find the L.C.D of each of the following and groups of fractions and then express the fractions of each group in terms of the L.C.D of that group... please show work
1\2,3\4,11\16
2\3,1\8,5\12
1\2,3\4,11\16 >> LCD = 16
What do you think the LCD of the other set is?
Use / to show fractions, not \
When finding the LCD you are looking for that number into which all denominators divide evenly
for the first that would be 16
for the 2nd it would be 24
To find the least common denominator (LCD) for each group of fractions, you need to find the least common multiple (LCM) for the denominators in each group. The LCM is the smallest number that is divisible by all the given numbers.
1. Group: 1/2, 3/4, 11/16
- The denominators are 2, 4, and 16.
- Find the LCM of these numbers:
LCM(2, 4, 16) = 16
- The LCD for this group is 16.
2. Group: 2/3, 1/8, 5/12
- The denominators are 3, 8, and 12.
- Find the LCM of these numbers:
LCM(3, 8, 12) = 24
- The LCD for this group is 24.
Now that we have the LCD for each group, we can express the fractions of each group in terms of their respective LCD.
1. Group: 1/2, 3/4, 11/16:
- The LCD is 16.
- Express each fraction in terms of the LCD:
1/2 = (1 x 8) / (2 x 8) = 8/16
3/4 = (3 x 4) / (4 x 4) = 12/16
11/16 - already in terms of the LCD.
2. Group: 2/3, 1/8, 5/12:
- The LCD is 24.
- Express each fraction in terms of the LCD:
2/3 = (2 x 8) / (3 x 8) = 16/24
1/8 - already in terms of the LCD.
5/12 = (5 x 2) / (12 x 2) = 10/24
Therefore, after finding the LCD for each group, the fractions in terms of their respective LCD are as follows:
1. Group: 8/16, 12/16, 11/16
2. Group: 16/24, 1/8, 10/24