Earlier, you learned how to add fractions with unlike denominators.
The examples all had two fractions.
To add 3 or more fractions, you follow pretty much the same steps.
Let's add these three fractions together:
To add fractions, they must have the same denominator.
What are the denominators?
Yes, they're 2, 3, and 4.
We need to find the Least Common Denominator for them.
Tip: Start listing multiples of the largest denominator.
Which of these denominators is the largest?
It's 4.
The first multiples of 4 are:
4, 8...
Let's check if 8 is a multiple of 2 and 3 using division. 🕵
8 ÷ 2 = 4
8 ÷ 3 = 2 remainder 2
We see that 8 is a multiple of 2, but not of 3.
So let's list the next multiple of 4.
4, 8, 12...
Is 12 a multiple of both 2 and 3?
Yes, it's a multiple of 2 and 3.
So, 12 is the LCD. ✅
Now, let's find equivalent fractions with the denominator 12 for the three addends, or fractions we're adding.
We start with 1/2.
How do we convert it into an equivalent fraction with the denominator 12?
Divide 12, the LCD, by 2, the denominator.
12 ÷ 2 = 6
Why? Because this tells you how much to multiply the numerator by to get an equivalent fraction!
6 × 1 = 6
This gives us the numerator for the equivalent fraction:
6/12
Awesome!
Next, let's find the equivalent fraction for 2/3 with the denominator 12.
Divide 12 by the denominator, 3.
12 ÷ 3 = 4
Why?
Because this tells you how much to multiply the numerator, 2, by.
2 × 4 = 8
Awesome, so what have we done so far?
We've turned two of the three addends from our original equation into equivalent fractions with a common denominator of 12.
Lastly, let's do the same thing for the third addend, 3/4.
3/4 is equivalent to 9/12.
Now, we can rewrite the original problem with these three equivalent fractions:
Since the denominators are the same, we can add the numerators:
Our sum is 23/12.
To add fractions, they have to have the same denominator.
To add fractions with unlike denominators, turn each one into an equivalent fraction with a common denominator. Then just add the numerators.
Now, try the practice.