In the last lesson, you learned how to multiply fractions using area models.
Now, let's learn to use number lines to multiply fractions.
Let’s multiply a fraction with a whole number:
3/4 × 5 = ?
Since our denominator is 4, let's divide each whole into 4 parts:
How many steps forward do we take to get from 0 to 3/4?
Let's count:
There are 3 spots between 0 and 3/4.
This means that we make 3/4 every time we jump 3 spots.
This is the same as:
3/4 × 1 = 3/4
So, what is 3/4 × 5? 🤔
This is the same as making 5 jumps of 3/4 each.
On which point did we end up?
Yes, we got to 15/4.
3/4 × 5 = 15/4 ✅
15/4 is the same as 3 3/4.
Excellent work. 👏
Let's rewrite 5 as 5/1 in the problem above.
To multiply any two fractions, first multiply their numerators together, and then multiply their denominators together.
Let’s try another example.
What's 2/5 × 1/2? 🤔
This problem is actually asking us to figure out 2/5 of 1/2.
First, let's draw 1/2 on a number line.
Next, we find 2/5 of 1/2.
Let’s divide the length of ½ into 5 parts.
Each mark is 1/5 of 1/2.
Where is 2/5 of 1/2? 🤔
We jump 2 spots from zero.
Where did that get us?
Yes! At 2/10. ✔️
Tip: We can simplify 2/10 to 1/5.
2/5 × 1/2 = 1/5
Great job.
1/3 × 3/5 = ?
We know that 1/3 × 3/5 is the same thing as 1/3 of 3/5.
Let's use a number line to solve the problem.
What's the bigger factor? 🤔
That's correct. It's 3/5.
Now, what is 1/3 of 3/5.
1/3 means we're talking about 1 part out of 3 total parts.
We see that 3/5 already has 3 equal parts.
Now we find 1/3 of 3/5.
What's our answer?
That's right. It's 1/5.
1/3 × 3/5 = 1/5
Great work.
Tip: you can also find the answer without number lines:
Why does that work? 🤔
Well, it's a shortcut for all of these steps:
It's kind of like if you divide and multiply by the same thing, you end up where you started.
That's why you can cancel out numerators and denominators that are the same. 👍
Great job learning to multiply fractions with and without number lines.
Now, start the practice.