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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.
mathsFractionsFractions : Fundamentals

### Fractions: Part of a whole

Fractions are introduced as part of a whole. Numerator and Denominator are introduced and explained in detail.

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Count the number of flowers in the picture.

• 1
• 5
• 5

The answer is '5'

What are natural numbers or counting numbers?

• numbers used in counting.
• numbers 1, 2, 3, cdots
• both the 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 numbers and 0
• numbers 0,1,2,cdots
• both the above
• both the above

The answer is "both the above".

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 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
• 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
• 1
• 3

The answer is '1'

How many pizzas are there in the picture?

• 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
• 3 whole and 1 piece
• 3 whole and 1 piece

The answer is '3 whole and 1 piece'

How many pizzas are there in the picture?

• 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?

• one 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?

• 2 pieces
• 2 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 known that the wholes are 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
• 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 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
• 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
• 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
• 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?

• Pronunciation : Say the answer once

What is 4 called in the fraction 3 /4?

• Pronunciation : Say the answer once

What is 3 called in the fraction 3/4?

• Pronunciation : Say the answer once

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/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.

Solved Exercise Problem:

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

• 1/4
• 1/4
• 4

The answer is '1/4'.

Solved Exercise Problem:

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

• 1/3
• 1/3
• 4/9

The answer is '4/9'.

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