# Subtracting Through Twenty

Now that we have single digits out of the way, let's look at some numbers between one (1) and twenty (20). If you were comfortable adding single-digit numbers, these**subtraction**problems will be easy.

We've been saying that subtraction problems are the opposite of addition problems. If you look at the equations written out you will see a pattern.

4 + 5 = 9 can also be written 9 = 5 + 4

9 - 5 = 4

Do you see that when you shift one of the values to the other side of the equals sign it becomes a subtraction problem? What you're really doing is two subtraction problems at the same time. In our example of 4 + 5 = 9, what happens when you subtract 5 from both sides of the equation?

4 + 5 - 5 = 9 - 5

Those fives on the left side cancel each other out (5-5=0). All of a sudden you are left with 4=9-5. You can see how closely addition and subtraction are related.

You will view subtraction problems with larger values in a different way. Let's say you see two numbers that just don't click in your head. Try looking at the smaller number and ask, "What number added to the smaller number will give me the bigger answer?" Your work with addition can help you when doing subtraction problems.

**Example:**

15 - 7 = ?

(1) If you don't have the answer memorized, ask yourself "What number plus seven (7) is equal to fifteen (15)?"

(2) You might remember that 7 + 8 = 15

(3) If 7 + 8 = 15, then 15 - 7= 8

Try that idea with these examples.

**Examples:**

15 - 7 = ? (remember that 7 + 8 =15)

18 - 9 = ? (remember that 9 + 9 = 18)

12 - 8 = ? (remember that 8 + 4 = 12)

# Column by Column

You already know that subtraction problems need a**minus**(-) sign. They can also be written in two ways. On our pages you will usually see the problem in a left-to-right format. For simple numbers, this layout works fine. As you start to use larger numbers, you will see subtraction problems in a

**vertical**(up and down) format. You will move through the problem in the same way you did with addition. Break the problem up into several smaller subtraction problems. Start with the

**column**of numbers on the right (in the ones column). Once you finish with the ones column you will move to the tens, hundreds, and any other columns of numbers that you have. Just take simple steps.

**Example:**

19- 613 |

Step two: 1-0=1 (tens column)

# Empty Space

When you use that "up and down" layout, you will find numbers that don't match. If you have the problem 15,687 - 5, there are whole columns of numbers that have no values. Just treat those empty spaces like**zeros**(0).

**Example:**

15,687 - 5 = ?

-or-

15687- 5? |

7 - 5 = 2 (ones)

8 - 0 = 8 (tens)

6 - 0 = 6 (hundreds)

5 - 0 = 5 (thousands)

1 - 0 = 1 (ten thousands)

So 15,687 - 5 = 15,682

- Overview
- Operations
- Addition
**Subtraction**- 1 to 10
**1 to 20**- Borrowing
- Borrowing-2
- 2-Digit Numbers
- 3-Digit Numbers
- Multiple Values
- Integers
- Integers-2
- Workbooks
- Multiplication
- Division
- Activities

# Useful Reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Arithmetic*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/arithmetic*

**Encyclopedia.com:**

*http://www.encyclopedia.com/topic/arithmetic.aspx*