MA6-WEEK2-INTRODUCTION-TO-RATIONAL-NUMBERS

Introduction to Rational Numbers

Start

Objectives

Rational Numbers

Summary

Number Line

Integer NumberSystem

Integer Number System

Well, if I buy the game for $50, I'll have $70 - $50 = $20 left.

Let's start with a simple scenario. Imagine you're at a store, and you're considering buying a video game. The game you want costs $50. Now, let's say you have $70 in your pocket. How much money do you have left after buying the video game?

Well, If I don't buy the game, I still have $70. So, zero means I didn't make any purchases.

Correct. Now, let's consider a different scenario. What if you really want the game, but you only have $40?

Correct! Now, what if you decide not to buy the game at all?

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That's right. When you're short on cash, we represent that with a negative number. So, if you're $10 short, it's like having -$10.

Oh no, I don't have enough money to buy it!

Absence of quantity

Having certain amount of anything (objects, money, any property,...)

Not having enough amount of anything (objects, money,...)

Negative numbers:

Zero 0:

Positive numbers:

Kinds of Integer Numbers

+1, +,2, +3, ... 0 -1, -2, -3,...

Integer Numbers: Are positive, zero, and negative whole numbers.

Positive numbers: Zero: Negative numbers

Example 3: Negative Number "My uncle did not paid the $10 000 he borrowed from the bank" So, his balance is -$10 000.

Example 2: Zero "The bedroom is empty" So, there are zero elements in the room.

Example 1: Positive Number "I have +5 kilograms of chicken in the fridge".

Let's see some examples:

Try it by yourself:

Number Line

Numbers are increasing from left to right

Positive numbers from right to zero

The arrows indicate that numbers increase indefinitely to the right ( positive numbers) and decrease indefinitely to the left (negative numbers).

Negative numbers are from left to zero

Number Line: It is an ordering representation of integer numbers.

Example 1: As seen in the number line, we have the following statements:

0<1 -8<10 -5<-3 4≥1

which is read as 0 is less than to 1 which is read as -8 is less than to 1 which is read as -5 is less than to -3 which is reads as 4 is greater than or equals to 1

Let's see some examples:

Interpret information

Write data with their signs.

Givens

• Height of the scuba diver: -30m
• Height of the fish: -50m
• Height of the bird: +50m

A girl is scuba diving 30 m below sea level. There is also a bird flying 50 m above and trying to catch a fish which is 50 m below sea level.

70

50

-40

30

-20

-50 -10 0 10 20

Solution

Exercise 1: Place the numbers in order on the straight line.

Try it by yourself:

Rational Numbersand Number Line

Listen, read, & solve

Try it out

Imagine that we have to place 10 watermelons in 4 baskets. How would you distribute them equally?

Solution

After reviewing the story, it is evident that

The result of a fraction does not always outputs an integer number

Negative

Non-integer divisions

Zero

Positive

integer

Non-integer

Rational Numbers are every quotient of any division , where q≠0

Placement of Fractions in Number Line

A fractional number is located by partitioning the number line into as many parts as the denominator indicates and then selecting as many divisions as the numerator indicates.

For instance, place 10/4 on the number line.

Let's see some examples:

Example 2: Place -3/2

Example 1: Place 7/2 on the number line.

Let's see some examples:

Example 3: Place 16/2

Example 3: Place 11/3

Try it by yourself:

Whole Numbers

Integer Numbers

Rational Numbers

• Numbers are represented in an ordered way on number line

Summary

6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

See you next time

Great job!

A journey soon begin through Social Science experiences!

Welcome 6th graders!

Solution

Standard 1: Extend knowledge of numbers to negative numbers and develop an understanding of absolute value. MA.6.NSO.1.1 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.

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• Sed do eiusmod tempor incididunt ut.
• Labore et dolore magna aliqua.

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70

50

-40

30

-20

-50 -10 0 10 20

Solution