An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types 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 the help of a few word problems. Solve the following word problems using various rules of operations of integers.
Word problems on integers Examples:
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?
Total amount deposited= Rs. 150
Amount overdrew 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, the current balance is Rs. 92.
Example 2: Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?
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 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?
Initial position = 20 m (above sea level)
Final position = 250 m (below sea level)
Total depth it submerged = (250+20) = 270 m
Thus, the submarine travelled 270 m below sea level.
Time taken to submerge 1 meter = 1/5 minutes
Time taken to submerge 270 m = 270 (1/5) = 54 min
Hence, the submarine will reach 250 m below sea level in 54 minutes.
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