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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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There are 5 flowers in the picture. 5 is a whole number used to represent the count or number of objects.

Natural numbers or counting numbers are numbers 1, 2, 3, cdots. Early humans naturally used hands to count and the numbers they used are 1, 2, 3.

Whole numbers are numbers 0,1,2,cdots.

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

For example, 2 in numbers 23 and 213 has face-value 2.

The value represented by the digit in the position it has, is the place-value of the digit.

For example, 2 in the numbers 23 and 213 has place values 20 and 200 respectively.

We have reviewed whole numbers, face-value, and place-value.

Consider the number of pizzas shown in the picture. The picture represents one pizza.

There are 3 pizzas represented in this picture.

Consider the pizzas shown in the picture. It shows 3 whole pizzas and 1 piece.

The number of pizzas in the picture is half. Knowing that a pizza is circular, it is easily identified that the given piece is only half of the whole.

Consider the picture. The small portion is referred as one piece of the whole. Till now, whole number is used to count either the whole pizzas or the pieces.

Consider the two pieces of pizzas shown in the figure. The two pieces are not equal in size. It has to be counted as two unequal pieces of pizza. 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

Consider the part shown in color. 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.

The word "numerator" means something that specifies a number. Numero is from root word counting. In fractions, numerator is the count of the part of the whole.

The English word denominator means something that specifies a standard. In fractions, the denominator is the place value of the part of the whole.

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.

The English word fraction means: broken down or fractured into smaller parts.

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.

familiarize with the terminology
fraction

familiarize with the terminology
denominator

familiarize with the terminology
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/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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