The ratio 1 3/4 : 12/3 ∶ 1 5/6 written in simplest form is:
A. 1,75 : 1,67 : 1,83 B. 7 : 5 : 11 C. 21 : 20 : 22
To simplify the ratio, we need to convert the mixed numbers to improper fractions.
1 3/4 = (4 * 1 + 3)/4 = 7/4
1 5/6 = (6 * 1 + 5)/6 = 11/6
The simplified ratio is:
7/4 : 12/3 : 11/6
Next, we need to convert 12/3 to an improper fraction:
12/3 = (3 * 4)/3 = 4
The ratio becomes:
7/4 : 4 : 11/6
To compare these fractions, we need to find a common denominator. The least common multiple of 4 and 6 is 12.
So, the ratio becomes:
(7/4) * (3/3) : (4) * (3/3) : (11/6) * (2/2)
21/12 : 12/12 : 22/12
Now, the ratio can be simplified further by dividing all the fractions by their greatest common divisor, which is 2.
21/6 : 12/6 : 22/6
This can be written as:
7/2 : 2 : 11/3
The ratio 1 3/4 : 12/3 ∶ 1 5/6 written in simplest form is 7/2 : 2 : 11/3.
To simplify the given ratio, we need to convert the mixed numbers to improper fractions and find the least common denominator (LCD).
1 3/4 = (4 * 1 + 3) / 4 = 7/4
1 5/6 = (6 * 1 + 5) / 6 = 11/6
Now the ratio is:
7/4 : 12/3 : 11/6
To find the LCD, we need to find the least common multiple (LCM) of the denominators, which are 4, 3, and 6. The LCM of 4, 3, and 6 is 12.
Now we can rewrite the ratio with the same denominator:
7/4 : (4 * 12/3) : (2 * 11/6)
= 7/4 : 48/3 : 22/6
= 7/4 : 16 : 11/6
To convert the fractions to whole numbers:
7/4 = 1.75
11/6 = 1.83
So the simplified ratio is 1.75 : 16 : 1.83
The correct option is A. 1.75 : 16 : 1.83