Addition, Subtraction, and Whole Numbers

Background 

Now that we have learned about Whole Numbers, Addition, and Subtraction, let's work a problem (there's more problems in the Practice Problem section)

Question 

Find 5 + 2 - 3 - 1 + 6 - 0 + 0

Answer 

9

Analysis  

In prior entries, we've worked individual calculations, say like 5 + 2, both with and without the number line. We'll do the same here but we'll start on with the leftmost term and work our way through the different operations (the plusses and minuses).

We're evaluating 5 + 2 - 3 - 1 + 6 - 0 + 0

We can start with a number line and a red dot on the number 5:



So let's colour the 5 in our expression red: 5 + 2 - 3 - 1 + 6 - 0 + 0

Our first operation is plus 2 (+ 2). We move our point two numbers to the right, to 7 (I'll show that with blue):

5 + 2 - 3 - 1 + 6 - 0 + 0



Now starting at the blue dot at 7, we subtract 3 (- 3), or move 3 spots to the left. We'll land on the 4. I'll show that with green:

5 + 2 - 3 - 1 + 6 - 0 + 0



Starting at 4, we subtract 1 more to land on 3 (I'll show that in orange):

5 + 2 - 3 - 1 + 6 - 0 + 0



Now we add 6. Starting from the 3, we'll land on 9 (shown in purple):

5 + 2 - 3 - 1 + 6 - 0 + 0



And now we're asked to first subtract 0 and then add 0. Notice that when we add or subtract 0, the dot doesn't move! And so we leave our dot at 9.

This ability, to add and subtract 0 as many times as you want to any number and not change that number's value (like what we did with the 9 - we didn't change its value at all by adding or subtracting 0), gives 0 a special name - the additive identity.

Ok - so now let's work this same problem one more time, but this time without the number line. Here we go:

5 + 2 - 3 - 1 + 6 - 0 + 0

7 - 3 - 1 + 6 - 0 + 0

4 - 1 + 6 - 0 + 0

3 + 6 - 0 + 0

9 - 0 + 0

9

We start on the left and work our way to the right.

Vocabulary:

• Whole Numbers - The set of numbers that starts with 0 and increases by 1 (0, 1, 2, 3,...)

For more information check out these links (comment to add your favourite link): 
Where might you have come from? 

Fact-orials Index

Numbers:

• The Number 0
• Whole Numbers

Operations:

• Addition
• Subtraction

Graphing:

• Number Line

Where might we go?

Operations:

• Grouping Terms, Parentheses

Operations with different kinds of numbers:

• Addition, Subtraction, and Whole Numbers - Practice Problems
• Multiplication, Division, and Whole Numbers
• Addition, Subtraction, and Integers

Properties:

• Associative Property