In this video, we are going to talk about
adding and subtracting single digit numbers using our soroban. In the first video of the soroban series,
we looked at how to properly move the beads with our fingers. If you recall, we used the thumb to add the
"one bead". We use the index finger to remove the "one bead" or to add the "five bead" And we saw that we also use the index finger
to remove the "five bead". Okay so let's take into account the proper
fingering and add some numbers. Before we begin, lets clear our soroban. No beads on the soroban should be touching
the bar at this point. We are going to start with 1+3. If you remember correctly, we should be using
only our thumb. I am going to enter 1 with my thumb and use
my thumb again to add 3. Let's do 5+2. I am going to use my pointer to enter 5, then
use my thumb to add 2. How about 7+2. Now remember, when I set a number from 6 to
9, I will chunk the "five bead" and the "one bead"
with both my fingers. So for seven, we chunk the "five bead" and
the 2 "one beads", that gives us seven, and add 2
with our thumb. The added total is nine. Alright, now lets do 9-7. Dont forget to chunk the beads for the 9 and
then you take away 7. The fingering is little tricky here, remember
when we chunk the numbers from 6 to 9, we chunk them with our thumb and our pointer
at the same time, but when subtracting, we take
away first the bottom "one beads" followed by the "five bead",
and use only the pointer when subtracting seven. Alright, this was pretty straight forward. we only had to move the beads representing
the numbers once. But there are times when you would have to
move the beads more than once to perform a single operation. We call these adding and subtracting using
complementary numbers, but before moving on,
lets take a look at a triangle that should help us visualize the order in which we should
use our fingers. What we have here is a triangle, but we are
only concerned with whether the triangle is straightup or upside down. If it is upside down, which would be the case
for adding or subtracting complementary numbers with respect to 5,
in that case we add first and then we do the subtraction. If the triangle is straightup, as in the calculation
involving complementary numbers with respect to 10,
in that case we subtract first and then do the addition part. "add subtract using complementary numbers
with respect to 5" "add/subtract using complementary numbers
for 5" Okay lets add another one, 1+4. We enter one, and now we want to add 4, but
we dont have 4 "one beads" here in the ones column in which
to add, so we are going to add five and then take away 1 which is the same as adding 4. So the way we do this "add 4" on the soroban
is we first add the "five bead" with our pointer and then subtract the
"one bead" with the same pointer again. Lets do this one more time, 1+4. We add 1, and for the add 4, we do "5 take
away 1". Let's do another one,
3+2. We set three, and now we want to add 2, but
since we dont have 2 "one beads" in our ones column,
we are going to add five and then take away 3 which is the same as adding 2. So the way
we do this "add 2" on the soroban is we first add the "five bead" with our pointer and then
subtract the "one bead" with our pointer again. Let's repeat this, 3+2. We add 3, and for the add 2, we do "5 take
away 3". Okay, let's do subtraction next, 5-3. We set 5, and now we want to remove 3, but
since we dont have "one beads" to subtract in our ones column,
we are going to subtract five and then add back 2 which is the same as subtracting 3. So the way
we do this "subtract 3" on the soroban is we first add 2 "one beads" with our thumb
and then subtract the "five bead" with our index finger. Lets do this one more time, 5-3. We add 5, and for the subtract 3, we do "2
take away 5". Let's try, 5-1. We enter 5, and now we want to remove 1, but
since we dont have "one beads" to subtract in our ones column,
we are going to subtract five and then add back 4 which is the same as subtracting 1. So the way
we do this "subtract 1" on the soroban is we first add 4 "one beads" with our thumb
and then subtract the "five bead" with our pointer. Lets do this one more time, 5-1. We add 5, and for the subtract 1, we do "4
take away 5". Our answer is four. Now let's do addition that involves the tens
column. 4+6
We enter 4, and now we want to add 6, but we dont have enough beads to add 6 in our
ones column, so we are going to add 10, that means adding
a single "one bead" on the tens column, and then take away 4 which is the same as
adding 6 in the first place. So the way
we do this "add 6" on the soroban is we first subtract four "one beads" with our pointer
and then add back ten with our thumb. Let's do this one more time, 4+6. We set 4, and for the add 6, we do "take away
4 add 10". Let's try, 9+3
We chunk the 9, and now we want to add 3, but we dont have enough beads to add 3 in
our ones column, so we are going to add 10, using the "one
bead" on the tens column, and then take away 7 which is the same as
adding 3 in the first place. Take away 7 is the tricky one, remember? we
take away first the 2 bottom beads followed by
the "five bead", By now, hopefully we are getting a hang of
this triangle, we first do the subtraction followed by the
addition. Lets do this one more time, 9+3. We set 9, and for the add 3, we do "take away
7 add 10". Now let's do subtraction using complementary
numbers with respect to ten. 11-3
We enter 11, and now we want to subtract 3, but we dont have enough beads to subtract
3 in our ones column, so we are going to subtract 10, with our pointer
finger, and then add 7 which is the same as subtracting
3 in the first place. When we add back 7, remember that we chunk
the upper and lower beads at the same time. Looking at the triangle, the order in which
we do the subtraction is we first do the subtract 10 followed by
the add back 7. Lets do this one more time, 11-3. We set 11, and subtract 3 becomes
"take away 10 add 7". Let's try,
13-4 We enter 13, and now we want to subtract 4,
but we dont have enough beads to subtract 4 in our ones column,
so we are going to subtract 10, with our pointer finger,
and then add 6 which is the same as subtracting 4. The order in which we do the subtract 4
is we first do the subtract 10 followed by the add back 6. Lets do this one more time, 13-4. We set 13, and subtract 4 becomes
"take away 10 add 6". We get our answer 9. Now lets take a look back, and see why we
move the beads in the order we do. For the addition involving complementary numbers
with respect to 5, for example for add 4, we did
"5 take away 1" "take away 1 add 5" in the reverse order would
certainly yield the same answer, but we would notice that the finger movement
going down then up in that case would be unnatural compared to just sweeping down our
pointer finger as in "5 take away 1". When using complementary numbers with respect
to 5 for addition we sweep down our pointer finger. If we are doing subtraction using complementary
numbers with respect to 5 we only have to remember to sweep from bottom
to the upper "five bead". Once you start to get the hang of this sweeping
finger movement, you will realize that you are no longer actively
thinking of the "five bead", but instead thinking only of the complementary number
and the "five bead" comes along the ride naturally. "add 4" becomes "subtract 1",
"add 2" becomes "subtract 3", "subtract 1" becomes "add 4",
"subtract 3" becomes "add 2". Now lets shift to addition involving complementary
numbers with respect to 10. For example in 4+6,
for add 6, we do "take away 4 add 10", and not "add 10 take away 4". Again, there is a good reason behind this. Keep in mind that when we set 4 in the beginning
of the calculation, our fingers are hovering over the ones column. Following this with add 6, it is natural to
start with the ones column subtracting 4 then moving on to the next column
to add ten. If we reverse the order, we would be starting
at the ones column, moving to the tens column to add 10
and then returning back to the ones column to subtract 4. Here again, after some practice, you begin
concentrating only on the complementary number, so "add 6" becomes "subtract
4" and the final "add 10" part follows without much thought. And finally for the subtraction involving
complementary numbers with respect to 10, For example in 11-3,
for "minus 3" we do "subtract 10 add 7" This is because once we realize we dont have
enough beads to subtract 3 from the ones column, we shift to the tens column and start our
operation from there. This is in line with the natural order of
attention. If we were to reverse this order,
we would have to shift our attention back to the tens column to subtract 10 after adding
7. The advantage of these proper finger
movements start becoming more apparent when we start calculating larger numbers. In this video, we looked at the usage
of complementary numbers and their proper order of operation
when the calculation involves moving the beads twice. In the next video we will still be looking
at adding and subracting single digit numbers, but there we will be moving the beads three
times for a single operation.
