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# Lesson 9:  Basic Subtraction

Many older students have trouble understanding how basic subtraction works.  Sometimes this is because they learned the procedure, but never really learned why the procedure worked.  Other times it's because they became used to doing every computation on the calculator.  It's very important to have a very clear understanding of how subtraction works.

Don't forget to watch the embedded YouTube video clip for this lesson at the bottom of the page.

To subtract one number from another, all we really have to do is count backwards starting from the larger number.  If we want to subtract 8 - 3, we should start with the bigger number, 8, and then count down three numbers....7...6...5, and that is our answer.  For small numbers, it's important that you able to do this quickly and easily.  The best way to practice this is with flashcards, either store-bought, or home-made.  Keep quizzing yourself until you can subtract two small numbers very easily.

Many older students are permitted to use calculators on every exam, but if you have trouble doing very basic math in your head, you'll have a hard time figuring out if you made a mistake with your calculator, which is very easy to do.

Subtracting two-digit numbers can be hard to do in your head.  There is a procedure for subtracting them, and it's important to understand how the procedure works, as well as knowing how to use it.

Look at problem 1 below.  To subtract two, two-digit numbers, line them up one on top of the other.  Remember to line up the ones places and the tens places right on top of each other.  Always start on the right, which is the ones place.  In problem 1, we'll subtract 8 - 2 to get 6, which we'll write below the line in the ones column.  Then we'll move left to the tens column, and subtract 3 - 1 to get 2, which we'll write in the 10 column, giving us a final answer of 26.

Take a look at problem 2.  First we need to subtract the ones column, but now there is a problem.  We need to do 3 - 5, but since the first number is smaller than the second number, we have to do something special.  If we look in the tens column of the first number, we'll see that there is a 6, which means 6 tens.  What we can do is "borrow" a ten, and move that ten into the ones column.  That is OK because we're not changing the value of the number.  We'll change the 6 into a 5 as shown, and then put a little 1 to the left of the 3, making it a 13.  We borrowed a ten from the tens column, and increased the value of the ones column by ten.  Now we can do 13 - 5 which is 8, and then for the tens column we can do 5 - 1 which is 4, giving us 48.

Take a look at problem 3.  This one is trickier.  First we have to do 3 - 9 in the ones column, but we can't, for the same reason as in problem 2.  We'll borrow a ten from tens column, crossing out the 2 and making it a 1.  Now we can subtract 13 - 9 in the ones column to get 4.  Moving left, we see that we have to subtract 1 - 5 in the tens column.  Remember, we borrowed a ten, and so the 2 became a 1.  But we can't do 1 - 5, so we'll borrow from the hundreds column, using the same logic.  We'll decrease the number in the hundreds column by one, and move that one into the tens column.  So the 1 that was in the tens column is now 11, and we can subtract 11 - 5 to get 6.  All we have in the hundreds column is a 4, and so we can bring it down below the line, and get a final answer of 464.

Look at problem 4.  This is a bit different.  In the ones column, we have to do 0 - 3, which we can't, so we'll borrow from the tens column to the left.  But the problem is that the tens column has a 0 in it, so we can't subtract anything from it.  The way to handle that is to immediately borrow from the hundreds column, for the sake of the tens column. We'll borrow a hundred to make the 8 into a 7, and then we'll add that one to the left of the zero in the tens column, making it 10.  Now we are able to borrow one from the tens column for the sake of the ones column.  We can subtract one from the 10 to get 9 in the tens column, and add it to the ones column, which gives us a 10 in the ones column.  The answer then becomes 757.

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