MA6-WEEK10-POSITIVE-AND-NEGATIVE-NUMBERS

Positive and Negative Numbers (With negative results)

Objectives

Start

Story

Addition and Subtraction

Multiplication and Division

Order of Operations

Summary

Story

Test your Knowledge:

Addition and Substraction

Numbers with the same sign are added

Example 2:

Example 1:

(-5)+(-6)=-11

5+6=11

In framed diagram:

In framed diagram:

Meaning: I have 5 and 6, in total I have 11

Meaning: I owe 5 and owe 6, in total I owe 11

Numbers with Different Sign are Substracted

Example 2:

Example 1:

4+(-7)=-3

7-4=3

In framed diagram:

In framed diagram:

Meaning: I have 7 and owe 4, so I end up with 3

Meaning: I have 4 and owe 7, so I still owe 3

Try it by yourself:

Multiplication and Division

Multiplying either + or -numbers is also done by a repeated sum

Example 2:

Example 1:

-(3x4)=-12

2x(-3)=(-3)+(-3)=-6

In framed diagram:

In framed diagram:

Meaning: 2 times the opposite of 3 equals -6

Meaning: The opposite of 3 times 4 equals -12

Division is done as usual but now take in mind that one "-" means the opposite of.

For instance:

-15÷3=-15

In framed diagram:

Meaning:

The opposite of 15 is shared in 3 equal parts of -5

Order of Operations

When we have to do several operations, how do we know which ones are performed first?

A pnemonic rule to remember operation order is called PEMDAS. As explained in the next page.

PEMDAS ( ),()³,x,÷,+,-

FIRST

(), [],

Parenthesis (Kind of)

()²,()³,...

Exponentials (and roots)

Multiplications and Divisions

x, ÷

Additions and substractions

+,-

LAST

Let's see some examples:

Example 1: Calculate 1 + 2 × 3

Example 2: Perform 5x(4+3)+1

5x(4+3)+1 = 5x(7)+1, = 35+1,

4 + 2 × 3 = 4+6,

= 10

= 36

Example 3: Perform (-5) × (2 - 1) + 4

(-5) × (2 - 1) + 4 = -5× (1) + 4 = -5 × 1 + 4 = -5 + 4

=-1

Now, let's see how to summarize all of the cases we've seen in two rules.

Summary

Rule of Signs for addition and subtraction.

Subtraction

Addition

Rule of Signs is applied when multipliying or dividing two numbers

Division

Multiplication

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

6TH-POSITIVE-AND-NEGATIVE-NUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

Standard 1: Extend previous understanding of numbers to define rational numbers. Plot,order and compare rational numbers. MA.6.NSO.1.2 Given a mathematical or real-world context, represent quantities that have opposite direction using rational numbers. Compare them on a number line and explain the meaning of zero within its context. MA.6.NSO.1.4 Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value. Standard 3: Apply properties of operations to rewrite numbers in equivalent forms. MA.6.NSO.3.3 Evaluate positive rational numbers and integers with natural number exponents. Standard 4: Extend understanding of operations with integers. MA.6.NSO.4.1 Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency. MA.6.NSO.4.2 Apply and extend previous understandings of operations with whole numbers to multiply and divide integers with procedural fluency.