Question

If the entire square tile has a value of 1, what is the value of each region?

Answer 1

a = 1/4, b = 1/16, c = 1/8, d = 1/4

Explanation:

What is a fraction?

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

The easiest way to solve this is to look at it as a whole.

Looking at a, you may be able to tell that it takes up a total of
`(1)/(4)` of the shape. We know this because the lines stay in the very corners of the shape, and join together at the center.

Therefore, shape a takes up
`(1)/(4)` of the space, 0.25 or 25%.

Before you look at the b shapes, think of the square as cut into fourths. A line going across, and diagonally. The b shapes take up
`(1)/(2)` of that space, and then it is cut in half to form the two triangles. An equation to solve for the size of the triangles can look like this:

• 
  `(1)/(4)` ÷ 2 ÷ 2 =
  `(1)/(16)`

Therefore, the sizes of shape b are
`(1)/(16)`, 0.06 or 6.25%

Again for shape c, think of it as cut into fourths. Before, we solved for two triangles, but what about only one? Well, all we need to do is the same equation, but without dividing it by 2.

• 
  `(1)/(4)` ÷ 2 =
  `(1)/(8)`

Therefore, the size of shape c is
`(1)/(8)`, 0.125, 0.25%

The last shapes, shape d are
`(1)/(4)`. We know this because half the shape is already taken up, and the last
`(1)/(2)` is divided by 2,

`(1)/(2)` ÷ 2 =
`(1)/(4)`

Therefore, the sizes of shape d are
`(1)/(4)`.