Lesson: What is a fraction? (part 2)

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Let’s consider the fraction $\frac{3}{4}$ to understand what a fraction is.

Whenever you talk about a fraction, you need to do three things:

1. Identify what the "whole" or "1" is.
2. Describe or indicate the number of "equal" parts into which the whole has been divided. (DENOMINATOR)
3. Describe or emphasize the number of those equal parts being considered. (NUMERATOR)

STEP 1: The first thing we need in order to talk about a fraction is the “one whole thing”. The whole thing represents the value of 1. Sometime “one whole” is a rectangle, or a circle, or a line segment or a set of dots.

STEP 2: Now that we know what represents the “one whole thing”, we need to divide it into a certain number of “equal” parts. This number is always represented by the bottom number of the fraction called the “denominator”. In our case the denominator is 4, so each of the objects representing the “one whole thing” needs to be cut into 4 equal parts.

STEP 3: The final part of our definition deals with the top number called the “numerator”, which in this case is 3. The numerator tells us how many of the equal parts I am emphasizing...or how many parts I have...or how many parts I have eaten...etc. Sometimes we emphasize the parts by shading them in, crossing them out, or making little hops along the number line.

Example 1: Use the three-part definition of a fraction to determine whether this picture represents a fraction.

Example 2: Use the three-part definition of a fraction to determine whether this picture represents a fraction.