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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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  think,
  figure-out, &
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User Guide   

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

  trek,

  jogger,

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nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

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trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

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jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

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exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

summary of this topic

Fractions : Fundamentals

Fractions : Fundamentals

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Fractions Fundamentals


 »  Whole is split into pieces


 »  Fraction `5/12`
    →  whole is divided into `12` equal parts
    →  `5` pieces is the given number
    →  `1/12` is the place value


 »  Fraction `5/8`
    →  whole is divided into `8` equal parts
    →  `5` pieces is the given number
    →  `1/8` is the place value


 »  fraction in the form `p/q`
    →  `p` numerator (given number)
    →  `q` denominator (the place value or standard)

Consider the two numbers of fraction: numerator as the given number, and the denominator as the place value. That will make the fraction arithmetic easy to understand.

Fractions: Part of a whole

plain and simple summary

nub

plain and simple summary

nub

dummy

Numerator is the number of parts specified in a fraction.

Denominator is the number of parts that make a whole, and the place value of the given numerator.

Fraction is part of a whole, specified as numerator by denominator.

simple steps to build the foundation

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simple steps to build the foundation

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Fractions are introduced as part of a whole.


Keep tapping on the content to continue learning.
Starting on learning "Fractions given as part of a whole". ;;

Count the number of flowers in the picture.number 5 whole

  • `1`
  • `5`

The answer is '`5`'

What are natural numbers or counting numbers?

  • numbers used in counting.
  • numbers `1, 2, 3, cdots`
  • both the above

The answer is "Both the Above". Early humans naturally used hands to count and the numbers they used are 1, 2, 3.

What are whole numbers?

  • Natural numbers and `0`
  • numbers `0,1,2,cdots`
  • both the above

The answer is "both the above". The number `0` is added to natural numbers for place value system.

What are Integers?

  • whole numbers and negative of whole numbers
  • numbers `cdots,-2,-1,0,1,2,cdots`
  • both the above

The answer is "both the above". Integers means "untouched", that is, the numbers are not cut into smaller pieces or fractions.

What is face value of a number?

  • there is no such term as "face value"
  • the actual value of the digits 0 to 9 without taking the position into consideration

The answer is 'the actual value of the digits 0 to 9 without taking the position into consideration'.

In a number `23`, the number with face value `2` represents `20`. What is the value `20` called as?

  • place value
  • large value

The answer is 'place value'. The place value of a digit takes the position of the digit in a number into consideration.

How many pizzas are there in the picture?one whole

  • `1`
  • `3`

The answer is '`1`'

How many pizzas are there in the picture?number 3 whole

  • `1`
  • `3`

The answer is '`3`'

The picture shows a pizza that is cut into `8` pieces and `7` pieces have been taken away. How many pizzas are remaining in the picture? number 3 one eight whole

  • `1`
  • `3` whole and `1` piece

The answer is '`3` whole and `1` piece'

How many pizzas are there in the picture?half

  • `1`
  • half

The answer is 'half'. Knowing that a pizza is circular, it is easily identified that the given piece is only half of the whole.

How many pizzas are there in the picture?small piece

  • one piece
  • cannot specify the amount

The answer is 'one piece'. The small portion is referred as one piece of the whole.

How do you describe the two pieces of pizza in the picture?compare

  • `2` pieces
  • `2` unequal pieces

The answer is '`2` unequal pieces'. The two pieces are not equal in size. The interesting question is how to measure and specify these pieces.

How would one specify one piece from another piece?compare fractions It is considered the whole is of equal sizes. So the piece can be specified with reference to the whole object.

Consider the picture which shows the whole and one piece cut from the whole.fraction part of whole The whole is cut into `8` equal parts. `1` part is considered. This is given as `1` part in `8` parts of the whole. This is represented by a fraction `1/8`

What is the fraction represented by the colored portion in the picture?fraction illustration

  • `3/3`
  • `3/8`

The answer is '`3/8`'.

The whole is represented by a full circle. The whole is cut into `8` equal parts. The colored portion represents `3` parts in the `8` parts of whole.

The fraction is `3/8`.

Consider the picture which shows the whole and one piece cut from the whole.fraction part of whole In the fraction `3/8`:

`3` specifies the number of pieces considered, that is the face value of the fraction.

`8` specifies the number of pieces that makes a whole. So, "`1/8`" is the place value of the fraction.

Both face value and the place value, together form the fraction `3/8`.

Consider the picture which shows the whole and one piece cut from the whole.fraction part of whole The whole is cut into `12` equal parts. `1` part is considered. This is given as `1` part in `12` parts of the whole. This is represented by a fraction `1/12`.

In this, `1` is the numerator of the fraction, and `12` is the denominator of the fraction.

What does the word 'numerator' mean?

  • something that specifies a number
  • something that carries from one floor to another

The answer is 'something that specifies a number'. Numero is from root word "counting".

What does the word 'denominator' mean?

  • something that specifies a standard
  • staircase that connects all the floors

The answer is 'something that specifies a standard'.

Denominator is derived from a root word meaning "de:that + nomi:naming + nator:noun suffix". The place value of the fraction is specified by the denominator.

In a fraction `p/q`
the denominator specifies the standard divisions on the whole
the numerator provides the number of such divisions given by the fraction.numerator and denominator The picture specifies the fraction `3/8` as
the total number of parts the whole is divided into : the denominator `8`
The total number of parts that the fraction specifies : the numerator `3`.

What does the word 'fraction' mean?

  • broken down or fractured into smaller parts
  • framed in a metal case

The answer is 'broken down or fractured into smaller parts'.

What is the fraction represented by the colored portion in the picture?fraction illustration

  • `5/12`
  • `1/12`

The answer is '`5/12`'.

The whole is represented by a full circle. The whole is cut into `12` equal parts. The colored portion represents `5` parts in the `12` parts of whole.

The fraction is `5/12`.

What is the term used to call part of a whole?

  • Practice Saying the Answer

The answer is 'fraction'.

What is `4` called in the fraction `3 /4`?

  • Practice Saying the Answer

The answer is 'denominator'.

What is `3` called in the fraction `3/4`?

  • Practice Saying the Answer

The answer is 'numerator'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Fraction as part of whole: A fraction represents the number of parts out of the total number of parts in a whole.
Fraction is represented as `p/q`, where `p` and `q` are integers and
`q` is the denominator or the number of parts in a whole or the place value of `p`.
`p` is the numerator or the number of parts represented by the given fraction.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

What is the fraction represented by the colored portion in the picture?fraction illustration

  • `1/4`
  • `4`

The answer is '`1/4`'.

What is the fraction represented by the colored portion in the picture?fraction illustration

  • `1/3`
  • `4/9`

The answer is '`4/9`'.

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Progress

Count the number of flowers in the picture.
1
1
5
5
The answer is ' 5 '
What are natural numbers or counting numbers?
used;counting
numbers used in counting.
one;1;2;3;two;three
numbers 1, 2, 3, et cetera
both;above
both the above
The answer is "Both the Above". Early humans naturally used hands to count and the numbers they used are 1, 2, 3.
What are whole numbers?
natural;and
Natural numbers and 0
one;1;2;two
numbers 0, 1, 2, et cetera
both;above
both the above
The answer is "both the above". The number 0 is added to natural numbers for place value system.
What are Integers?
negative;whole
whole numbers and negative of whole numbers
minus;zero;1;2
numbers minus 2, minus 1, zero, 1, 2 et cetera
both;above
both the above
The answer is "both the above". Integers means "untouched", that is, the numbers are not cut into smaller pieces or fractions.
What is face value of a number?
1
there is no such term as "face value"
5
the actual value of the digits 0 to 9 without taking the position into consideration
The answer is 'the actual value of the digits 0 to 9 without taking the position into consideration'.
In a number 23 , the number with face value 2 represents 20 . What is the value 20 called as?
place
place value
large
large value
The answer is 'place value'. The place value of a digit takes the position of the digit in a number into consideration.
How many pizzas are there in the picture?
1
1
3
3
The answer is ' 1 '
How many pizzas are there in the picture?
1
1
3
3
The answer is ' 3 '
The picture shows a pizza that is cut into 8 pieces and 7 pieces have been taken away. How many pizzas are remaining in the picture?
1
1
3;piece;and
3 whole and 1 piece
The answer is ' 3 whole and 1 piece'
How many pizzas are there in the picture?
1
1
half
half
The answer is 'half'. Knowing that a pizza is circular, it is easily identified that the given piece is only half of the whole.
How many pizzas are there in the picture?
1
one piece
cannot
cannot specify the amount
The answer is 'one piece'. The small portion is referred as one piece of the whole.
How do you describe the two pieces of pizza in the picture?
2;
2 pieces
unequal;pieces
2 unequal pieces
The answer is ' 2 unequal pieces'. The two pieces are not equal in size. The interesting question is how to measure and specify these pieces.
How would one specify one piece from another piece?;;It is considered that the whole is of equal sizes. So the piece can be specified with reference to the whole object.
Consider the picture which shows the whole and one piece cut from the whole. ;; The whole is cut into 8 equal parts. 1 part is considered. This is given as 1 part in 8 parts of the whole. This is represented by a fraction 1 by 8.
What is the fraction represented by the colored portion in the picture?
by 3
3 by 3
by 8
3 by 8
The answer is '3 by 8'. ;; The whole is represented by a full circle. The whole is cut into 8 equal parts. The colored portion represents 3 parts in the 8 parts of whole. The fraction is 3 by 8.
Consider the picture which shows the whole and one piece cut from the whole. In the fraction 3 by 8 : 3 specifies the number of pieces considered, that is the face value of the given fraction. ;; 8 specifies the number of pieces that makes a whole. So, "1 by 8" is the place value of the fraction. ;; Both face value and the place value, together form the fraction 3 by 8.
Consider the picture which shows the whole and one piece cut from the whole. ;; The whole is cut into 12 equal parts. 1 part is considered. This is given as 1 part in 12 parts of the whole. This is represented by a fraction 1 by 12. ;; In this, 1 is the numerator of the fraction, and 12 is the denominator of the fraction.
What does the word 'numerator' mean?
specifies;number
something that specifies a number
carries;from;floor
something that carries from one floor to another
The answer is 'something that specifies a number'. Numero is from root word "counting".
What does the word 'denominator' mean?
specifies;standard
something that specifies a standard
connects;all;floors
staircase that connects all the floors
The answer is something that specified a standard. Denominator is derived from root word meaning, de is that, nomi is naming, and nator is the suffix in noun form. ;; The place value of the fraction is specified by the denominator.
In a fraction p by q, the denominator specifies the standard divisions on the whole. The numerator provides the number of such divisions given by the fraction. The picture specifies the fraction 3 by 8, as the total number of parts, the whole is divided into : the denominator : 8;; the total number of parts at the fraction specifies : the numerator : 3
What does the word 'fraction' mean?
broken;down;fractured;into;smaller
broken down or fractured into smaller parts
framed;metal;case
framed in a metal case
The answer is 'broken down or fractured into smaller parts'.
What is the fraction represented by the colored portion in the picture?
5
5/12
1
1/12
The answer is '5 by 12'. ;; The whole is represented by a full circle. The whole is cut into 12 equal parts. The colored portion represents 5 parts in the 12 parts of whole. The fraction is 5 by 12.
What is the term used to call part of a whole?
fraction
The answer is 'fraction'.
what is 4 called in the fraction 3 by 4?
denominator
The answer is 'denominator'.
what is 3 called in the fraction 3 by 4?
numerator
The answer is 'numerator'.
Numerator is the number of parts specified in a fraction. ;; Denominator is the number of parts that make a whole, and the place value of the given numerator. ;; Fraction is part of a whole, specified as numerator by denominator.
Fraction as part of whole: A fraction represents the number of parts out of the total number of parts in a whole.;; Fraction is represented as p by q, where p and q are integers and , q is the denominator or the number of parts in a whole or the place value of p. ;; p is the number of parts represented by the fraction.
What is the fraction represented by the colored portion in the picture?
1
1 by 4
4
4
The answer is '1 by 4'. ;;
What is the fraction represented by the colored portion in the picture?
1
1 by 3
4;9
4 by 9
The answer is '4 by 9'.

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