Question

Please help on this 7th grade question

Which choice has a value that is closest to the value of the following expression? 17/12 - 49/40


A. 1/4


B. 1/5


C. 1/6


D. 1/7

Answer 1

B

Explanation:

Answer 2

Option B

The choice has a value that is closest to the value of the following expression 17/12 - 49/40 is
`(1)/(5)`

Solution:

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

`(17)/(12) - (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 (17 * 10)/(12 * 10) - (49 * 3)/(40 * 3)\\\\\rightarrow (170)/(120) - (147)/(120)\\\\\rightarrow (170-147)/(120)\\\\\rightarrow (23)/(120) = 0.1916 \approx 0.2`

`0.2 = (1)/(5)`

Thus correct answer is option B