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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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.

Read in the blogs more about the unique learning experience at nubtrek.continue

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.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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,

exercise.

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

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

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

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

Voice

Voice

Home

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)

*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*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

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Fractions are introduced as part of a whole.

Starting on learning "Fractions given as part of a whole". ;;

Count the number of flowers in the picture.

- `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?

- `1`
- `3`

The answer is '`1`'

How many pizzas are there in the picture?

- `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?

- `1`
- `3` whole and `1` piece

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

How many pizzas are there in the picture?

- `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?

- 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?

- `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? 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. 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?

- `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. 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. 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. 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?

- `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?

- `1/4`
- `4`

The answer is '`1/4`'.

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

- `1/3`
- `4/9`

The answer is '`4/9`'.

*your progress details*

Progress

*About you*

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'.