Abacus Math Program – Lesson 14 – Reverse Double Five

In Lesson 13 we explored the Forward Double Fives in the forward direction for addition. Now let’s take a look at the double fives in the reverse direction for subtraction. We will use the exact same technique but this time we will perform the 10 pair subtraction rule using two 5 pair movements. Let’s work through some examples.

In this first example we start by adding 17 to the abacus placing 1 on rod A and 7 on rod B. Next we add 47 to 17 by first adding 4 to 1 on rod A using a 5 pair adding 5 and subtracting 1, the 5 pair of 4, leaving 5 on rod A. Next we add 7 to 7 on rod B using the 10 pair addition rule. First add 1 to 5 on rod A leaving 6 on rod A. Then subtract 3, the 10 pair complement of 7, from 7 on rod B using a 5 pair adding 2 and subtracting 5 leaving 4 on rod A. The interim sum is now 64. Lastly we subtract 19 from 64 by first subtracting 1 from 6 on rod A leaving 5 on rod A. Next we subtract 9 from 4 on rod B using the 10 pair subtraction rule which will require the Reverse Double Five. First subtract 1 from 5 on rod A using a 5 pair adding 4, the 5 pair of 1, and subtracting 5 leaving 4 on rod A. Finally add 1, the 10 pair of 9, to 4 on rod B again using a 5 pair adding 5 and subtracting 4 leaving 5 on rod B. The final answer is 45. 

In the last double five example we start by adding 40 to the abacus placing 4 on rod A. Next we add 43 to 40 by adding 4 to 4 on rod A using a 5 pair adding 5 and subtracting 1 leaving 8 on rod A. Next we add 3 to 0 on rod B for an interim sum of 83. Next we subtract 37 from 83 by first subtracting 3 from 8 on rod A leaving 5 on rod A. Then we subtract 7 from 3 on rod B using the 10 pair subtraction rule. First subtract 1 from 5 on rod A using a 5 pair adding 4 and subtracting 5 leaving 4 on rod A. Then add 3, the 10 pair complement of 7, to 3 on rod B using a 5 pair adding 5 and subtracting 2 leaving 6 on rod A. The final answer is 46.

Next up Lesson 15 Forward Double Rod.