Math Lesson 3.1.1 - Definition of Fractions

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Welcome to our Math lesson on Definition of Fractions, this is the first lesson of our suite of math lessons covering the topic of The Meaning of Fractions. Equivalent Fractions. Simplifying Fractions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Definition of Fractions

Let's consider a pizza divided in 8 equal slices, as shown in the figure.

Mathematically, we denote each of these slices as 1/8. This notation means "1 slice out of 8 available", as shown below.

Thus, we have three slices detached from the pizza shown in the first figure. If somebody eats them, we say he/she has eaten 3 out of 8 slices or 3/8 of a pizza. This method of expressing a part of a whole is called a fraction.

The condition for a fraction to exist is that the whole must be divided in equal parts; otherwise, we cannot accept it. If the whole is not divided in equal parts, we apply tinier divisions until we obtain equal slices, as shown in the figure below.

Example 1

What are the fractions that correspond to the coloured parts of each square in the figure?

Solution 2

1. The first square is divided into 9 equal parts where 4 of them are coloured. Hence, this figure represents the fraction 4/9.
2. The second square is divided into 6 × 4 = 24 equal parts, where 6 + 3 = 9 of them are coloured. Hence, this figure represents the fraction 9/24.
3. The third square is divided into 9 × 4 = 36 equal parts, where 7 + 4 + 3 + 2 = 16 of them are coloured. Hence, this figure represents the fraction 16/36.

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7. Continuing learning fractions - read our next math tutorial: Proper and Improper Fractions. Mixed Numbers

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