Adding Fractions

Adding Fractions exercise

• Adding fractions.

  Hints

  Remember that when we add fractions with the same denominator, we only need to look at the numerators and add these.

  When we add fractions with the same denominator, this stays the same.

  Solution

  • $\frac{4}{12}$ + $\frac{6}{12}$ = $\frac{10}{12}$

  • $\frac{3}{10}$ + $\frac{5}{10}$ = $\frac{8}{10}$

  • $\frac2 7$ + $\frac1 7$ = $\frac3 7$

  • $\frac3 9$ + $\frac5 9$ = $\frac8 9$

• Add the fractions of shells.

  Hints

  The denominator is how many parts (shells) we have in total. It always remains the same.

  How many shells have been painted in each colour? This is our numerator as it is the parts of the whole.

  Solution

  There are 8 shells in total, so this is our denominator.

  3 out of 8 are painted yellow, this is $ \frac3 8$.

  2 out of 8 are painted red, this is $ \frac2 8$.

  In total, there are 5 out of 8 painted, $ \frac5 8$.

• Painted shells.

  Hints

  Remember that when we find fractions of amounts, the total amount in the group is the denominator (the bottom part of the fraction). In this image there are 5 shells in total, so the denominator would be 5.

  The parts that we are counting (here, the painted shells) is the numerator. In this example it is 3.

  Solution

  There are 6 shells in total. 3 are painted purple and 2 are painted red. The fraction of shells that have been painted is $\mathbf{\frac{5}{6}}$

  To find the total fraction of shells that have been painted, we need to add $\mathbf{\frac{2}{8}}$ and $\mathbf{\frac{3}{8}}$ to get $\mathbf{\frac{5}{8}}$

  There are 5 shells in total. $\mathbf{\frac{1}{5}}$ + $\mathbf{\frac{2}{5}}$ = $\mathbf{\frac{3}{5}}$.

• Pizza fractions.

  Hints

  Remember that when we add fractions with the same denominator, we only add the numerators together. The denominator stays the same.

  How many slices was each pizza originally cut into? This is your denominator.

  How many slices are left? This is the numerator. In this example there is one slice left out of four, so $\frac1 4$ remains.

  Solution

  The image shows the answer to the pepperoni pizza:

  $\frac3 8$ + $\frac4 8$ = $\frac7 8$.

  Mushroom pizza:

  $\frac2 6$ + $\frac3 6$ = $\frac5 6$.

  Olive pizza:

  $\frac2 5$ + $\frac2 5$ = $\frac4 5$.

  Cheese pizza:

  $\frac4 8$ + $\frac2 8$ = $\frac6 8$.

• Fractions of fish.

  Hints

  When we are trying to find $ \frac4 7$ of an amount, we know that there are 7 items in total as this is the denominator.

  What is the numerator? This is how many out of the total that are colourful. In this example, the numerator is 4.

  Solution

  The tank with $ \frac4 7$ of the fish being colourful, is the tank with 7 fish in the tank - this is the denominator - and 4 fish coloured in the tank (3 orange and 1 yellow fish) - this is the numerator.

• Add fractions.

  Hints

  Remember that we can simplify fractions by dividing the numerator and the denominator by the same factor, to find an equivalent fraction.

  Here $ \frac2 4$ has been simplified to $ \frac1 2$ by dividing the numerator and the denominator by 2.

  Solution

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

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

  • $\frac2 6$ + $\frac2 6$ = $\frac4 6$ .

  • We can simplify $\frac4 6$ to $\frac2 3$ by dividing both the numerator and denominator by 2.

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

  • $\frac2 8$ + $\frac2 8$ = $\frac4 8$.

  • We can simplify $\frac4 8$ to $\frac1 2$ by dividing both the numerator and denominator by 4.

  • $\frac{4}{10}$ + $\frac{1}{10}$ = $\frac{5}{10}$.

  • We can simplify $\frac{5}{10}$ to $\frac1 2$ by dividing both the numerator and denominator by 5.

  $\mathbf{\frac{4}{5}}$

  • $\frac3 5$ + $\frac1 5$ = $\frac4 5$.

  • $\frac{6}{10}$ + $\frac{2}{10}$ = $\frac{8}{10}$.

  • We can simplify $\frac{8}{10}$ to $\frac4 5$ by dividing both the numerator and denominator by 2.