Rename 3/5 and 11/20 using the least common denominator
well 5*2 = 10
5*3 = 15
5*4 = 20 so try
12/20 and 11/20
To rename 3/5 and 11/20 using the least common denominator, we need to find the least common multiple (LCM) of the denominators, which in this case are 5 and 20.
Step 1: Prime factorization of each number:
5 = 5
20 = 2 x 2 x 5
Step 2: Take the highest power of each prime factor from the prime factorization of both numbers.
The highest powers are 2 x 2 x 5 = 20.
So, the least common denominator is 20.
Now we can rewrite the fractions with the least common denominator:
3/5 can be renamed as 12/20
11/20 remains the same since the denominator is already 20.
Therefore, 3/5 and 11/20 can be renamed as 12/20 and 11/20, respectively, using the least common denominator 20.
To rename fractions using the least common denominator (LCD), you need to find the smallest multiple both denominators have in common.
Step 1: Find the prime factors of both denominators, and write them as a product of primes:
- 3/5 has a denominator of 5, which is a prime number itself.
- 11/20 has a denominator of 20, which can be factored as 2 * 2 * 5.
Step 2: Identify the common prime factors and use them to calculate the LCD:
- In this case, the only common prime factors are 2 and 5.
- Multiply the common prime factors: 2 * 2 * 5 = 20.
- So, the Least Common Denominator (LCD) is 20.
Step 3: To rename 3/5 and 11/20 using the LCD (20), you need to modify the numerators accordingly:
- For the fraction 3/5, since the original denominator is 5 and the LCD is 20, you need to multiply the numerator by 4 (20 ÷ 5 = 4): 3 * 4 = 12. Therefore, 3/5 can be renamed as 12/20.
- For the fraction 11/20, since the denominator is already 20, no changes are necessary.
So, after renaming, 3/5 becomes 12/20, and 11/20 remains unchanged as it already has the LCD as its denominator.