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Equal Parts

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Last updated date: 24th Jul 2024
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What is Part?

Talking about a part, it is a fraction of the whole substance. It is a fragment or a portion of something which we can define as something less than the entire object. Similarly, a part has been defined by different terms, including a fraction, element, share, portion, piece, and many more. When it is about defining a part, there comes a new term called equal parts. The article below will understand what a part is, how parts make up a new substance, its basic definition, and some fun facts. 

What is the Definition of Part?

Let us define part with the help of a basic example of a circle. When we draw a line joining one point on the circle to the other point, it will be divided into parts. These may be equal or unequal. If these parts are unequal, then they will form a big and a small part. Look in the figure below:

Cutting of a circle

In the diagram above, AB is the line drawn from one point to another point of the circle. With this line, the circle is divided into two uneven parts of maths. It clearly explains the part definition. 

I am considering the same circle. Now we will learn how it is divided into equal parts. Let the line pass through the centre of the circle that is a diameter. Look for the below diagram:

Half of a circle

In the diagram above, a line is drawn passing through the centre of the circle. Thus it will divide the circle into two equal parts. 

It is even easy to divide a circle into different uniforms and even parts. The fact is, angle subtended by arcs must be equal. As if the arcs subtend 120° in the centre of the circle, then the circle is divided into three equal parts. 

Counting and Comparing Uniform Parts

Before we say parts are equal, we need to look into various facts, including looking and comparing each part with others. When you find parts in the same shape and size, they are equal and identical. 

One basic example that we generally study before diving into the concept of even parts is folding a sheet of paper. Let us take a sheet of paper and divide it from the centre by drawing a straight line. Make a fold along this line, the sheet will be divided, and it is to define parts in even shape and size. 

Now try the same activity and explain it to your friends by dividing this paper into non-uniform parts of maths. 

Now try to find what common problems your friend has faced. The fact is, students fail to recognise if the parts are equal or of identical size. It could happen if we place one shape in the inverted form to another. However, it is their mental ability to catch the right results. 

More Examples for Part Definition

1: Count and Tell if Parts are Uniform and Equal.

Count and Tell if Parts are Uniform and Equal

In the above picture, there are three squares. In the first example, a square is divided into 2 Halves, a second into 3 thirds, and a third into 4 fourths.

2: According to the part definition of uniform part, check if the below diagram gives you equal shapes or not.

According to the part definition of uniform part, check if the below diagram gives you equal shapes or not

In the above picture, there are three figures (A), (B), and (C). In figure (A), there are four equal squares. In figure (B), 6 equal triangles make one hexagon, and in figure (C), there are two unequal parts as the division is uneven. 

3: Count the equal shapes and find the numbers to find the total.

Count the equal shapes and find the numbers to find the total

According to the above question, the first example has 1+2= 3 apples. 

Second example has 2 + 2 = 4 apples.

Third example has 3 + 1 = 4 apples. 

Fun Facts For Parts of Maths

  • You divide if a shape has equal divisions by looking at its parts and comparing if these are equal.

  • If a shape has three uniform parts, it is called thirds.

  • To name the number of equal shapes, count them, and give the total count ending with “s” (valid till number four).  

  • When we divide an object into two parts, there is a possibility of equal or unequal. 

  • In the concept of a fraction as a whole, the numerator must be divisible by the denominator. 

FAQs on Equal Parts

1. How Can You Say the Parts are Equal?

Ans: When you look at two shapes, they must be equal and uniform to define matching parts; if the shapes have the same area, portion, division, segment, then equal shapes. The concept of similar parts is applied when you have to divide something into the same number: volume of the object, the weight of the object, the shape of the object, equal dimensions, etc. When the fact is about equal shares, each share will be having an equal number of objects. Suppose we have ten kites with 5 having yellow shade and 5 having pink shade. To divide these into equal shares among five friends, we will keep one yellow and one pink for each of them. The concept of equality in maths gives rise to an important calculation method called division. 

2. Give Naming Convention For Identical Parts in Mathematics.

Ans: When the identical division is between two parts, it is called halves. When it is three and four parts, it is called thirds and fourths. However, moving beyond this, the naming convention changes, and we consider the concept of a fraction as a whole. Suppose we divide a hexagon by joining each vertex to its centre; we get six equal triangles. Each part is named one-sixth of the hexagon, which means each triangle's portion is equal to other triangles and one-sixth of the whole part. Thus, while writing the figure is maths, we write ⅙. But when we add up all, the value becomes 6/6 = 1. Hence, when the numerator becomes equal to the denominator, it becomes whole without leaving any remainder behind.