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Objectives

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Introduction to Rational Numbers

Integer NumberSystem

Number Line

Summary

Rational Numbers

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Integer Number System

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

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

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

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

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

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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.

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Kinds of Integer Numbers

Positive numbers:

Zero 0:

Negative numbers:

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

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

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Absence of quantity

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Positive numbers:Zero:Negative numbers

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

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

Positive numbers might or might not have "+" sign: E.g.: +1=1, +2=2, 3=+3,...

Zero is the neutral number, then it is optional to include any sign: E.g.: +0=-0=0

Negative numbers must have always "-" sign: E.g.: -1, -2, -3,... read minus one, minus two, minus three,... and its sign is part of the number.

Let's see some examples:

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

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

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

Try it by yourself:

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Number Line

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

Negative numbers are from left to zero

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

Positive numbers from right to zero

Numbers are increasing from left to right

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Note that the distance (separation) between each number is the same. That is, the distance between 0 and 1 is the same of 1 and 2, 2 and 3 and so on.

Let's see some examples:

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

0<1-8<10-5<-34≥1

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

< : means less than to < : means greater than to ≤: means less than or equals to ≥: means greater than or equals to

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.

Givens

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

Write data with their signs.

Interpret information

Note that the scale leaps in steps of 10 units, rather than individual unit steps.

Try it by yourself:

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

Solution

-50 -10 0 10 20

-20

30

-40

50

70

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Rational Numbersand Number Line

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Solution

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

Try it out

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Listen, read, & solve

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

After reviewing the story, it is evident that

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

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Non-integer

integer

Positive

Zero

Non-integer divisions

Negative

..., -7/2, -5/2, -3/2, 1/2, 3/2, 5/2, 7/2, ... ..., -5/3, -4/3, -2/3, 1/3, 2/3, 4/3, 5/3, ... ..., -3/4, -2/4=-1/2, -1/4, 1/4, 2/4=1/2, 3/4, 5/4, ... .... Remember that each fraction sign "/" is also a division "÷"

1÷1=1, 2÷1=2, 3÷1=3,...

Zero is the result of the division of itself with any number distinct to zero 0÷1=0, 0÷2=0

..., -3÷1=-3, -2÷1=-2, -1÷1=-1

For instance, place 10/4 on the 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.

Placement of Fractions in Number Line

Divisions of 4 as indicated by the denominator

After dividing, count 10 divisions (as indicated by the numerator) and place the number

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

Example 2: Place -3/2

Let's see some examples:

1st, divide the number line into halve (provided that denominator is 2) 2nd, count all of the divisions until you reach to the number 7 (numerator is 7)

Example 3: Place 11/3

Example 3: Place 16/2

Let's see some examples:

Try it by yourself:

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Summary

  • Numbers are represented in an ordered way on number line

Rational Numbers

Integer Numbers

Whole Numbers

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

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

Solution

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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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Solution

-50 -10 0 10 20

-20

30

-40

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70