# Ordering Fractions on a Number Line

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## Basics on the topicOrdering Fractions on a Number Line

Axel, Tank, and Dundee just finished a cake eating contest and want to see who won! They need to figure out who has the least amount of cake left by ordering fractions on a number line so they can identify the smallest fraction of cake left!

### TranscriptOrdering Fractions on a Number Line

"This cake eating contest was fun! I wonder who won?" "It seems like we each have a fraction of cake left. Whoever has the LEAST amount of cake left is the winner." Wait, how do we figure out who won?" Let's help Axel and Tank by Ordering Fractions on a Number Line. We can use a number line like THIS to help us with ordering fractions. For example, Dundee has four-tenths of cake left, Axel has five-eighths left, and Tank has one-fourth left. Since we are comparing cakes, we will use fraction circles to model the fractions. HERE we see four-tenths, five-eighths, and one-fourth represented using fraction circles. Now that we've represented the fractions using fraction circles, let's represent them using number lines. Let's start with four-tenths. The denominator tells us that the number line is divided into ten equal parts. That means these lines HERE represent tenths. Now, count the number of parts from zero shown in the numerator, which is four, and label four-tenths HERE. The next fraction we need to label is five-eighths. The denominator tells us that the number line is divided into eight equal parts. That means these lines HERE represent eighths. What is the next step? Now, count the number of parts from zero shown in the numerator, which is five, and label five-eighths HERE. The last fraction we need to label is one-fourth. What is the first step? Look at the denominator and divide the number line into four equal parts. What is the next step? Now, count the number of parts from zero shown in the numerator, which is one, and label one-fourth HERE. Now that we have put each fraction on a number line let's put them together to see which fraction is the SMALLEST? One-fourth is the smallest because it is first on the number line. Tank has the LEAST amount of cake left, that means he won the cake eating contest! Remember, we can use a number line to help us with ordering fractions. When we label fractions a number line, first, look at the denominator of each fraction. Next, divide up the number line into equal parts based on the denominator. Last, count the number of parts from zero shown in the numerator and label the fraction. Repeat these steps until all the fractions are labeled on the number line. "Ughhhh, maybe I shouldn't have had all those cakes for breakfast." "Dundee! Are you alright!?" "I'm fine! When's dessert?"

## Ordering Fractions on a Number Line exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Ordering Fractions on a Number Line .
• ### Match the written fraction with the fraction circle representation.

Hints

Look at the colored sections; they represent the number in the numerator.

The numerator is the number at the top of the fraction and denominator is the number at the bottom.

The denominator represents the total number of pieces in the circle.

Solution

• ### How many equal parts should be on the number line?

Hints

The denominator tells us how many equal parts there should be on a number line.

The denominator is the bottom number of a fraction.

The numerator is the top part of the fraction and lets us know how many parts are being counted or shaded.

Solution

This is the correction representation for the fraction $\frac{7}{12}$ because there are 7 shaded spaces which is shown in the numerator and there are 12 spaces in the whole which is shown in the denominator.

• The numerator tells us how many spaces we should shade and the denominator tells us how many spaces there are in the whole.

• ### Determine the fractions and order them.

Hints

Once you have labeled each number line with a fraction, you can use the fraction bars to compare which fraction is largest.

Which number line shows the largest fraction?

Solution

The image above shows the fractions in the correct order from largest to smallest.

• $\frac{3}{4}$
• $\frac{5}{10}$
• $\frac{3}{8}$

• ### Order the fractions from smallest to largest,

Hints

Find the number line that would best represent each fraction.

Place each fraction on the one of the number lines by counting the spaces of the number line to find the which fraction dominator it represents.

Try finding the largest and smallest fractions first:

• The fraction that is closest to 0 on the number line is smallest.
• The fraction that is closes to 1, or equal to 1, is the biggest.

The numerator will let you know which how many spaces should be filled in on the number line.

After filling the number lines with the fractions, compare the fractions.

Solution

The order of the fractions from smallest to largest:

• $\frac{2}{8}$
• $\frac{2}{5}$
• $\frac{2}{3}$
• $\frac{3}{3}$

• ### Where do these fractions fall on the number line?

Hints

All the fractions have the same denominator so focus on the numerator to place the fraction.

To place the fraction, count the number of parts shown in the numerator from zero.

Place the fraction exactly underneath the counted interval.

Solution

Check the image for the correct number line.

• $\frac{1}{6}$ should be the first line from 0
• $\frac{3}{6}$ should be the third line from 0
• $\frac{5}{6}$ should be the fifth line from 0

• ### Order the fractions from smallest to largest,

Hints

Use an extra sheet of paper to make a number line for each fraction.

When fractions have the same numerator, the fraction with the smallest denominator is largest.

When fractions have the same denominator, the fraction with the largest numerator is largest.

Solution

One example above shows the correct way to solve.

• The judges created 3 number lines and plotted each fraction on a number line. After seeing each fraction on a number line, they were able to order them from smallest to largest like this - $\frac{2}{8}$, $\frac{1}{3}$, $\frac{3}{5}$ ✔️
• $\frac{9}{10}$, $\frac{3}{5}$, $\frac{1}{4}$ ❌
• $\frac{5}{6}$, $\frac{3}{6}$, $\frac{4}{6}$ ❌
• $\frac{4}{10}$, $\frac{4}{8}$, $\frac{4}{5}$ ✔️