Find the least common denominator (LCD) for fractions with the given denominators. 1/3 + 5/12 + 4/5
I start with the largest denominator and find the smallest number that all three denominators divide evenly.
12, 24, 36, 48, 60, 72, 84, 96
One of the above numbers is evenly divisible by 3, 12, and 5. Can you see which one it is?
would it be 60?
Yes. You're right! :-)
5/10+4/20?
36
To find the least common denominator (LCD) for fractions with different denominators, we need to find the smallest number that all the denominators can divide evenly into.
Step 1: Find the prime factorization of each denominator.
- The prime factorization of 3 is 3.
- The prime factorization of 12 is 2 * 2 * 3.
- The prime factorization of 5 is 5.
Step 2: Identify the highest power of each prime factor.
- The highest power of 2 is 2 * 2 = 4.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor.
- 2 * 2 * 3 * 5 = 60
The least common denominator for the fractions with denominators 3, 12, and 5 is 60.
Now, let's add the fractions with a common denominator of 60.
1/3 = (1 * 20) / (3 * 20) = 20/60
5/12 = (5 * 5) / (12 * 5) = 25/60
4/5 = (4 * 12) / (5 * 12) = 48/60
Now we can add the fractions:
20/60 + 25/60 + 48/60 = (20 + 25 + 48) / 60 = 93/60
The sum of the fractions 1/3, 5/12, and 4/5 is 93/60.