What are Equal Shares?
If a shape is divided into parts of the same size, we get equal shares. We can divide shapes like triangles, squares, rectangles, and circles partitioning shapes into equal shares. On the other hand, if a shape is divided in such a way that we get parts of different sizes, we get unequal shares. Let’s take a look at how a triangle can be divided into equal shares and unequal shares.
In the first case, the triangle is divided along the middle, giving us two equal parts, or equal shares. But in the second case, we have a random line that divides the triangle into two unequal parts or unequal shares. This is how we can create equal shares and unequal shares in squares and circles.
In the case of equal shares and unequal shares, we get the whole shape by adding all the shares of the figure.
An interesting property of equal shares is that they need not have the same shape as the original. In the above figure, we can see that two equal rectangles are joined to form a square. So, the equal shares of a square are not always a square.
What are Halves and Fourths?
We learned that the equal parts of a shape are known as equal shares. If a shape is divided into two equal parts, it that means the shape has two halves. A half is one of two equal parts into which a shape is divided.
Something interesting happens when we divide each half again into two equal parts. Now, the shape will be divided into four equal parts. Each of these parts is known as a fourth or a quarter of the whole figure.
Let us take a look at some real-life examples to see how we use the concept of halves and quarters. We cut a pizza into halves while sharing it with another person. If we want to share it with three other people, we cut it into four parts, or quarters.
We cut birthday cakes the same way.
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Solved Equal Shares Examples
Example 1: Choose the diagram that which is divided into unequal shares.
Solution: A is divided into four equal parts. Hence, the shape is divided into equal shares.
B is divided into two equal shares.
C is not divided into equal parts. Hence, C is made up of unequal shares.
So, only C has unequal shares.
Example 2: Is this shape divided into equal shares?
Solution: The heart shape can only be divided into equal shares with a standing line or vertical line along its center.
A sleeping line or a horizontal line divides the heart shape into two unequal shares.
As you can see, the top part of the shape does not look the same as the bottom part of the shape.
Hence, the provided shape is not divided into equal shares.
Example 3: Choose the shapes that are divided into two halves.
Solution: Shape A is divided into halves. The top-left part of the shape is equal to the bottom-right part of the shape.
Similarly, shape B is also divided into two halves.
Shape C, on the other hand, is not divided into two equal parts.
The part on the right side of the white line is much smaller than the part on the left side of the white line.
Hence, only A and B are divided into two halves.
Example 4: Which of the following shapes shows fourths?
Solution:
Figure A is a rectangle that is divided into four equal parts. Hence, we have four-fourths in A.
In figure B, we have three lines dividing the circle into four parts. But in this case, the parts are not of an equal size. Hence, B is not divided into fourths.
In figure C, we have a diamond divided into four equal parts. So, we have four-fourths in this figure as well.
So, only A and C are divided into fourths.
Example 5: Jane cuts a square into halves. Hardy cuts a square of the same size into fourths. Who has larger parts?
Solution: If a square is divided into two equal parts, we will get two halves. To divide a square into fourths, we are essentially dividing each half again into two equal parts. This means that the quarters are half the size of each half when a square is divided into equal shares.
Hence, each part of Jane’s square is larger than each part of Hardy’s square.
We get equal shares when a shape is divided into equal parts, and we get unequal shares when a shape is divided into unequal parts.
In certain shapes, equal shares can be created in multiple ways. Let’s consider a square as an example. The halves of a square can be obtained in the following ways.
In all these cases, the square is divided into equal shares of two halves.