How to Use Chisanbop (Korean Finger Math) for Basic Addition and Counting eHow.com
Difficulty: Easy
Instructions
Step 1
In Chisanbop you'll be using your two hands and ten fingers to represent numbers from 0 to 99. Start out with your hands out in front of you with closed fists. This represents 0. Each finger (not thumb) on your right hand represents 1. To represent 3, just press down three right hand fingers. Your right thumb represents 5. To represent 7, press down your right thumb and 2 right hand fingers. Think of your right hand as the ones or units place (column).
Step 2
Your left hand represents the tens place (column). Each finger on your left hand is worth 10. For example, to represent 30, press down three left hand fingers. To represent 38, do the same, but also use your right hand to represent 8 as described above. Your left thumb represents 50. To represent 86, press down your left thumb and three left hand fingers for the 80, and your right thumb and one right finger for the 6.
Step 3
Each rod is like a thumb and 4 fingers
Practice by thinking of numbers from 0 to 99 and representing them using this method. You can also practice representing the numbers sequentially, or counting by twos. Make sure you understand why we aren't able to represent three-digit numbers with Chisanbop. Think about what the fingers and thumb would represent if we had a third hand that we could use. It would be the hundreds place, with each finger representing 100, and the thumb representing 500. That would allow us to go as high as 999.
Step 4
Now that you know how to form numbers and count, we can do some basic addition. Before we start, there are a few basic math facts to review which you already know, but which you must be able to instantly reference. Since our right thumb is worth 5, you need to instantly realize that 3+2 and 4+1 both equal 5 since we'll often need to break up 5 in that way. Similarly, since the left thumb is worth 10, you need to instantly recognize these ways of forming 10: 5+5, 6+4, 7+3, 8+2, and 9+1. We could say that 3 and 2 are complements with respect to 5, and 7 and 3 are complements with respect to 10. You'll be working with complements very often, but it will quickly become second nature.
Step 5
To add 1+3 is easy. Start by representing 1. Add 3 right fingers, giving us 4. To add 3+2 we would start by representing 3. Then add 1 right finger, but we still need to add one more. To do that we just tuck in our four right fingers and replace them with our right thumb, showing 5. We can do this with the tens column as well. To add 62+21, add two left fingers for the tens place, and one right finger for the ones place. You should end up with 83 represented.
Step 6
To add 3+9, subtract 1 and add 10
It starts to get a little trickier when we run out of fingers on one hand, and essentially need to carry a digit into the tens place like we do when adding traditionally. That is where the concept of complements comes in. Let's say we want to add 3 + 9. If you start with 3, you'll see that you can't possibly add 9 on the right hand. We could add our one remaining finger and our thumb, but that would only add 6 instead of 9. Certainly we could do that and then just count off three more, switching to one left finger when we get to 10, but there is an easier way. Rather than adding 9, it is far easier to add 10, and then subtract 1 since we added one too many. Adding 10 is easy, just extend your left thumb. Taking away 1 is also easy. Just tuck in one right finger. We instantly get 12. You can even do both of those steps at the same time.
Step 7
Adding to 91
Let's try one more. We'll add 63+28. Start by breaking the 28 into 20+8. Add 20 to the left hand by extending two fingers. Now we're looking at 83, but we still have to add the 8. We don't have enough room to add 8 to the 3 in our right hand. Instead, realize that adding 8 is the same as adding 10 and subtracting 2 (its complement). Subtract 2 from the right hand, and simultaneously add 10 to the left hand. You should have 91 which is our answer.
Step 8
Adding to 94
Let's try a tricky one that involves an additional step. We'll add 55+39. Start by breaking the 39 into 30+9, and add 30 to the left hand by extending three fingers. Now we're looking at 85, but we still have to add the 9. We don't have enough room to add 9 to the 5 in our right hand. Instead, realize that adding 9 is the same as adding 10 and subtracting 1 (its complement). We now have a new problem. We don't have an extended finger on the right hand that we can just tuck in like we had in the previous example. In this case we'll have to utilize the fact that if we take away 5 (our right thumb), but then add back 4 (four right fingers), it will have the net effect of subtracting 1, so we'll do that. Now that we subtracted 1 on the right hand, we must remember that we did this so that we could add 10 and have the net effect of adding 9, which was our original intent. Add 10 the left hand by extending a finger. If you do this you now should be looking at 94 which is our answer.
Step 9
A 7-digit Japanese abacus
Note that it is easy to use Chisanbop to do subtraction by essentially doing the these procedures in reverse, but that goes outside the scope of this article. Now that you know how add with Chisanbop, you actually know how to add using a Japanese abacus (soroban) in which each column (rod) has a single bead at the top (representing your thumb), and four beads at the bottom (representing your fingers).
Difficulty: Easy
Instructions
Step 1
In Chisanbop you'll be using your two hands and ten fingers to represent numbers from 0 to 99. Start out with your hands out in front of you with closed fists. This represents 0. Each finger (not thumb) on your right hand represents 1. To represent 3, just press down three right hand fingers. Your right thumb represents 5. To represent 7, press down your right thumb and 2 right hand fingers. Think of your right hand as the ones or units place (column).
Step 2
Your left hand represents the tens place (column). Each finger on your left hand is worth 10. For example, to represent 30, press down three left hand fingers. To represent 38, do the same, but also use your right hand to represent 8 as described above. Your left thumb represents 50. To represent 86, press down your left thumb and three left hand fingers for the 80, and your right thumb and one right finger for the 6.
Step 3
Each rod is like a thumb and 4 fingers
Practice by thinking of numbers from 0 to 99 and representing them using this method. You can also practice representing the numbers sequentially, or counting by twos. Make sure you understand why we aren't able to represent three-digit numbers with Chisanbop. Think about what the fingers and thumb would represent if we had a third hand that we could use. It would be the hundreds place, with each finger representing 100, and the thumb representing 500. That would allow us to go as high as 999.
Step 4
Now that you know how to form numbers and count, we can do some basic addition. Before we start, there are a few basic math facts to review which you already know, but which you must be able to instantly reference. Since our right thumb is worth 5, you need to instantly realize that 3+2 and 4+1 both equal 5 since we'll often need to break up 5 in that way. Similarly, since the left thumb is worth 10, you need to instantly recognize these ways of forming 10: 5+5, 6+4, 7+3, 8+2, and 9+1. We could say that 3 and 2 are complements with respect to 5, and 7 and 3 are complements with respect to 10. You'll be working with complements very often, but it will quickly become second nature.
Step 5
To add 1+3 is easy. Start by representing 1. Add 3 right fingers, giving us 4. To add 3+2 we would start by representing 3. Then add 1 right finger, but we still need to add one more. To do that we just tuck in our four right fingers and replace them with our right thumb, showing 5. We can do this with the tens column as well. To add 62+21, add two left fingers for the tens place, and one right finger for the ones place. You should end up with 83 represented.
Step 6
To add 3+9, subtract 1 and add 10
It starts to get a little trickier when we run out of fingers on one hand, and essentially need to carry a digit into the tens place like we do when adding traditionally. That is where the concept of complements comes in. Let's say we want to add 3 + 9. If you start with 3, you'll see that you can't possibly add 9 on the right hand. We could add our one remaining finger and our thumb, but that would only add 6 instead of 9. Certainly we could do that and then just count off three more, switching to one left finger when we get to 10, but there is an easier way. Rather than adding 9, it is far easier to add 10, and then subtract 1 since we added one too many. Adding 10 is easy, just extend your left thumb. Taking away 1 is also easy. Just tuck in one right finger. We instantly get 12. You can even do both of those steps at the same time.
Step 7
Adding to 91
Let's try one more. We'll add 63+28. Start by breaking the 28 into 20+8. Add 20 to the left hand by extending two fingers. Now we're looking at 83, but we still have to add the 8. We don't have enough room to add 8 to the 3 in our right hand. Instead, realize that adding 8 is the same as adding 10 and subtracting 2 (its complement). Subtract 2 from the right hand, and simultaneously add 10 to the left hand. You should have 91 which is our answer.
Step 8
Adding to 94
Let's try a tricky one that involves an additional step. We'll add 55+39. Start by breaking the 39 into 30+9, and add 30 to the left hand by extending three fingers. Now we're looking at 85, but we still have to add the 9. We don't have enough room to add 9 to the 5 in our right hand. Instead, realize that adding 9 is the same as adding 10 and subtracting 1 (its complement). We now have a new problem. We don't have an extended finger on the right hand that we can just tuck in like we had in the previous example. In this case we'll have to utilize the fact that if we take away 5 (our right thumb), but then add back 4 (four right fingers), it will have the net effect of subtracting 1, so we'll do that. Now that we subtracted 1 on the right hand, we must remember that we did this so that we could add 10 and have the net effect of adding 9, which was our original intent. Add 10 the left hand by extending a finger. If you do this you now should be looking at 94 which is our answer.
Step 9
A 7-digit Japanese abacus
Note that it is easy to use Chisanbop to do subtraction by essentially doing the these procedures in reverse, but that goes outside the scope of this article. Now that you know how add with Chisanbop, you actually know how to add using a Japanese abacus (soroban) in which each column (rod) has a single bead at the top (representing your thumb), and four beads at the bottom (representing your fingers).
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