Adding Fractions on a Number Line — Let's Practice!

Adding Fractions on a Number Line — Let's Practice! exercise

• Add the fractions.

  Hints

  What is the first fraction you are adding? Start here on the number line.

  Look at the numerator of the second fraction you are adding, count forward by this amount.

  Solution

  $\mathbf{\frac{2}{5}}$ + $\mathbf{\frac{2}{5}}$ = $\mathbf{\frac{4}{5}}$ When we add fractions, we only add the numerators and the denominator stays the same.

  • We start at $\mathbf{\frac{2}{5}}$ and count forward by $\mathbf{\frac{2}{5}}$.
  • 2 + 2 = 4.
  • So $\mathbf{\frac{2}{5}}$ + $\mathbf{\frac{2}{5}}$ = $\mathbf{\frac{4}{5}}$

• Add the fractions with the same denominator.

  Hints

  You could start by drawing a number line and splitting it into the number of parts that is the same as the denominator.

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

  Solution

  A bucket is filled to $\mathbf{\frac{3}{8}}$, another $\mathbf{\frac{2}{8}}$ are added. Now the bucket is filled to $\mathbf{\frac{5}{8}}$.

• Add the fractions using the number line.

  Hints

  Start by finding the first fraction to add on the number line, this is $\frac{2}{6}$.

  Then, count forwards by the numerator of the second fraction you are adding.

  Solution

  $\mathbf{\frac{2}{6}}$ + $\mathbf{\frac{3}{6}}$ = $\mathbf{\frac{5}{6}}$

  • When we add fractions, we only add the numerators and the denominator stays the same.
  • We start at $\mathbf{\frac{2}{6}}$ and count forward by $\mathbf{\frac{3}{6}}$.
  • 2 + 3 = 5.
  • So $\mathbf{\frac{2}{6}}$ + $\mathbf{\frac{3}{6}}$ = $\mathbf{\frac{5}{6}}$

• What is $\frac{3}{9}$ + $\frac{2}{9}$?

  Hints

  You could start by drawing a number line and splitting it into the number of parts that is the same as the denominator.

  Start by finding the first fraction to add on the number line.

  Then, count forwards by the numerator of the second fraction you are adding.

  Solution

  $\mathbf{\frac{3}{9}}$ + $\mathbf{\frac{2}{9}}$ = $\mathbf{\frac{5}{9}}$

  • When we add fractions, we only add the numerators and the denominators stay the same. 3 + 2 = 5.
  • So $\mathbf{\frac{3}{9}}$ + $\mathbf{\frac{2}{9}}$ = $\mathbf{\frac{5}{9}}$

• Add the fractions together.

  Hints

  Start by finding the first fraction to add on the number line, then count forwards by the numerator of the second fraction.

  The numerator in the second fraction to add is 2. What do you end up on when you count forward two from $\frac{5}{8}$?

  Solution

  $\mathbf{\frac{5}{8}}$ + $\mathbf{\frac{2}{8}}$ = $\mathbf{\frac{7}{8}}$

  • When we add fractions, we only add the numerators and the denominator stays the same.
  • We start at $\mathbf{\frac{5}{8}}$ and count forward by $\mathbf{\frac{2}{8}}$.
  • 5 + 2 = 7.
  • So $\mathbf{\frac{5}{8}}$ + $\mathbf{\frac{2}{8}}$ = $\mathbf{\frac{7}{8}}$

• What is $\frac{3}{7}$ + $\frac{4}{7}$ ?

  Hints

  When we add fractions with the same denominator, the denominator stays the same and we add the numerators together.

  We can simplify fractions by dividing the numerator and denominator by the same factor.

  When the numerator is the same as the denominator, the fraction can be simplified to one whole.

  Solution

  $\mathbf{\frac{3}{7}}$ + $\mathbf{\frac{4}{7}}$ = $\mathbf{\frac{7}{7}}$

  • When we add fractions, we only add the numerators and the denominators stay the same. 3 + 4 = 7.

  • We can simplify $\mathbf{\frac{7}{7}}$ to 1 whole by dividing the numerator and denominator by the same factor.
  • When we divide the numerator and denominator of $\mathbf{\frac{7}{7}}$ by 7, we get $\mathbf{\frac{1}{1}}$ which is equivalent to one whole.