Question

Please help on this 7th grade question

Answer 1

Option B

The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is $\frac{1}{5}$

Solution:

Given that we have to find the value that is closest to the value of following expression

$\frac{17}{12} - \frac{49}{40}$

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:

$\rightarrow \frac{17 \times 10}{12 \times 10} - \frac{49 \times 3}{40 \times 3}\\\\\rightarrow \frac{170}{120} - \frac{147}{120}\\\\\rightarrow \frac{170-147}{120}\\\\\rightarrow \frac{23}{120} = 0.1916 \approx 0.2$

$0.2 = \frac{1}{5}$

Thus correct answer is option B