Adding Fractions on a Number Line

Adding Fractions on a Number Line exercise

• What are the steps to add fractions?

  Hints

  Before you start adding the fractions, what do you need to check is the same?

  Once you have divided your number line into equal parts, what do you need to locate?

  Solution

  First, check that the fractions you are adding have the same denominator.

  Next, divide the number line into equal parts as shown by the denominators.

  Then, locate the first fraction on the number line.

  Finally, count forward the number of parts, as shown by the numerator on the second fraction.

• How much petrol is in the tank?

  Hints

  Each interval on the number line goes up in steps of $\frac1 6$. How many jumps will be needed to add $\frac3 6$?

  There was already $\frac1 6$ in the tank, so start your jumps from here.

  Solution

  • As we are adding $\frac1 6$ + $\frac3 6$, we start at $\frac1 6$.
  • Next, look at the numerator of the fraction we are adding; in $\frac3 6$ the numerator is 3 so we make 3 jumps.
  • This gets us to $\frac4 6$.
  • So $\frac1 6$ + $\frac3 6$ = $\frac4 6$

• Which number lines show the correct way of adding the fractions?

  Hints

  The number line should be divided into equal parts based on the numerator. What is the numerator in the fractions that Axel and Tank are adding here?

  The friends added $\frac1 9$ and $\frac6 9$. There are two ways to add these fractions, depending on which order they are added.

  To add $\frac1 9$ and $\frac6 9$, the friends could start at $\frac1 9$ and make 6 jumps, or they could start at $\frac6 9$ and make 1 jump.

  Solution

  • There are two correct options to add $\frac1 9$ + $\frac6 9$.
  • Both correct options have the number line divided into 9 equal parts because the numerators in $\frac1 9$ + $\frac6 9$ are 9.
  • To solve starting with the smaller fraction: $\frac1 9$ + $\frac6 9$, start at $\frac1 9$ and jump forward 6.
  • To solve starting with the larger fraction: $\frac6 9$ + $\frac1 9$, start at $\frac6 9$ and jump forward 1.

• Practise adding fractions.

  Hints

  To add the fractions on a number line, first partition the number line to the number of parts that is in the denominator.

  Find the first fraction on the number line, then count forward by the numerator of the second fraction.

  Can you simplify your answer by dividing the numerator and denominator by the same factor?

  Solution

  • $\frac2 8$ + $\frac2 8$ = $\frac1 2$.

  Start on $\frac2 8$, count forward by two which takes you to $\frac4 8$. $\frac4 8$ can be simplified to $\frac1 2$ by dividing both the numerator (4) and the denominator (8) by 4.

  • $\frac3 6$ + $\frac1 6$ = $\frac2 3$.

  Start on $\frac3 6$, count forward by one which takes you to $\frac4 6$. $\frac4 6$ can be simplified to $\frac2 3$ by dividing both the numerator (4) and the denominator (6) by 2.

  • $\frac1 7$ + $\frac3 7$ = $\frac4 7$.

  Start on $\frac1 7$, count forward by three which takes you to $\frac4 7$. This cannot be simplified any further.

  • $\frac3 5$ + $\frac2 5$ = 1.

  Start on $\frac3 5$, count forward by two which takes you to $\frac5 5$. $\frac5 5$ can be simplified to 1 by dividing both the numerator (5) and the denominator (5) by 5.

• Add the fractions on the number line.

  Hints

  Start by locating the first fraction in the equation on the number line.

  How many parts do you need to jump forward?

  The numerator in the second fraction ($\frac4 7$) is 4, so jump forward 4 parts.

  Solution

  • Start at $\frac2 7$
  • As we are adding $\frac4 7$, look at the numerator of that fraction.
  • The numerator of $\frac4 7$ is 4, so we make 4 jumps forward.
  • This gets us to $\frac6 7$.
  • So $\frac2 7$ + $\frac4 7$ = $\frac6 7$.

• Adding and simplifying fractions.

  Hints

  To simplify a fraction, divide the numerator and denominator by the same factor. In this example $\frac{4}{10}$ is simplified to $\frac2 5$ by dividing both by 2.

  Sometimes, it may be a fraction in the question that has already been simplified and needs expanding. For example, $\frac1 3$ can be expanded by multiplying both the numerator and denominator by 2 to get $\frac2 6$.

  Solution

  1) This answer was correct. $\frac3 8$ + $\frac3 8$ = $\frac6 8$. Divide numerator and denominator by 2 to get $\frac3 4$.

  2) This answer was correct. $\frac4 9$ + $\frac1 3$ = $\frac7 9$. First expand $\frac1 3$ by multiplying the numerator and denominator by 3 to get $\frac3 9$. $\frac4 9$ + $\frac3 9$ = $\frac7 9$.

  3) This answer was incorrect. $\frac2 6$ + $\frac2 6$ = $\frac4 6$. Divide numerator and denominator by 2 to get $\frac2 3$.

  4) This answer was incorrect. $\frac{4}{10}$ + $\frac{4}{10}$ = $\frac{8}{10}$. Divide numerator and denominator by 2 to get $\frac4 5$.

  5) This answer was correct. $\frac{3}{12}$ + $\frac{5}{12}$ = $\frac{8}{12}$. Divide numerator and denominator by 4 to get $\frac2 3$.

  6) This answer was correct. $\frac{1}{16}$ + $\frac{1}{16}$ + $\frac{2}{16}$ = $\frac{4}{16}$. Divide numerator and denominator by 4 to get $\frac1 4$.