Word Problems: Add, Subtract, Multiply, Divide

Word Problems: Word Problems are an important aspect of the primary curriculum because they require students to apply their understanding of various topics to “real-life” circumstances. They also assist students in becoming acquainted with mathematical terminology like more, fewer, subtract, difference, altogether, equal, share, multiply, reduced, etc.

A word problem consists of a description of a real-life scenario where a mathematical calculation is required to solve a problem. Students need to learn how to solve word problems as it enables them to apply mathematical concepts to various real-life scenarios. This means that to understand the word problem, students must be familiar with the terminology linked with the mathematical symbols they are used to. Let us learn in detail about Word Problems in this article.

What is a Word Problem?

In real life, mathematical problems do not usually present themselves as \(2+3\) or \(6-4.\) Instead, they are a bit more complex than we think. Authors of mathematical curriculum sometimes implement word problems to help students understand how they are related to the real world.

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Word problems often show mathematics happening more naturally in the real world. Word problems can vary from simple to complex.

Examples:
Here are a few examples to get you some ideas:
1. Keerthi had \(5\) apples. Her mother gave her \(7\) more apples. Now, how many apples does Keerthi have altogether?
2. There were \(18\) pencils and \(9\) pens. How many more pencils than pens are there?
3. Spurti has one dozen eggs. Her friends ate \(4\) for breakfast. Now, how many eggs are left with Spurti?
4. There are \(18\) apples. Swetha, Priya, and Rachana want to eat them in equal share. How many apples will each of the friends get?

As you can notice, word problems involve addition, subtraction, multiplication, division, or even multiple operations.

Word Problems on Quadratic Equation

Handling Maths Word Problems in General

Steps for Solving a Word Problem:

To work out any word problem, follow the steps given below:

1. Read the Problem: First, read through the problem once.

2. Highlight Facts: Then, read through the problem again and underline or highlight important facts such as numbers or words that indicate an operation.

3. Draw a Picture: Drawing a picture sometimes help visualise the problem more clearly. It can also help understand clearly the algebraic operations that need to be carried out.

4. Determine the Operation(s): Next, determine the operation or operations that need to be performed. Is it addition, subtraction, multiplication, division? What needs to be done? Drawing the picture should be a big help in figuring this out. However, look for clues in words such as:
(i) Addition: add, total, brought, plus, altogether, and, combine, more, in all
(ii) Subtraction: subtract, fewer, take away, than, left
(iii) Multiplication: total, times, triple, twice, in all
(iv) Division: each, per, out of, equal pieces, split, average

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5. Make a Math Sentence: Next, translate the word problem and drawings into a math or number sentence. This means write a sentence such as \(18+3=\)

6. Solve the Problem: Then, solve the number sentence and find the solution—for example, \(3+8=11.\)

7. Check Your Answer: Finally, check the result obtained to ensure the correct answer.

With the above \(7\) steps, solving word problems in mathematics becomes easy.

Addition Word Problems

Addition word problems arise in situations where there is an increase of something or gain as a result of combining one or more numbers. Think of addition as combining parts to form a whole.
Example: Teena has \(6\) chocolates, her brother gives her \(4\) chocolates. How many chocolates in total does Teena have?
To find the total chocolates, we add the number of chocolates Teena has and the number of chocolates her brother gave her.

Thus, Teena has \(10\) chocolates now.

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Subtraction Word Problems

Subtraction word problems arise in situations where there is a decrease of something or loss as a result of deducting a number from another.
Example: Arya plucked \(10\) cherries from the tree, and her friend asked her to give \(4\) cherries to her. How many cherries are left with Arya?
Here we subtract the number of cherries given to Arya’s friend from the total cherries plucked by Arya.

Thus, the number of cherries left with Arya is \(6.\)

Multiplication Word Problems

Multiplication word problems are helpful for students to develop their multiplication knowledge by applying it to real-life situations. In this kind of multiplication word problem, one quantity is compared with another quantity, larger or smaller. Work out the multiplication problem using the clues provided.
Example: Ajay has two bunch of tomatoes. Each bunch has \(4\) tomatoes. What is the total number of tomatoes does Ajay have?
Here, we multiply the number of the bunch by the number of tomatoes in each bunch

Thus, Ajay has \(8\) tomatoes in total.

Division Word Problems

Division word problems are more confusing for students to understand. The words generally used in division word problems are “shared among” or “given to each” or similar phrases that imply total quantity to be split evenly into groups. We use division or multiplication when the problem involves equal parts of a whole. 

Example: He divides \(12\) apples evenly among \(4\) friends. How many apples did John give to each of his friends?
To find how many apples John gave to each of his friends, we divide the total number of apples by the number of friends.

Hence, each of John’s friends gets \(3\) apples.

Fraction Word Problems

Fraction word problems look more complex, but in reality, fraction word problems are just as easy as those involving whole numbers. Here, one extra step of simplification may be needed in some cases. Students should know the operations with fractions to solve word problems on fractions.

Example: Swaroop had half an apple, and his mother gave him another quarter of an apple. What portion of apple does Swaroop have?
The given example is the addition word problem that involves fractions.
Here, we add the portion of apple Swaroop initially had with the portion his mother gives. i.e., \(\frac{1}{2} + \frac{1}{4} = \frac{{2 + 1}}{4} = \frac{3}{4}.\)

Thus, Swaroop has \(\frac{3}{4}\)th of apple.

Solved Examples

Q.1. The male population of a village is \(76138,\) and the female population is \(13776.\) What is the total population of the village?
Ans: Male population \(=76138\)
Female population \(=13776\)
Total population of the village \(=\) male population \(+\) female population \(=76138+13776 \)
\(=89914 \)

Thus, the total population of the village is \(89914.\)

Q.2. Likith had collected \(208\) coins. He lost of \(52\) coins. How many coins are left with Likith?
Ans: Total coins Likith collected \(=208\)
The number of coins lost \(=52\)
Number of coins left \(=208 – 52=156\)

Thus, the number of coins left is \(156.\)

Q.3. The cost of one shirt is \(₹206.\) A retailer wants to buy \(68\) such shirts. How much should he pay?
Ans: Given that the cost of one shirt \(=₹206\)
Number of shirts a retailer wants to buy \(=68\)
Total amount to be paid \(=₹206×68\)

Therefore, the total amount to be paid is \(₹14008.\)

Q.4 If \(4472\,{\rm{kg}}\) of rice is packed in \(52\) bags, how much rice will each bag contain?
Ans: Since \(52\) bags contain rice of \(4472\,{\rm{kg}}\)
Therefore, \(1\) bag contains rice \( = \left( {\frac{{4472}}{{52}}} \right){\rm{kg}}\)
\( = 86\,{\rm{kg}}\)

Thus, each bag of rice contains \( = 86\,{\rm{kg}}.\)

Q.5. One-half of the students in a school are boys, \(\frac{4}{5}\) of these boys are studying in lower classes. What fraction of boys are studying in lower classes?
Ans: Fraction of boys studying in school \( = \frac{1}{2}\)
Fraction of boys studying in lower classes \( = \frac{4}{5}\) of \(\frac{1}{2}\)
\( = \frac{4}{5} \times \frac{1}{2}\)
\( = \frac{2}{5}\)
Therefore, \(\frac{2}{5}\) of boys studying in lower classes.

Q.6. Celena planned to interview some candidates for a position in her office. If she scheduled half an hour to meet each of them, how much time did she schedule for all \(6\) candidates?
Ans: Time spent to meet each candidate \( = \frac{1}{2}\) hour
Number of applicants \(=6\)
Time scheduled for all \(6\) candidates \( = \frac{1}{2} \times 6 = 3\) hours
Thus, Celena scheduled \(3\) hours for the interview.

Summary

In this article, we studied the meaning and steps to solve word problems. Then we have discussed in detail taking an example of how to do the addition word problem, subtraction, multiplication, division and fraction word problem. 

We have solved word problem examples for students to understand the concept clearly.

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Frequently Asked Questions on Word Problems

We have provided some frequently asked questions on Word Problems here:

Q.1. What are word problems in maths?
Ans: A word problem is a few sentences describing a real-life scenario where a problem needs to be solved by a mathematical calculation.

Q.2. What are numberless word problems? 
Ans: Numberless word problems are designed to provide scaffolding that allows students to understand the underlying structure of word problems.

Q.3. What is addition word problems?
Ans: Addition word problems appear when there is a gain or an increase of something due to combining one or more numbers. Think of addition as combining parts to form a whole.

Q.4. What are the steps in solving word problems?
Ans: Solving word problem requires the following steps: 
1. Read the problem
2. Highlight facts 
3. Draw a picture
4. Determine the operation/s.
(i) Addition
(ii) Subtraction
(iii) Multiplication
(iv) Division
5. Make a mathematical sentence
6. Solve the problem
7. Verify your answer

Q.5. What is an example of a word problem?
Ans: The typical examples of word problems in algebra are distance problems, age problems, percentage problems, work problems, mixtures problems and number problems.

Now you are provided with all the necessary information on Maths word problems and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.