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Introduction to Fractions
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A fraction is another way to represent division. The following is an example:

$$\displaystyle 5\div7=\frac{5}{7}$$

The top (numerator) represents the number of pieces of the whole. The bottom (denominator) represents the number it takes to make one whole. Another way to think of this is that the denominator tells us the size of each piece. The bigger the denominator, the smaller each piece is within the whole thing.

### Quick Tip

This is where we get the / to mean division. Fractions can be written as $$\dfrac{5}{7}$$ or they might be written as $$5/7$$. You may see them written either way in this course.

Introduction to Fractions

### Practice Problems

1. In the fraction $$\dfrac{2}{3}$$, what is the numerator and what is the denominator? (
Solution
Solution: The numerator is 2, and the denominator is 3
Details: The numerator is the number on the top of the fraction. The denominator is the number on the bottom of the fraction. In this case, the numerator is 2, and the denominator is 3.
)
2. Suppose you invited seven friends to a party and five of them attended. Give a fraction that represents the proportion of your friends who attended the party. (
Video Solution
Solution: $$\dfrac{5}{7}$$
Details:

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3. What fraction of the whole does the shaded portion represent?

(
Video Solution
Solution: $$\dfrac{5}{8}$$
Details:

(Video Source | Transcript)
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4. What fraction of the whole does the shaded portion represent?

(
Solution
Solution: $$\dfrac{2}{3}$$
Details:
The whole shape is divided into 3 parts. Two of those parts are shaded. We can think of a fraction in the following way:

$$\displaystyle \frac{\text{The number of parts we have}}{\text{The number of parts to make a whole}}$$

so in this case, our fraction is $$\dfrac{2}{3}$$.
)

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