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# The Number System 7.NS

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on 15 December 2013

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#### Transcript of The Number System 7.NS

The Number System 7.NS

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Vocabulary Recap

Integer
Any whole number and/or the additive inverse of a whole number is an integer.
The additive inverse of a number is the opposite of that number, that is, the additive inverse of a number x is -x. The sum of a number and its additive inverse is always zero, that is, x + (-x) = 0.

Whole Numbers
The set of integers whose members are zero and the counting numbers (natural numbers). Symbol: W.
Counting numbers usually exclude zero.
Negative Number
Any real number that is less than zero. Negative numbers are usually used to represent quantities that are below a specified reference point.
Positive Number
Any real number that is greater than zero.
Positive numbers are usually used to represent quantities that are above a specified reference point.
Number Line
A straight line on which each point represents a real number. It is a geometric representation of numerical values.
I
ntroducing:
Negative Numbers
Absolute Value:

Sometimes we are interested only in the distance a number is from zero.
Here's an official math definition for you:
The absolute value of a number is
its distance from zero on the number line.

* For the notation, we use two big vertical lines.

| a |
= a

| -a |
= a

Check it out:

Find the absolute value of 4:

| 4 |
= 4

Find the absolute value of -5:

| -5 |
= 5
Absolute Value
The magnitude of a number regardless of its sign. Hence, the absolute value of a number "n" is always positive or zero, written as |n|. When the number "n" is represented on a number line, its absolute value is the distance from the origin to that number.
So, what's the absolute value of 0?

How far is it away from itself on the number line? Nothing!

| 0 | = 0

Here's another one:

Find the absolute value of -2.31:

| -2.31 | = 2.31

Find the absolute values:

| 10 |
...
| -101 |
...
| 0.59 |
...
| -6.1 |
...
| -3/2 |
...
| 1/6 |
So, let's look at what happens when you add two negative numbers:
-2 + -3

Look at the number line:
-2 + -3 = -5
So, when you add two negative numbers, you get a negative answer!
So... What if some of the numbers are positive and some are negative?
2 + -5

Look at the number line:
2 + -5 = -3
Here's another one:
6 + -2
Here it is on the number line:
6 + -2 = 4
Now you try it
Try it:

Do these on a number line:

5 + -7 =

-3 + 6 =

-9 + 4 =

8 + -1 =
Lets check our understanding...
More Number Line practice
ELD Standard A4: Collaborative, Adapting Language Choices.
Journal Entry
Why is the absolute value | | of -7 and 7 the same?
Answer I expect (in correct form) from my ELL's:
"We know that -7 is seven units away from zero on the number line. Positive 7 is also 7 units away from zero on the number line. Therefore they both have the same absolute value."
"...

..."