4.1 Visualize fractions

Understand the meaning of fractions

Andy and Bobby love pizza. On Monday night, they share a pizza equally. How much of the pizza does each one get? Are you thinking that each boy gets half of the pizza? That’s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.

In math, we write $\frac{1}{2}$ to mean one out of two parts.

On Tuesday, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has $\frac{1}{4}$ of the pizza.

On Wednesday, the family invites some friends over for a pizza dinner. There are a total of $12$ people. If they share the pizza equally, each person would get $\frac{1}{12}$ of the pizza.

A fraction is a way to represent parts of a whole. The denominator $b$ represents the number of equal parts the whole has been divided into, and the numerator $a$ represents how many parts are included. The denominator, $b,$ cannot equal zero because division by zero is undefined.

In [link] , the circle has been divided into three parts of equal size. Each part represents $\frac{1}{3}$ of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.

What does the fraction $\frac{2}{3}$ represent? The fraction $\frac{2}{3}$ means two of three equal parts.

Name the fraction    of the shape that is shaded in each of the figures.

Solution

We need to ask two questions. First, how many equal parts are there? This will be the denominator . Second, of these equal parts, how many are shaded? This will be the numerator .

ⓐ
$\begin{array}{cccc}\text{How many equal parts are there?}\hfill & & & \text{There are eight equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill & & & \text{Five parts are shaded}\text{.}\hfill \end{array}$

Five out of eight parts are shaded. Therefore, the fraction of the circle that is shaded is $\frac{5}{8}.$

ⓑ
$\begin{array}{cccc}\text{How many equal parts are there?}\hfill & & & \text{There are nine equal parts}\text{.}\hfill \\ \text{How many are shaded?}\hfill & & & \text{Two parts are shaded}\text{.}\hfill \end{array}$

Two out of nine parts are shaded. Therefore, the fraction of the square that is shaded is $\frac{2}{9}.$

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Name the fraction of the shape that is shaded in each figure:

1. ⓐ $\frac{3}{8}$
2. ⓑ $\frac{4}{9}$

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Name the fraction of the shape that is shaded in each figure:

1. ⓐ $\frac{3}{5}$
2. ⓑ $\frac{3}{4}$

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