Subtraction without Borrowing: Subtraction by Steps

Subtractions which do not require regroupings or “borrowings” can be easily solved mentally. There are simple techniques which can help us avoid “borrowing. The first of these is what I called “Subtraction by Steps” in my book “25 Math Short Cuts”.

This technique works best when the minuend is just above a base while the subtrahend is just below it. Knowledge of our previous Math tips, “completing the whole” and “all from 9 and the last from 10” is essential in quickly performing this type of calculation.

In our example here, 12,432 – 9,789, we notice that there is a convenient base, 10,000, between the two numbers.

Our mental solution can be performed in 3 simple steps.

Step 1: The difference 12,432 – 10,000 is quickly done by just removing the leading digit 1 in the minuend resulting into 2432.

Step 2: By applying “All from 9 and the last from 10” to 9,789, its 10’s complement is easily determined to be 211.

Step 3: Adding 211 to 2, 432 requires little effort since there is no regrouping to get the final answer of 2,643.

More examples of this type of subtraction is discussed in chapter 3 of my book “25 Math Short Cuts”

In February, I will conduct a special Online course where I will discuss all the techniques and application of the 25 Math Short Cuts for ages 8 to 88 but this will be most beneficial to elementary school pupils specially those competing in Math contests.

Try to solve the following mentally using subtraction by steps:

1. 222 – 198 =
2. 334 – 289 =
3. 715 – 476 =
4. 1, 123 – 987 =
5. 5, 323 – 889 =
6. 6,145 – 798 =
7. 23,456 – 9, 897 =
8. 55, 432 – 49,678 =
9. 523, 321 – 478, 787
10. 1,222,111 – 777,889

Answers will be posted next week.

Here are the answers to last week’s practice exercises: “All from 9 and the Last from 10”

1. 1,000 – 456 = 544
2. 10,000 – 3,859 = 6,141
3. 100,000 – 83,942 =16,058
4. 1,000,000 – 598,274 = 401,726
5. 1 – 0.24 = 0.76
6. 1 – 0.789 = 0.211
7. 1 – 0.4587 = 0. 5413
8. 1 – 0.68942 = 0.31058
9. P100 – 24.75 = P75. 25
10. P1,000 – 786.38 = P 213.62