Question

A driver is 20m below sea level. If he goes further down by 10m, then find his new position.
A) 10m
B) -10m
C) 30m
D) -30m

Answer 1

Hint: This question is solved with the help of integer’s concept. Integers are whole numbers, both positive and negative. We can perform four basic math operations on them: addition, subtraction, multiplication, and division.
A number line is a reference for comparing and ordering numbers. Every number on the number line is plotted with respect to the origin (zero), and the position of number on a number line determines the value of that number. This implies that any number right to zero is known as positive numbers, and the numbers left to zero are known as negative numbers.
When we add two negative numbers, the result will always be a negative number; the direction of move will always be the left side.

Complete step-by-step answer:
Let assume sea level as the reference, the position below it will be taken as negative and above sea level we will take it as positive.
So, Sea level = 0m
Original position = -20m (since he is below the sea level)
As he goes further down by 10m below the sea level, therefore we will add it in the previous position to find his new position.
New position = -(20+10)m
New position = -30m

Note: There are a few properties of integers which determine its operations:
1) Commutative Property: It is the property of multiplication and addition which states that order of terms doesn’t matter, the result will be the same. Let x, y be any two integers, then
$\begin{gathered}
  x + y = y + x \\
  x \times y = y \times x \\
\end{gathered} $
2) Associative Property: It states that the way of grouping of numbers doesn’t matter, the result will be the same. Let x, y and z be any three integers, then
$\begin{gathered}
  x + \left( {y + z} \right) = \left( {x + y} \right) + z \\
  x \times \left( {y \times z} \right) = \left( {x \times y} \right) \times z \\
\end{gathered} $
3) Distributive Property: It explains the distributing ability of operation over another mathematical operation within a bracket. Here integers are added or subtracted first and then multiplied or multiplied first with each number within the bracket and then added or subtracted. Let x, y and z be any three integers, then
$\begin{gathered}
  x \times \left( {y + z} \right) = x \times y + x \times z \\
  x \times \left( {y - z} \right) = x \times y - x \times z \\
\end{gathered} $