1.4+Subtraction

Section 1.4 - Subtraction
Subtraction is the opposite of addition, but the minus sign gives some people such a problem that all of Chapter Two is devoted to it. In this section, we will cover just the basics of subtracting whole numbers.

First, a few vocabulary terms:

Minus - While this may refer to a negative number (less than zero), it is also what you do in a subtraction problem. Just like "plus" is for addition, "minus" is for subtraction. However, it matters which order the numbers are listed (unlike addition). 8 minus 3 does not equal 3 minus 8. If the problem says 8 - 3, you will start with 8 and subtract 3 (or take 3 away from 8).


 * Difference - The answer to a subtraction problem. ** If you are looking at a numberline and want to know the difference between two numbers, you could count the number of spaces between them. Or, you could subtract - the bigger number minus the littler one.

By the way, does it matter which direction you counted on the numberline? If a problem asks you for the difference between two numbers, or two measurements, you will need to subtract (the little from the big).

The subtraction rule is: ** Subtract the smaller number from the larger number and use the sign of the larger number! ** Sign refers to whether a number is positive or negative, but we'll deal with that in Chapter 2. When you are subtracting whole numbers, they are all positive, even though there is no + sign in front of them.

On a numberline, it works like this - If you have two numbers, the one on the right will always be larger than the one on the left. Always.

Notice these two ways to describe a subtraction problem:


 * Seven minus three.
 * Subtract three from seven.

These are the same problem, and would be written either of these ways:

Subtract the three by counting down three spaces on the numberline from seven. 7 - 3 = 4.

Here's the Khan Academy video explaining basic subtraction.

media type="youtube" key="incKJchBCLo?fs=1" height="385" width="480"


 * Subtracting Multiple Digit Numbers**

If there is no digit for a particular place, leave it blank and consider it a zero.

The Khan Academy videos introducing borrowing or regrouping. The first is a basic introduction. The second is an explanation of why borrowing works. The third is excellent practice with more complex numbers.

media type="youtube" key="ZaqOUE3H1mE?fs=1" height="385" width="480" media type="youtube" key="fWan_T0enj4?fs=1" height="385" width="480" media type="youtube" key="omUfrXtHtN0?fs=1" height="385" width="480"



If you need to borrow from a zero, first borrow 1 from the next column to make the zero a 10.




 * Subtracting More than Two Numbers**

Don't do it. If the problem looks like: 450 - 153 - 197 - 42 subtract two numbers at a time, always starting at the left side. Subtract the first two, then use that answer (difference) and subtract the next number, and so forth.



The Associative and Commutative Properties that work for addition DO NOT work for subtraction. You can't go in any order you want - it must be left to right, two at a time.


 * Application Problems with Subtraction**

With subtraction, you are ready to read bar and line graphs (Sections 10.2 and 10.3)

**Where to from here?**
1.1 Place Value 1.2 Rounding and Estimating Numbers 1.3 Addition 1.4 Subtraction 1.5 Multiplication 1.6 Division 1.7 Exponents 1.8 Order of Operations 1.9 Prime Numbers
 * Chapter One Review**
 * Chapter One Homework**