Question

The difference of two integers is 18. If one of them is -40. Find the other.

Answer 1

Hint:
Here, we have to use the basic concept of the sum and difference to find out the second integer. We will assume the other integer as some variable and subtract \[ - 40\] from it. We will then equate the expression to 18. We will solve the equation to find out the other integer.

Complete step by step solution:
Let \[a\] and \[b\] be the two integers.
One of the integers given is\[ - 40\]. Therefore, \[a = - 40\] and assume \[b > a\].
It is given that difference between two integers is 18 which means
\[b - a = 18\] ……….. (1)
So, by putting the value of a in the above equation we will be able to find out the value of \[b\].
Therefore, equation (1) becomes
\[ \Rightarrow b - ( - 40) = 18\]
By opening the bracket, the negative and negative sign turns into the positive sign. Therefore, we get
\[ \Rightarrow b + 40 = 18\]
So, by solving the above equation i.e. by taking the term 40 to the other side of the equation, we get
\[ \Rightarrow b = 18 - 40 = - 22\]

Hence, the value of another integer is \[ - 22\].

Note:
Integers are the numbers which can be positive or negative but integers can never be in fractional form or decimal form. Natural numbers are the positive integer numbers.
Addition of two numbers is the process of combining two numbers to make a single number and subtraction is the process of finding the difference between the two numbers.
Even numbers are any integer that can be divided exactly by 2 is an even number. The last digit is 0, 2, 4, 6 or 8. An even number is an integer which takes the form \[n = 2k\], where \[k\] is an integer.
Odd numbers are the numbers that cannot be divided by 2. They are integers and not fractions. An odd number is an integer which takes the form \[n = 2k + 1\], where k is an integer.