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Word Problems on Arithmetical Operations

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Last updated date: 17th May 2024
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What is a Word Problem?

A word problem is a compilation of several easy-to-understand sentences describing real-life scenarios where a specific problem needs a solution using stepwise mathematical calculation.

Word problems are a crucial part of learning in the curriculum of primary school students because they need children to apply their knowledge about a variety of different concepts to find solutions to a real-life problems.

In classroom settings, children are taught about the acronym RUCSAC which stands for:

i. R- Read

ii. U- Understand

iii. C- Choose

iv. S- Solve

v. A- Answer

vi. C- Check

These values help students to work their minds and apply prior knowledge to yield accurate solutions to problems.


Four Operations of Word Problems

There are four types of operations included in the topic Word Problems. These four operations perform different kinds of functions in different kinds of Word Problems. Students are trained in school to identify the Word Problem and apply the operations required to successfully calculate the result of the Problem.


The Four Operations of Word Problems are explained below in detail.

  • Addition: Addition is the first operation that a Word Problem may contain. Addition, as its name justifies, is about calculating the ‘sum’ of the given numbers. In simple words, it means to add the given numbers together and find a solution.

  • Subtraction: Subtraction is the second operation introduced to students. It is a little more complicated than addition. The subtraction operation is used to calculate ‘take-aways’ from the given numbers. In simple words, it means to subtract one quantity from the larger given quantity and calculate results.

  • Multiplication: Multiplication is the third operation in the list of Word Problems. According to its name, it helps us to calculate the product of two given numbers. In other words, multiplication operates as the process of multiplying the given quantities to yield a result.

  • Division: Lastly, Division is introduced as the fourth operation in the list of operations for Word Problems. Division is a technique through which we can divide the given quantities in a problem. To put it plainly, division operation splits the larger quantity or number into smaller parts.


Word Problems On Four Operations

1. Word Problem Based on Addition: In a class on the day of the examination, the total number of students present in each room was 50. How many students do two examination rooms have?


You need to add the number of students present in both the rooms (50+50) to find the accurate solution to the given problem.


Answer: There are a total of 100 students in 2 examination halls.


2. Word Problem Based on Subtraction: Paul and Amber entered a Card Challenge. They made a huge pyramid from 13687 cards, but Amber accidentally knocked 2956 pieces of cards to the floor before the judges saw their finished work. How many cards were left standing?


The number of cards on the floor (2956) must be subtracted from the total number of cards (13687) to calculate how many cards were still standing.


Answer: There are 10,731(13687-2956) cards standing.


3. Word Problem Based on Multiplication: You are the manager of a furniture company that produces 1350 chairs each month. In a year, how many chairs does the company make?


To calculate this, you need to multiply the number of chairs produced in each month (1350) by the number of months contained in each year (12).

Answer: In a year, a total of 16,200(1350 12) chairs are produced.


4. Word Problem Based on Division: 7000 books need to be arranged equally on a few shelves. If each bookshelf can hold 1000 books, how many bookshelves are required to fit them all?


To answer this problem, you need to divide the number of books one shelf can hold (1000) by the number of total books given (7000).


Answer: 7 bookshelves are required to hold 70000 books.


Mixed Operation Word Problems

Mixed Word Problems consists of the combination of more than one of the Four Operations as mentioned above (addition, subtraction, multiplication, division). They encourage a student to understand and link the various operations needed to solve the problem and build better concentration and think faster.

An Example: If each bottle needs 2 liters of syrup and there are 30 bottles, how much sugar syrup is needed to fill all of them, and how many drinks can be made from one bottle if each glass contains 200 ml syrup? This is a Mixed Word Operation.

Solution: Quantity of syrup each bottle can hold = 2L= 2000mL

Number of bottles = 30

Total quantity of sugar syrup = $30\times2$

Ans: i) 60L of syrup can be contained in 30 bottles.


Quantity of syrup in each glass = 200mL

Total number of drinks that can be made with one bottle of syrup = $\dfrac{2000}{200}mL$

= 10

Ans: ii) 10 drinks can be made from each bottle.


Solved Examples On Word Problem

An example of a Word Problem is given below:


Example:

Martha bought five apples from the market. She gave one to her mother, one to her brother Jimmy and one to her grandfather. How many apples does she have left?

Solution:

Total number of apples bought by Martha= 5

No. of apples, Martha gave to her mother, her brother, and grandfather= (1+1+1)

Therefore, the no. of remaining apples: 5- (1+1+1)

5- 3 = 2.

Martha has two apples left.


Practice Question MCQs

1. What is the average of: 1,2,3,5,9

  1. 3

  2. 4

  3. 5

  4. 8

Answer: B)


2. Find the value of: 0.0030.02

  1. 0.06

  2. 0.006

  3. 0.0006

  4. 0.00006

Answer: D)


Conclusion

The fundamentals of mathematics are arithmetic operations. It contains mostly arithmetic operations like addition, subtraction, multiplication, and division. These are also referred to as mathematical operations. In our daily lives, we employ mathematical operations to calculate overall business income and costs, create a monthly or yearly budget, measure lengths, and so on. We use them virtually every day, for example, while calculating the total number of questions given in homework, time, money, the number of chocolates we ate, the amount of marks gained in all courses, and so on.

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FAQs on Word Problems on Arithmetical Operations

1. What are Arithmetic Word Problems?

Answer: Amongst the most prestigious subject matters of Foundational Mathematics, the use of Arithmetic across various fields of study, ranging from Computer Science and Programming to solving simple word problems, is evident. Arithmetic forms a core segment of primary school education and holds importance throughout an individual's life across various fields.


In the branch of mathematics, word problems that require arithmetic calculations to achieve a successful result are known as Arithmetic Word Problems. These are generally included in the curriculum of Primary and Lower Secondary Students to exercise their mental ability and build a cognitive approach to learning.

2. What is the Significance of Word Problems in Mathematics?

Answer: Following is the importance of world problems:-

  • Ability to think: Word Problems push students to think out of the box to achieve the desired results. This is necessary to not only expand their knowledge but also form their own opinions and come up with methods to solve a particular problem.

  • Ability to Tackle Challenges: Tough Problems are always seen as a challenge. Students are equipped with the readiness to accept these challenges and tackle them well.

  • Building Confidence: By succeeding in solving challenging Math Problems, students feel confident to face tougher challenges that may come their way. This is important to build strong self-confidence.