Which of the following shows the next step using the least common denominator to simplify 7/8-5/6?
Which following?
What do you think?
To simplify the expression 7/8 - 5/6 using the least common denominator (LCD), we need to find the least common multiple (LCM) of the denominators 8 and 6. Here are the steps to find the LCD:
Step 1: Find the prime factorization of the denominators.
- The prime factorization of 8 is 2^3.
- The prime factorization of 6 is 2 * 3.
Step 2: Identify the highest power for each prime factor.
- The highest power of 2 is 2^3 for the denominator 8.
- The highest power of 3 is 3^1 for the denominator 6.
Step 3: Multiply the highest powers of each prime factor together.
- Multiply 2^3 * 3^1 = 8 * 3 = 24.
So the LCD of 8 and 6 is 24.
Now, let's simplify 7/8 - 5/6 using the LCD:
Step 4: Rewrite the fractions with the LCD as the denominator.
- To convert 7/8 to have a denominator of 24, multiply both the numerator and denominator by 3: (7 * 3) / (8 * 3) = 21/24.
- To convert 5/6 to have a denominator of 24, multiply both the numerator and denominator by 4: (5 * 4) / (6 * 4) = 20/24.
Step 5: Subtract the fractions with the same denominator.
- The expression 7/8 - 5/6 becomes 21/24 - 20/24.
Therefore, the next step in simplifying 7/8 - 5/6 using the least common denominator is to subtract the numerators, resulting in 1/24.