Which correctly renames7/8 and5/6 using a common denominator?
28/24 and 20/24
To correctly rename 7/8 and 5/6 using a common denominator, we need to find the least common multiple (LCM) of the denominators, which is the smallest number that both denominators can divide evenly into. Here's how you can find the LCM and rename the fractions:
Step 1: Find the denominators of the fractions: The denominators are 8 and 6.
Step 2: Find the LCM of 8 and 6: One way to do this is by listing the multiples of each number until you find a common multiple.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66...
From the list, we see that 24 is the smallest number that is a multiple of both 8 and 6. So the LCM of 8 and 6 is 24.
Step 3: Rename the fractions with the common denominator: Now we need to convert both fractions so that they have a denominator of 24.
To do this, we multiply the numerator and denominator of each fraction by a value that will result in 24 as the new denominator.
For the fraction 7/8:
Multiply the numerator (7) by 3 and the denominator (8) by 3 to get: (7 × 3)/(8 × 3) = 21/24.
For the fraction 5/6:
Multiply the numerator (5) by 4 and the denominator (6) by 4 to get: (5 × 4)/(6 × 4) = 20/24.
So, the correctly renamed fractions with a common denominator of 24 are 21/24 and 20/24.