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# Combination Explained

Following the specific discipline around combinations allows the students to quickly manipulate the abacus tool to quickly compute the correct answer. These discipline in combinations eliminate excessive movements of the fingers by forcing the hand to move in a single direction.

For example, a Young Buddy combination is +5 – 3 because the movement of the finger is all downward; the five-bead is pulled down and 3 of the ones-beads are also pulled down. Had it been the other way around, –3 + 5, then the student would need to push down 3 of the ones-beads and then move back up to bring the five-bead down as well. When in a competition, those fractions of a second could be the difference between 1st place and 2nd place.

When remembering the order of adding or subtracting first for the Young and Old Buddy combinations, an easy way to remember is to think of the combinations as a person. The Young Buddies are still growing up, so we need to add first so that they get older. And the Old Buddies wish that they were kids again, so we need to subtract first, so they don’t feel as old.

Between the Young Buddies and Old Buddies combinations, there is an overlap between adding and subtracting numbers 1 through 4. The distinction depends on if the five-bead is currently used or not. If we are adding to a digit less than 5, we will use the Young Buddy Combination, and if we are adding to a digit that is 5 or more, we will use the Old Buddy Combination.

Now, this begs the questions of when Double Combinations will be used instead of Old Buddies when adding or subtracting numbers 6 through 9. The Double Combinations are the Old Buddies mixed with the Young Buddies. When ADDING with the Old Buddy Combination, if you cannot subtract the given value, you must first do the respective Young Buddy Combination for the subtraction before continuing to +10.

Ex. To do 5 + 9, we would need to –1 +10 as is the combination for Old Buddy. However, since there is no one-bead to take away, we would need to do the Young Buddy to –1. We will first (+4 – 5) to take care of the –1 and then finish with the +10.

We do a very similar thing when SUBTRACTING with the Old Buddy Combination. After –10, if you cannot add the given value, you will first do the respective Young Buddy Combination for that additional bit.

When trying to remember what number to add and subtract for the Young Buddy Combinations, there are two ways to think about it: with “friends” or with negatives.

When ADDING with the Young Buddies, the “parent” 5 is coming in to take away the “friend” so he can go home. The “friend” is always the number needed to add up to 5 with the number we are currently adding. Say we needed to +4. We know that 4 + 1 = 5, so 1 would be the “friend.” Now using the story, the “parent” 5 is coming in to take away the “friend” 1 back home. This means to +4 on the abacus, we will +5 – 1.

When SUBTRACTING with the Young Buddies, the “friend” is coming to stay and the “parent” 5 will leave to let them play. If this time we need to –2, the “friend” will be 3 (because 2 + 3 = 5) and will be staying over to play while the “parent” 5 leaves them alone. So, on the abacus, it will be +3 – 5.

This can be applied to the Old Buddy Combinations as well, but with the “parent” being 10 instead of 5, and the “friend” will be the numbers that will add together make 10 instead of 5 as well. Also, keep in mind that Old Buddies will always be subtracting first, so the order of the “parent” and “friend” will be switched in the stories. When ADDING with Old Buddies, the “friend” needs to go home, so the “parent” comes in. When SUBTRACTING with Old Buddies, the “parent” is leaving to let the “friend” stay over.

When using the thought process of negatives, it more relates to the actual equation rather than a story. We just need to remember that for Young Buddies the positive number is always first and for Old buddies, the negative numbers are always first. We are also still considering the pairs that will add together to make 5’s and 10’s.

If we are ADDING for either Young Buddy or Old Buddy Combinations, the larger number will be positive, because we are trying to ADD (meaning have a poise number.) This always results in having +5 for Young Buddies and +10 for Old Buddies because the other number used for the combination is always smaller. So if we want to do +3 as a Young Buddy, we know that the combination starts with addition and will use the numbers 2 and 5. However, we want to make sure that the combination results with a positive answer. This means we have a –2 and a +5, and the resulting combination will be +5 – 2. Doing +3 as an Old Buddy, we know it will start with subtraction. The two numbers we use for this combination are 7 and 10, but since we need a positive 3, 10 will be the positive number. This will result in a combination of –7 + 10.

This same thought process can be brought over to subtraction by keeping in mind that the larger number must be negative now. So, you will have –5 and –10 for Young Buddy and Old Buddy Combinations respectively. You must also remember that Young Buddies are always adding first while Old Buddies are always subtracting first.