Subtracting Fractions on a Number Line

Subtracting Fractions on a Number Line exercise

• How do we subtract fractions on a number line?

  Hints

  What must be checked before you divide your number line?

  Where do we start jumping back from? By what do we jump backwards?

  Solution

  1. Check the fractions have the same denominator.
  2. Divide the number line into equal parts.
  3. Locate the first fraction on the number line.
  4. Find the numerator of the fraction being subtracted and jump backwards by this many.
  5. Don't forget to simplify your answer if needed.

• How much petrol will Axel and Tank have left?

  Hints

  Count how many parts the number line is divided into. Use the markers on the number line, and the numbers that are already there, to help you to place the fractions in the correct places.

  Some of the fractions have been filled in here, so use this number line to help you fill in the rest.

  Once you have a complete number line, locate the larger fraction $\frac{6}{7}$, and count backwards with the numerator of the smaller fraction.

  Solution

  Axel and Tank will have $\mathbf{\frac{2}{7}}$ of a tank left after their journey.

  Once we placed each fraction on the number line we needed to:

  • Locate the larger fraction from our equation, $\frac{6}{7}$.
  • Count backwards 4 (the numerator of the smaller fraction, $\frac{4}{7}$).
  • As we can see from the jumps, this takes us to $\frac{2}{7}$.

• How much chocolate is left?

  Hints

  The number sentence we are trying to solve is $\frac{9}{10}$ - $\frac{6}{10}$. Can you draw a number line to help?

  A number line split into tenths like this will help.

  Use the number line to locate the first fraction, $\frac{9}{10}$. What is your next step?

  Find the numerator in $\frac{6}{10}$ and count that many backwards.

  Solution

  Axel will have $\mathbf{\frac{3}{10}}$ of the chocolate bar left.

  • Locate the larger fraction, $\frac{9}{10}$, on the number line.
  • Find the numerator of the smaller fraction. The numerator in $\frac{6}{10}$ is 6.
  • Count 6 jumps backwards.
  • We land on $\frac{3}{10}$.

• Find the answers to these subtraction problems.

  Hints

  Look at the denominators of the fractions in the equations. Can you make a number line with this many parts to help you to subtract?

  For example, to solve $\frac{7}{10}$ - $\frac{3}{10}$, we could divide a number line into 10 equal parts like this.

  Once we have done that, we can locate the first fraction and count backwards by the numerator of the second fraction.

  Remember, answers are simplified if needed. For example, we could simplify $\frac{2}{8}$ to $\frac{1}{4}$ by dividing both the numerator and denominator by 2.

  Solution

  $\frac{7}{10}$ - $\frac{3}{10}$ = $\frac{2}{5}$

  • Counting 3 jumps backwards from $\frac{7}{10}$ on a number line gets us to $\frac{4}{10}$.
  • $\frac{4}{10}$ can be simplified to $\frac{2}{5}$ by dividing both the numerator and the denominator by 2.

  $\frac{5}{6}$ - $\frac{3}{6}$ = $\frac{1}{3}$

  • Counting 3 jumps backwards from $\frac{5}{6}$ on a number line gets us to $\frac{2}{6}$.
  • $\frac{2}{6}$ can be simplified to $\frac{1}{3}$ by dividing both the numerator and the denominator by 2.

  $\frac{7}{9}$ - $\frac{5}{9}$ = $\frac{2}{9}$

  • Counting 5 jumps backwards from $\frac{7}{9}$ on a number line gets us to $\frac{2}{9}$. This cannot be simplified further.

  $\frac{8}{12}$ - $\frac{2}{12}$ = $\frac{1}{2}$

  • Counting 2 jumps backwards from $\frac{8}{12}$ on a number line gets us to $\frac{6}{12}$.
  • $\frac{6}{12}$ can be simplified to $\frac{1}{2}$ by dividing both the numerator and the denominator by 6.

• How much petrol will be left?

  Hints

  The first step is to locate the larger fraction, $\frac{5}{8}$, on the number line.

  We then need to find the numerator of the smaller fraction. What is the numerator in $\frac{3}{8}$?

  We then need to jump backwards that amount.

  Solution

  They will have $\mathbf{\frac{2}{8}}$ of a tank of petrol left when they get home.

  • Locate the larger fraction, $\frac{5}{8}$ on the number line.
  • Find the numerator of the smaller fraction. The numerator of $\frac{3}{8}$ is 3.
  • Count backwards 3 from $\frac{5}{8}$.
  • We land on $\frac{2}{8}$.

• What fraction will be left?

  Hints

  Make sure the denominators are the same in each equation.

  For example if we were subtracting $\frac{5}{12}$ - $\frac{2}{6}$, we would multiply the numerator and the denominator of $\frac{2}{6}$ by 2 to make $\frac{4}{12}$. Now we can subtract $\frac{5}{12}$ - $\frac{4}{12}$.

  Draw your own number line to help you to solve. Divide your number line into equal parts as shown by the denominators.

  Remember to simplify your answer by dividing the numerator and denominator by the same number.

  Solution

  $\mathbf{\frac{1}{2}}$

  • $\frac{9}{10}$ - $\frac{2}{5}$ : first convert the fraction, $\frac{2}{5}$, by multiplying the numerator and denominator by 2 to make $\frac{4}{10}$, so both fractions in the equation have the same denominator.
  • $\frac{9}{10}$ - $\frac{4}{10}$ = $\frac{5}{10}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 5.
  • $\frac{7}{8}$ - $\frac{3}{8}$ = $\frac{4}{8}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 4.
  • $\frac{12}{14}$ - $\frac{5}{14}$ = $\frac{7}{14}$ which can be simplified to $\frac{1}{2}$ by dividing both the numerator and denominator by 7.

  $\mathbf{\frac{2}{3}}$

  • $\frac{5}{6}$ - $\frac{1}{6}$ = $\frac{4}{6}$ which can be simplified to $\frac{2}{3}$ by dividing both the numerator and denominator by 2.
  • $\frac{11}{12}$ - $\frac{1}{4}$ : first convert the fraction, $\frac{1}{4}$, by multiplying the numerator and denominator by 3 to make $\frac{3}{12}$, so both fractions in the equation have the same denominator. $\frac{11}{12}$ - $\frac{3}{12}$ = $\frac{8}{12}$ which can be simplified to $\frac{2}{3}$ by dividing both the numerator and denominator by 4.

  $\mathbf{\frac{3}{5}}$

  • $\frac{13}{15}$ - $\frac{4}{15}$ = $\frac{9}{15}$ which can be simplified to $\frac{3}{5}$ by dividing both the numerator and denominator by 3.
  • $\frac{17}{20}$ - $\frac{5}{20}$ = $\frac{12}{20}$ which can be simplified to $\frac{3}{5}$ by dividing both the numerator and denominator by 4.