2. Express the fractions 1/2, 3/16, and 7/8 with an LCD.
A. 1/4, 3/4, 7/4
B. 1/32, 3/32, 7/32
C. 4/8, 6/8, 14/8
D. 8/16, 3/16, 14/16
A
Nope.
To express the fractions 1/2, 3/16, and 7/8 with a least common denominator (LCD), we need to find the smallest common multiple of the denominators of these fractions.
The denominators of the given fractions are 2, 16, and 8.
To find the least common multiple (LCM) of these denominators, we can list their multiples and find the smallest number that appears in all three lists:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ...
Multiples of 16: 16, 32, 48, 64, 80, ...
Multiples of 8: 8, 16, 24, 32, 40, ...
From these lists, we can see that the smallest number that appears in all three lists is 16.
So, the least common denominator (LCD) is 16.
Divide the LCD (16) by each denominator and multiply both the numerator and denominator of each fraction by the result:
1/2 = (1 * 8) / (2 * 8) = 8/16
3/16 = (3 * 1) / (16 * 1) = 3/16
7/8 = (7 * 2) / (8 * 2) = 14/16
Therefore, the fractions 1/2, 3/16, and 7/8 with a least common denominator (LCD) of 16 are 8/16, 3/16, and 14/16.
Among the options provided, the correct answer is D. 8/16, 3/16, 14/16.