The product of two rational numbers is -40/3. If one of the two numbers is…
2024
The product of two rational numbers is -40/3. If one of the two numbers is -5/2, then the reciprocal of the other number lies between :
- A.
3/20 and 9/50
- B.
9/50 and 1/5
- C.
1/5 and 1/4
- D.
1/4 and 1/3
Show answer & explanation
Correct answer: B
Concept: If the product of two numbers and one of the numbers are known, the other number equals the product divided by the known number. The reciprocal of a non-zero number x = a/b is 1/x = b/a.
Application:
Let the two rational numbers be -5/2 and the unknown number x, so that (-5/2) × x = -40/3.
Solve for x: x = (-40/3) ÷ (-5/2) = (-40/3) × (-2/5) = 80/15 = 16/3.
Find the reciprocal of x: the reciprocal of 16/3 is 3/16, which equals 0.1875 in decimal form.
Cross-check: Multiplying the two numbers back gives 16/3 × (-5/2) = -80/6 = -40/3, which matches the given product. Comparing 0.1875 with the boundary values 9/50 = 0.18 and 1/5 = 0.2 shows that 0.18 < 0.1875 < 0.2, so the reciprocal of the other number lies between 9/50 and 1/5.