Option B
The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is [tex]\frac{1}{5}[/tex]
Solution:
Given that we have to find the value that is closest to the value of following expression
[tex]\frac{17}{12} - \frac{49}{40}[/tex]
Let us take L.C.M of denominators and solve the sum
L.C.M of 12 and 40
List all prime factors for each number
prime factorization of 12 = 2 x 2 x 3
prime factorization of 40 = 2 x 2 x 2 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 5 = 120
Thus the given expression becomes:
[tex]\rightarrow \frac{17 \times 10}{12 \times 10} - \frac{49 \times 3}{40 \times 3}\\\\\rightarrow \frac{170}{120} - \frac{147}{120}\\\\\rightarrow \frac{170-147}{120}\\\\\rightarrow \frac{23}{120} = 0.1916 \approx 0.2[/tex]
[tex]0.2 = \frac{1}{5}[/tex]
Thus correct answer is option B
