FractionConcepts1: Lesson: Generate equivalent fractions with a number line: Generate equivalent fractions with a number line

Generate equivalent fractions with a number line

Explore

Watch

Read

In this lesson students will continue informally generating equivalent fractions, only now using the number line. At this point, some students should be discovering the “official” rule for converting one fraction into a second equivalent fraction. For the students who have not yet discovered the rule, guide them to look for patterns (relationships) between the two fractions that are equivalent. Within this lesson of the next lesson we want students to discover the “official” rule that $\frac{a}{b}=\frac{a\times~m}{b\times~m}=\frac{am}{bm}$

Example 1: Find fractions equivalent to $\frac{2}{3}$ using the number line.

Let’s begin by drawing a number line of $\frac{2}{3}$ . Of course, this means the distance from 0 to 1 is cut into three pieces and we draw in two “hops”.

If we cut each third into two pieces, we now have a six smaller pieces from 0 to 1. In fact, we can see that 4 little hops of the sixths lands us in the same place on the number line as 2 bigger hops of thirds.

We can combine the two lines together into a single line.

Since the two fractions have the same location on the line, we now know that

$\frac{2}{3}=\frac{4}{6}$

What would happen if we started with the original $\frac{2}{3}$ number line and then cut each third into four pieces?

Since the distance traveled with two big hops - $\frac{2}{3}$ is the same distance as traveled with 8 small hops - $\frac{8}{12}$ , we now know that

$\frac{2}{3}=\frac{8}{12}$

If necessary, repeat this process again only showing each piece of the $\frac{2}{3}$ number line being cut into three pieces. This will demonstrate that $\frac{2}{3}=\frac{6}{9}$ .

So, here are the equivalent fractions we have generated:

$\frac{2}{3}=\frac{4}{6}$

$\frac{2}{3}=\frac{8}{12}$

$\frac{2}{3}=\frac{6}{9}$

Do we see a relationship between the equivalent fractions? If not that is okay...we will continue collecting some more information with the next example.

Example 2: Find fractions equivalent to $\frac{3}{4}$ using the number line.

Start with a number line of $\frac{3}{4}$ and then cut each fourth into two parts. How many eighths are needed to make $\frac{3}{4}$ ?

Start with a picture of $\frac{3}{4}$ and then cut each fourth into three parts. How many twelfths are needed to make $\frac{3}{4}$ ?

These two examples show us two fractions that are equal to $\frac{3}{4}$ :

$\frac{3}{4}=\frac{6}{8}$ and $\frac{3}{4}=\frac{9}{12}$

Press [Next] to begin the 5 practice problems.