An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different type of numbers including integers.

Integers are a special group of numbers that do not have a fractional or a decimal part. It includes positive numbers, negative numbers and zero. Arithmetic operations on integers are similar to that of whole numbers. Since integers can be positive or negative numbers i.e. as these numbers are preceded either by a positive (+) or a negative sign (-), it makes them a little confusing concept. Therefore they are different from whole numbers. Let us now see how various arithmetical operations can be performed on integers with help of few word problems.Solve the following word problems using various the rules of operations of integers.

### Some examples relating word problems on integers

**Example 1:** Shyak has overdrawn his checking account by Rs.38. The bank debited him Rs.20 for an overdraft fee. Later he deposited Rs.150. What is his current balance?

**Solution:**Given,

Total amount deposited= Rs. 150

Amount overdrawn by Shyak= Rs. 38

⇒ Debit amount = -38 [Debit is represented as negative integer]

Amount charged by bank= Rs. 20

⇒ Debit amount= -20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

⇒150 + (–58) = 92 [Subtract and give the sign of greater number]

Hence, current balance is Rs. 92.

**Example 2:** Anna is a microbiology student. She was doing a research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria Xneed optimum temperatureof -31˚C while bacteria Yneed optimum temperature of -56˚C. What is the temperature difference?

**Solution:**Given,

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

⇒ (-31) – (-56)

⇒ -31 + 56 = 25 [Subtract and give the sign of greater number]

Hence, temperature difference is 25˚C.

**Example 3: **A submarine submerges at the rate of 5m/min. If it descends from 20m above the sea level, how long will it take to reach 250m below sea level?

**Solution: **Distance travelled above sea level is denoted with a positive integer while distance travelled below sea level is denoted with a negative integer.

Given,

Initial position = +20 m (above sea level)

Final position = -250 m (below sea level)

Total depth it submerged = (-250) – (+20) = -270 m

The negative sign indicates that the submarine travelled below sea level. Thus, submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = \(\frac{1}{5}\)

Time taken to submerge 270m = \(270~\times~\frac{1}{5} \)

Hence, submarine will reach 250m below sea level in 54 minutes.

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