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## Adding Fractions with the Same Denominator

When adding fractions does the denominator change? This text will show how when adding fractions together, it is only the numerators that we add whilst the denominator stays the same.

Step # What to do
1 Check that the denominators are
the same, and write it in the total.
3 Write the numerator above
the denominator in the total.

If you follow these adding fractions rules you will be able to solve adding fractions word problems as well as more straightforward adding fractions questions.

Let’s take a look at an example of adding fractions with the same denominator and find out if when adding fractions does the denominator change? Here, we’ll add five-tenths plus three-tenths following the adding fractions rules.

• Step 1: Check that the denominators are the same, and write it in the total

• Step 2: Add the numerators

* Step 3: Write the numerator above the denominator in the total

Last, we can simplify eight-tenths into four-fifths.

Can you simplify when adding fractions? As shown in this example, yes we can, as we simplified eight-tenths to four-fifths.

## Adding Fractions with the Same Denominator – Summary

When adding fractions with like denominators, we keep in mind these rules for adding fractions. There are steps to adding fractions which should be followed:

• Step 1: Double check that the denominators are the same, and write it in the total
• Step 2: Add the numerators
• Step 3: Write the numerator above the denominator in the total

Want some more adding fractions practise? After watching this video on this website you can find adding fractions with the same denominator worksheet along with other activities, and exercises.

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video 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.

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.