How to Compare Fractions?

How to Compare Fractions? exercise

• Which symbol makes the following comparison statement correct?

  Hints

  Try using the fraction bars to help compare the fractions.

  The symbol should have the open side facing the greater fraction, unless it is equal!

  The fractions here are $\frac{1}{3}$ and $\frac{4}{5}$. Since the fraction bar for $\frac{1}{3}$ is smaller than the fraction bar for $\frac{4}{5}$, we use the less than symbol.

  $\frac{1}{3}$ < $\frac{4}{5}$.

  Solution

  Look at the fraction bar for $\frac{2}{3}$.

  Then, compare it to the fraction bar for $\frac{3}{4}$.

  The fraction bar for $\frac{2}{3}$ is smaller than the fraction bar for $\frac{3}{4}$.

  This means we need to use the less than symbol.

  The answer is: $\frac{2}{3}$ < $\frac{3}{4}$

• Match and compare the fraction bars.

  Hints

  This example fraction bar has five equal parts, with two parts shaded in.

  This represents $\frac{2}{5}$.

  The phrase for the comparison must compare the fraction bar on the left to the fraction bar on the right.

  Solution

  The first fraction bar has 8 equal parts, with 4 parts shaded in. This fraction bar represents $\frac{4}{8}$.

  The second fraction bar has 4 equal parts, with 1 part shaded in. This fraction bar represents $\frac{1}{4}$.

  Now, compare the fraction bars to help determine the correct symbol to use.

  $\frac{4}{8}$ is a bigger fraction than $\frac{1}{4}$.

  This means $\frac{4}{8}$ is greater than $\frac{1}{4}$.

• Can you compare the fractions?

  Hints

  Try using the fraction bars to help compare the fractions.

  > means the fraction on the left is greater than the fraction on the right

  < means the fraction on the left is less than the fraction on the right

  = means both fractions are equal.

  Solution

  $\frac{3}{4}$ > $\frac{1}{3}$. Compare the fraction bar for $\frac{3}{4}$ to the fraction bar for $\frac{1}{3}$. $\frac{3}{4}$ is bigger, so use the greater than symbol, >.

  $\frac{1}{2}$ = $\frac{2}{4}$. Compare the fraction bar for $\frac{1}{2}$ to the fraction bar for $\frac{2}{4}$. They are both the same size, so use the equal to symbol, =.

  $\frac{1}{3}$ < $\frac{2}{4}$. Compare the fraction bar for $\frac{1}{3}$ to the fraction bar for $\frac{2}{4}$. $\frac{1}{3}$ is smaller, so use the less than symbol, <.

  $\frac{4}{8}$ = $\frac{3}{6}$. Compare the fraction bar for $\frac{4}{8}$ to the fraction bar for $\frac{3}{6}$. They are both the same size, so use the equal to symbol, =.

• Which symbol makes the comparison true?

  Hints

  Try using the fraction bars to help compare the fractions.

  The symbol should have the open side facing the greater fraction, unless it is equal!

  Solution

  Compare the fraction bar for $\frac{2}{5}$ to the fraction bar for $\frac{3}{6}$. $\frac{2}{5}$ is smaller, so highlight the less than symbol, <.

  Compare the fraction bar for $\frac{4}{5}$ to the fraction bar for $\frac{2}{3}$. $\frac{4}{5}$ is bigger, so highlight the greater than symbol, >.

  Compare the fraction bar for $\frac{6}{8}$ to the fraction bar for $\frac{3}{4}$. They are both the same size, so highlight the equal to symbol, =.

• What do each of the comparison symbols mean?

  Hints

  Think about how you would read this fraction comparison statement from left to right.

  Remember, the comparison symbol always opens towards the larger fraction, unless they are the same.

  Solution

  > symbol means greater than.

  < symbol means less than.

  = symbol means equal to.

• Can you help Axel and Tank?

  Hints

  Draw equal sized fraction bars to help compare, like this one for $\frac{2}{4}$!

  Start by comparing two fractions first. Then compare the third fraction with both of these.

  Solution

  Create equal sized fraction bars for all of the distances to compare them.

  $\frac{7}{8}$ is greater than $\frac{4}{5}$, $\frac{2}{4}$, and $\frac{1}{3}$, so it goes first.

  $\frac{4}{5}$ is greater than $\frac{2}{4}$, and $\frac{1}{3}$, so it goes second.

  $\frac{2}{4}$ is greater than $\frac{1}{3}$, so it goes third.

  $\frac{1}{3}$ is the smallest fraction, so it goes fourth.