Let's learn from an example.
Sarah’s milkshake recipe needs 5 1/3 cups of milk. She only has 3 3/5 cups. How much more milk does Sarah need to buy so she can make her milkshake?
What do you think we should do to solve this problem?
You got it! 👍 We need to do subtraction.
We subtract the milk that Sarah has now from the milk that she needs for the milkshake.
In this lesson, we’re going to use the number line in doing our subtraction. 🙂
The numbers we have in our problem are mixed numbers.
Mixed numbers are numbers that are made up of a whole number and a fraction. They're always greater than 1.
Let’s represent, or show, 5 1/3 on a number line.👇
We need to have 5 wholes.
Then we extend it a bit more to include 1/3.
How many parts are each whole divided into? 🤔
Correct! 👏 They’re divided into 3 equal parts.
Now, let’s represent 3 3/5 on a number line.👇
We go to 3 on the number line.
Then, we add 3/5.
How many parts are each whole in this line divided into?
Yes! 👍 They're divided into 5 equal parts.
If we put our lines together, we see that they don’t match.
The wholes are divided into different numbers of equal parts. 😟
The fractions in 5 1/3 and 3 3/5 have unlike denominators.
Tip: We can subtract fractions only when they have like denominators.
👉 So we need to find a common denominator.
A denominator is the total number of equal parts a whole is divided into.
When we find a common denominator, we make the denominators of the fractions we're subtracting the same.
We're subtracting these numbers:
5 1/3 - 3 3/5 = ?
How do find a common denominator for them? 🤔
👉 First, we look at 5 1/3.
Each whole is divided into 3 parts.
We need to further divide each part into 5 smaller parts.👆
How do we know this? 🤔
We just looked at the denominator of the other number.
What's the other number?
Yes! 👏 It's 3 3/5.
What's the denominator of the fraction?
Correct! It's 5. 👍
That’s why we need to further divide each part of 5 1/3 into 5 equal parts.
There are now 15 equal parts between the whole numbers.
👉 Now we look at 3 3/5.
We need to further divide each part into smaller parts.👆
How many smaller parts should we divide each part into?
Fantastic! 🎊 We further divide each part into 3 smaller parts.
That's because the denominator of the other fraction 5 1/3 is 3.
How many equal parts are there between the whole numbers?
Yes! There are 15 equal parts. 😀
Now, both number lines show the same equal parts between the whole numbers.
Each part is 1/15 of the whole.
They now match! ✔️✔️
This means that we can subtract these mixed numbers now! 😺
When we subtract numbers on a number line, we move some steps backward from the point we’re starting with.
So, where do we start? 🤔
Yes! We start from 5 1/3. That’s the number we’re subtracting from.👇
We subtract 3 3/5 from it.
How many steps backward do we need to make?
3 3/5 is 54 steps away from 0.
This means we move 54 steps backward from 5 1/3.
Where did we land on? 🧐
We are now on 1 11/15.
It's 26 steps away from 0. So it's the same as 26/15.
Sarah needs 1 11/15 cups of milk to make her milkshake.
Excellent job! 🎉
Now, start the practice to try subtracting mixed numbers on your own. 💪