Let's learn with an example.
Amy jogged 2/3 of a mile in the morning. Then she jogged 3/4 of a mile in the afternoon. How far did Amy jog all day?
How do we find the answer?
We add the fractions:
2/3 + 3/4 = ?
The denominators of these fractions are unlike, or not the same.
Tip:
Denominators are the bottom numbers of fractions.
To solve our problem, we can draw the fractions on number lines.
To start, we draw a number line for 2/3.
We broke the number line into 3 equal parts between 0 and 1.
Then we marked the spot that shows 2/3. ✏️
Tip: The fraction for 1 is 3/3.
Next, we draw a number line for 3/4.
This time we broke the number line into 4 equal parts between 0 and 1.
Then we marked the spot for 3/4.
What did you notice?
The number of equal parts between 0 and 1 are not the same.
The number lines don't match.
This means that we cannot just add the fractions right away.
We need to find a common denominator for both fractions.
Common denominator just means that the denominators of both fractions are the same.
So, what can we do to find a common denominator?
We can further divide each section.
Let's divide each section in the number line for 2/3 into 4 equal parts.
Tip: The trick is to divide one section of the number line by the denominator of the other fraction.
For example, to figure out how many parts to divide each section in the number line for 2/3, we look at the denominator of 3/4. The denominator is 4. That's why we divided into 4 equal parts. 👍
We see that 2/3 is the same as 8/12.
Now, how many parts should we divide each section of the number line for 3/4 into? 🤔
That's right! Divide each into 3 equal parts.
That's because the denominator of the other fraction is 3.
🌟 We see that 3/4 is the same as 9/12.
Now, both the number lines are divided into 12 sections:
Finally, we're ready to add.
We need to make a new number line where we can add the fractions together.
By looking at the fractions, we know that our numerator will be more than 12.
This means that we create a number line that goes beyond 1.
So we make our number line from 0 to 2.
Now we mark 8/12 on the number line.
Now, we add 9/12 to 8/12.
To do this, we just move 9 spots from 8/12.
We end up at 17/12:
17/12 is the same as 1 and 5/12.
So here's the answer to our problem:
Amy ran 1 and 5/12 miles today.
Great job learning to add fractions with unlike denominators. 👏
Now, let's practice.