 4x500, 30x7, 30x60, 30x500, 200x7, 200x60, 200x500. BUT, before you start doing the multiplications, you need to know one important thing. When multiplying a number with zeros at the end of it, first, multiply the numbers, then add the zeros to the end of the answer. for example, 200x7.. 2x7=14.. now add 2 zeros to the end of the answer to get 1400. If both multipliers have zeros at the end, then you add those zeros together, like this; 200x500... 2x5=10.. and you have 2 zeros in the 200, 2 zeros in the 500.. add 2 zeros plus 2 zeros to get 4 zeros, then add them to the end of the answer, thus 10 0000 or 100,000.
Ok, now we can go back, and finish the example.
4x7=28, 4x60=24 0, 4x500= 20 00, 30x7= 21 0, 30x60= 18 00, 30x500= 15 000, 200x7= 14 00, 200x60= 12 000 and finally, 200x500 = 10 0000.
Oops, we have a problem. we have 9 answers! Actually, we have nine components of the answer. The final step is to add all these numbers together;
28
240
2000
210
1800
15000
1400
12000
+100000
----------
132678
So, the answer to 234x567 is 132,678.
Alright, this week, instead of giving you multiplications to work on, I want to to make sure you have memorized the multiplication table from 1 to 12.
See you next week for more math!
Today we will take a look at multiplication.
Multiplying is as easy as addition. In fact, sometimes it's easier.
Ok, how does multiplication work? Well, multiplication is merely adding the same number to itself a certain number of times. For example, 7x3, is really 7+7+7. Guess what? that's a simple single-digit addition, and then another single-digit number added to a double-digit number. The answer, as you've probably already figured out, is 21. (7+7=14 14+7=21).
All single-digit multiplications are just as easy, though it is advisable to memorize the multiplication table up to at least 12. Multiplication Table
When doing double-digit multiplication.. or greater, break them down into single-digit multiplication. Almost exactly the same way you break down additions, with one important point. Every number on one side of the multiply sign MUST be multiplied by every number on the other side.
Thus, in the equation 234x567, breaking it down into single-digit multiplications, will result in;
4x7, 4x60, 4x500, 30x7, 30x60, 30x500, 200x7, 200x60, 200x500. BUT, before you start doing the multiplications, you need to know one important thing. When multiplying a number with zeros at the end of it, first, multiply the numbers, then add the zeros to the end of the answer. for example, 200x7.. 2x7=14.. now add 2 zeros to the end of the answer to get 1400. If both multipliers have zeros at the end, then you add those zeros together, like this; 200x500... 2x5=10.. and you have 2 zeros in the 200, 2 zeros in the 500.. add 2 zeros plus 2 zeros to get 4 zeros, then add them to the end of the answer, thus 10 0000 or 100,000.
Ok, now we can go back, and finish the example.
4x7=28, 4x60=24 0, 4x500= 20 00, 30x7= 21 0, 30x60= 18 00, 30x500= 15 000, 200x7= 14 00, 200x60= 12 000 and finally, 200x500 = 10 0000.
Oops, we have a problem. we have 9 answers! Actually, we have nine components of the answer. The final step is to add all these numbers together;
28
240
2000
210
1800
15000
1400
12000
+100000
----------
132678
So, the answer to 234x567 is 132,678.
Alright, this week, instead of giving you multiplications to work on, I want to to make sure you have memorized the multiplication table from 1 to 12.
See you next week for more math!
Jan 31, 2012
Subtracting Apples from Bob
HT here.
This week, we will focus on subtraction. Which is as easy as taking apples from Bob.
Subtraction is the exact opposite of addition, so the methods you've learned for doing addition can be used for subtraction, with slight tweaking.
Take 6-4 for an example. We will use the l's method, thus;
This week, we will focus on subtraction. Which is as easy as taking apples from Bob.
Subtraction is the exact opposite of addition, so the methods you've learned for doing addition can be used for subtraction, with slight tweaking.
Take 6-4 for an example. We will use the l's method, thus;
As you can see, it's very similar to the l's addition method that you learned.
All you need is a good grasp of addition, and subtraction will be as easy as stealing cookie jars from the cookie. Oh, I mean, cookies from the cookie jar.
Once you have single-digit subtraction down-pat, 2-digit, and even larger subtraction problems will be a piece of cake. Work from right-to-left, subtracting the 1's first, then the 10's, and so on.
Take 17-11 for example. Subtract 7-1 to get 6, and subtract 10-10 to get 0. So your answer will be 06, or since the zero is only a placeholder, and not needed at the beginning of a number; 6.
Sometimes, you will get a scenario like this;
32-27=... dividing it into 1's and 10's, you get 2-7 and 30-20. Starting with 2-7, we run into a problem. 7 is greater than 2! What do we do? Simple, cross off the 3 in 32, and replace it with a 2, like this 20-20. now add that 10 to the 2, like this 12-7. Now it's easy to find the answer. 12-7=5, and 20-20 = 0, so your answer is 5
If the number you are subtracting with is greater than the number you are subtracting from, the easiest way to figure out the answer is to reverse the subtraction and then add a "-" sign to the answer.
Thus. 45-47=, 47 is greater than 45, so, switch it around, and subtract 47-45 to get 2. now, simply add a "-"sign to the answer, -2
Alright, here're some test questions to get you started. And remember, as before, keep your eyes open for subtraction problems.
5-3
256-213
34-13
95-23
311-41
143-64
732-141
41-32
Jan 23, 2012
Addition L2
Alright, HT here again.
Now we're going to be looking at larger addition problems. 3, 4.... even 5-digit additions.
The principle is exactly the same as 2-digit addition, except you have a few extra numbers to keep track of.
So, enough talk, let's get to an example;
115+435... simple enough... let's break it down into 3 single-digit problems. 100+100, 10+30 and 5+5..
We know that 5+5= 10, so let's add another one to the 30, making it 10+40, which equals 50.. now you've got just one problem left.. 100+100.. easy, right? The answer, then, is 250.
4-digit addition? no sweat.
4613+9846... break it down into single-digit additions; 4000+9000, 600+800, 10+40, 3+6.
which gives the answers, 13000, 1400, 50 and 9. Add them together to get 14,459.
And in case you didn't know, it's easier to add from right to left. Yep, you heard me, right to left. Add the 1's first. Then, if you get an answer of 10 or more, add 10 to the 10's place, and remove it from your initial answer. Need an example?
45+36... 5+6 equals 11.. so add 10 to the 10's place.. which gives 50+30, or 40+40... leave the 1 as the initial answer.. then add the 50+30.. which is 80. Add the two answers, 80+1 to get 81.
Your turn!
Try these problems;
154+334
434+453
8435+4311
3545+9877
1234+5678
90454+43513
24942+56721
Remember, break them down into single-digit additions, and then add the answers.
HT Fact:
The Handsome Toddler encourages you to look for math problems to do.
Now we're going to be looking at larger addition problems. 3, 4.... even 5-digit additions.
The principle is exactly the same as 2-digit addition, except you have a few extra numbers to keep track of.
So, enough talk, let's get to an example;
115+435... simple enough... let's break it down into 3 single-digit problems. 100+100, 10+30 and 5+5..
We know that 5+5= 10, so let's add another one to the 30, making it 10+40, which equals 50.. now you've got just one problem left.. 100+100.. easy, right? The answer, then, is 250.
4-digit addition? no sweat.
4613+9846... break it down into single-digit additions; 4000+9000, 600+800, 10+40, 3+6.
which gives the answers, 13000, 1400, 50 and 9. Add them together to get 14,459.
And in case you didn't know, it's easier to add from right to left. Yep, you heard me, right to left. Add the 1's first. Then, if you get an answer of 10 or more, add 10 to the 10's place, and remove it from your initial answer. Need an example?
45+36... 5+6 equals 11.. so add 10 to the 10's place.. which gives 50+30, or 40+40... leave the 1 as the initial answer.. then add the 50+30.. which is 80. Add the two answers, 80+1 to get 81.
Your turn!
Try these problems;
154+334
434+453
8435+4311
3545+9877
1234+5678
90454+43513
24942+56721
Remember, break them down into single-digit additions, and then add the answers.
HT Fact:
The Handsome Toddler encourages you to look for math problems to do.
Jan 16, 2012
Starting out
Hello,
I'm the Handsome Toddler, and I am here to help YOU learn math with ease.
Ok, enough talk about myself. Let's get started, shall we?
This week, we will just focus on simple, single-digit addition (and a few double-digits). Most of you probably have this down-pat, but a little practice won't hurt, and it will help you get into the habit of actually doing the problems. I know too many instances where someone grabs a math book and reads through it, but does not do the problems because "they're too complicated".
So, first let me show you a few addition problems. Then I will give you a few problems to solve. And the rest of this week, I want you to keep your eyes open for single or double-digit additions. Or you can even make some up.
Ok, first example;
1+1... you're laughing, right? This is so easy. The answer's 2.
Alright, smarty pants, WHY does 1+1= 2? Alright, so you know the answer to that. Good!
Maybe I should say something before I go on to the next example.
2 is equivalent to two 1s.
3 is equivalent to three 1s. and so on.
Alright, on to the next example;
3+6... so, you have three 1s added to six 1s... (1+1+1) + (1+1+1+1+1+1).. now you can count them up. The answer is 9.
A little bit tougher;
6+9... alright, we have six 1s added to nine 1s.. pretty easy, right? let's see (1+1+1+1+1+1) + (1+1+1+1+1+1+1+1+1)... count them up and you get 15.
Ok, we've covered single-digit addition. Now for a few double-digits. If you get stuck, try counting 1s.
27+58... uh oh! where do I start? Well, let's break it down into two problems. You have 20+50 and you have 7+8. Hey, guess what? They're single-digit additions! And since we just covered those, you should get this one pretty quickly. 20+50=70... 7+8= 15... add them together and you get 85.
Last example;
87+92... sometimes double-digit additions have triple-digit answers. But don't panic! First, let's break it down into single-digit additions. 80+90 and 7+2.. You know that 8+9 = 17, so 80+90 must equal 170.. add 9 and you're done. Now, was that so hard?
Congratulations! You're on your way to mastering math. Remember, though you may know some of these steps, you must get to know them so well that you can do them in your sleep.
Alright! Now I've got a few problems for you to solve. And remember, keep an eye open for any other single or double-digit addition problems this week.
4+7
3+2
37+42
95+71
88+37
99+99
12+41
HT Fact:
The Handsome Toddler is grateful to Caroline Keeth and Kayla Jade for their inspiration and encouragement. He is also grateful to Mara Clipner for naming him the Handsome Toddler.
See you next week!
I'm the Handsome Toddler, and I am here to help YOU learn math with ease.
Ok, enough talk about myself. Let's get started, shall we?
This week, we will just focus on simple, single-digit addition (and a few double-digits). Most of you probably have this down-pat, but a little practice won't hurt, and it will help you get into the habit of actually doing the problems. I know too many instances where someone grabs a math book and reads through it, but does not do the problems because "they're too complicated".
So, first let me show you a few addition problems. Then I will give you a few problems to solve. And the rest of this week, I want you to keep your eyes open for single or double-digit additions. Or you can even make some up.
Ok, first example;
1+1... you're laughing, right? This is so easy. The answer's 2.
Alright, smarty pants, WHY does 1+1= 2? Alright, so you know the answer to that. Good!
Maybe I should say something before I go on to the next example.
2 is equivalent to two 1s.
3 is equivalent to three 1s. and so on.
Alright, on to the next example;
3+6... so, you have three 1s added to six 1s... (1+1+1) + (1+1+1+1+1+1).. now you can count them up. The answer is 9.
A little bit tougher;
6+9... alright, we have six 1s added to nine 1s.. pretty easy, right? let's see (1+1+1+1+1+1) + (1+1+1+1+1+1+1+1+1)... count them up and you get 15.
Ok, we've covered single-digit addition. Now for a few double-digits. If you get stuck, try counting 1s.
27+58... uh oh! where do I start? Well, let's break it down into two problems. You have 20+50 and you have 7+8. Hey, guess what? They're single-digit additions! And since we just covered those, you should get this one pretty quickly. 20+50=70... 7+8= 15... add them together and you get 85.
Last example;
87+92... sometimes double-digit additions have triple-digit answers. But don't panic! First, let's break it down into single-digit additions. 80+90 and 7+2.. You know that 8+9 = 17, so 80+90 must equal 170.. add 9 and you're done. Now, was that so hard?
Congratulations! You're on your way to mastering math. Remember, though you may know some of these steps, you must get to know them so well that you can do them in your sleep.
Alright! Now I've got a few problems for you to solve. And remember, keep an eye open for any other single or double-digit addition problems this week.
4+7
3+2
37+42
95+71
88+37
99+99
12+41
HT Fact:
The Handsome Toddler is grateful to Caroline Keeth and Kayla Jade for their inspiration and encouragement. He is also grateful to Mara Clipner for naming him the Handsome Toddler.
See you next week!
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