Ordering Fractions on a Number Line

Ordering Fractions on a Number Line exercise

• Can you find the matching pairs?

  Hints

  Look at the coloured sections; they represent the numerator.

  The total number of parts in the fraction circle represents the denominator.

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

  Solution

  Here are the matching pairs.

• 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 number of the fraction and lets us know how many parts are being counted.

  Solution

  This is the correct representation for the fraction $\frac{7}{12}$.

  • The denominator is 12 and there are 12 parts altogether.
  • The numerator is 7 and there are 7 parts shaded.

• Determine the fractions and order them.

  Hints

  First, work out what fraction is being represented by each number line.

  • The total number of parts represents the denominator.
  • The green parts represent the numerator.

  Once you have labelled 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? Put the largest fraction next to number 1.

  Solution

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

  1) $\frac{3}{4}$

  2) $\frac{5}{10}$

  3) $\frac{3}{8}$

• Order the fractions from smallest to largest.

  Hints

  Find the number line that would best represent each fraction.

  Remember, the denominator is represented by the total number of parts. You can then shade in the amount of the numerator.

  The number line with the fraction plotted closest to zero shows the smallest fraction.

  Use this image to help with ordering the first two 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 of 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.

  Here we can see $\frac{1}{6}$ in the correct spot. Use this to help you fill in the other fractions.

  Solution

  Here we can see the fractions placed correctly on the number line.

• 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.
  • $\frac{2}{8}$, $\frac{1}{3}$, $\frac{3}{5}$ ✔️
  • $\frac{4}{10}$, $\frac{4}{8}$, $\frac{4}{5}$ ✔️ is also a correct choice.

  Incorrect choices

  $\frac{9}{10}$, $\frac{3}{5}$, $\frac{1}{4}$

  • The correct order would be $\frac{1}{4}$, $\frac{3}{5}$, $\frac{9}{10}$

  $\frac{5}{6}$, $\frac{3}{6}$, $\frac{4}{6}$

  • The correct order would be $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$