Amongst the most well-known constituents of Foundational Mathematics, Arithmetic is used across different fields of study from database operations to Computer Science and Programming. It forms a core part of primary school education and stays relevant throughout the life of an individual. Not to mention, it is highly important for competitive examinations held all over the world, including GMAT, GRE and other international eligibility tests too. One of the most widely used tools to teach students Arithmetic Operations is word problems. In this blog, we would be focusing on Word Problems based on Arithmetic Operations and how to solve them.
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What is Arithmetics?
Arithmetics can be understood as a study of numbers, their properties, and the basic operations of numbers. Number theory largely borrows from Arithmetic, which can be traced back to the ancient Middle Eastern scholars from Egypt and Africa. This is one of the most useful forms of formal and informal education on the face of Earth. Whether literate or not, most of us have an innate awareness of numbers and manipulations in them. The fundamental theorem of Arithmetic states that every number greater than 1 has constituent prime factors in a unique combination. These include basic operations such as Addition, Subtraction and others.
Types of Arithmetic Operations
Arithmetic operations encompass every single Mathematical operation that manipulates numbers or presents them in a different way. Basic arithmetic operations are the Fundamental concepts of modern Mathematics. It constitutes the four basic operations of Mathematics that are:
- Addition: The process of putting items together is known as an addition. The process of addition is indicated by the ‘+‘ sign. It entails merging two or more integers into a single expression. Furthermore, the sequence of the procedure is irrelevant. It indicates that the process of addition is commutative. It can involve any sort of number, including real and complex numbers, fractions, and decimals.
- Subtraction: The difference between two numbers is given by the subtraction operation. The ‘-’ symbol represents subtraction. It is nearly identical to addition, however, it is the conjugate of the second word. It is the opposite of addition. Subtraction is the adding of the phrase to the negative term. This procedure is primarily used to determine how many people remain once certain items are removed.
- Multiplication: Multiplication is also referred to as repeated addition. It is marked by a ‘×‘ or a ‘*’. It can also be combined with two or more values to produce a single value. The multiplicand and multiplier are involved in the multiplication process. The result of the multiplication of multiplicand and the multiplier is called the product
- Division: Division is the inverse of multiplication and is generally represented by the symbol ‘÷’. It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to provide a single term value. When the dividend is larger than the divisor, the result is greater than one; otherwise, the result is less than one.
Importance of Arithmetic Problems
Arithmetic is the foundation of mathematics and is used in solving every equation. Be it any graph or a complex problem, it can be broken into smaller equations and can be used with addition subtraction, multiplication, and division. If maths is considered as a language, these are its alphabets that help solve problems. These basics are proven mechanisms of arithmetics that simplify complicated problems. The properties of arithmetic are fundamental in the world of numbers and their applications.
Common Applications of Arithmetic Operations
Every other operation or Mathematical process requires these functions of Mathematics to move ahead. Here are some of the common applications of Arithmetic Operations:
- Fractions: Fractions represent a part of a whole number, usually with a numerator on top of a denominator. Fractions use the basics of division, taking it a step further where the divisor is greater than the dividend.
- Decimals: Similar to Fractions, Decimals represent real numbers other than whole numbers, whose value lies between two whole numbers. Decimal points are generally put between Ones and Tenths.
- Ratios: Ratios are a way to represent the relationship between two values, showcasing them as numbers with no common factors, i.e. in their reduced form. It can be used for determining quantities in ingredients, as well as to determine the number of chemicals to be used.
- Measures and Unit Arithmetic: Measures are used in day-to-day life in a variety of domains. Arithmetic operations play a key role in interchanging these measures with others, as it is the only way a measure can be understood and be of use. For example, converting Metres to Kilometres.
- Percents: Percentages are used to describe how large or tiny one quantity is in comparison to another. A percentage, in other terms, is a quantity or ratio represented as a fraction of 100. A percentage is often used to express a portion of or a change in a quantity.
- Averages: The arithmetic mean, or average, of a group of numbers represents the data set’s “middle” or “typical” value. An arithmetic mean is the sum of a set of numbers divided by the number of numbers in the set, and it is sometimes referred to as the “average.”
So, let’s put our theory to practice by going through some standard Arithmetic questions. All of these questions contain more than one operation, and some also use decimals.
- Total cost of 25 shirts is equal to $50,000. The total cost of 16 pairs of pants is equal to $40,000. What will be the unit cost of buying two shirts and one pants?
- Find the cost of one shirt by dividing the total cost of buying shirts($50,000) by the number of shirts(25). The per unit cost comes out to be $2,000.
- Similarly, we will find the per unit cost of a pant by dividing the total cost of pants($40,000) by the total number of pants(16), the per unit cost of pants comes out to be $2500.
- As per the question, we have to find the cost of two shirts and one pant. For this, we will multiply the cost of one shirt by 2, the resultant being $4000.
- Finally, we will add the two numbers to arrive at the total cost. The total cost of purchasing two shirts and one pant is $6500.
- What is the ratio of 5 meters to 12 feet?
- To begin with such questions, students must convert the measures of length into a common measure.
- For metres to feet conversion, one metre equals 3.048 feet. Hence, to convert 5 metres into feet, we will multiply 5 with 3.048. The resulting value will be 15.240.
- Now, we have to find the ratio of 15.24 to 12.For this, we will reduce the numbers to the lowest value possible.
- Upon simplification, the answer would be 1.27:1. This is the required answer.
- A shoe factory manufactured 70,000 shoes in 40 days. How many shoes did it manufacture per day?
- Total number of shoes manufactured by the shoe factory= 70,000
- Number of days taken to manufacture 70,000 shoes= 40 days
- Number of shoes manufactured per day= 70,000/40= 1750
- Hence the factory produced 1750 shoes in a single day.
- The cost of a table is Rs. 9370. How much will 120 such tables cost?
- The cost of 1 table= Rs. 9370
- Cost of 120 such tables= Rs. 9370 x 120= Rs. 11,24,400
- Hence the cost of 120 such tables will be Rs. 11,24,400
- In an election, 52496 people voted for Samrat, 44929 people for Harshit, and 36824 people for Manan in a town. If everyone voted in the town, what is the total number of voters?
- Number of people who voted for Samrat= 52496
- Number of people who voted for Harshit= 44929
- Number of people who voted for Manan= 36824
- Total number of people who voted= 52496 + 44929 + 36824= 1,34,249
- Hence, the total number of voters that voted in the elections are 1,34,249
Practice Questions on Arithmetic Operations
Here are some more questions for you to practice your knowledge of Arithmetic operations:
- The total money earned by the company is Rs. 42425. The money is to be divided into 15 equal parts for partners. Find the total share of 3 partners.
- There are 45 boys and 48 girls in a school. The students have to be allotted seats in 3 classes equally. Find the number of students in each class.
- An Athlete runs 15 km in one hour. He decides to go on a run 5 days a week, for 5 hours a day. How much distance does he cover in a week?
- A piece of cloth of length 10 metres is worth Rs. 250. A trader orders 0.79 kilometres worth of that cloth from the supplier. Due to international trade, he has to pay the supplier in CAD. 1 CAD is equal to 7 USD. Find the total amount he has to pay to the trader(in CAD).
- Ajay works for 6 hours a day. He gets $10 for working for 1 hour. How much money will he be able to earn in one year, given he works for 25 days every month, excluding 40 sickness breaks?
- Meera bought 96 toys priced equally for Rs. 12960. The amount of Rs. 1015 is still left with her. Find the cost of each toy and the amount she had.
- There are 1,45,968 bags of sugar, 2,36,487 bags of wheat and some bags of rice in a godown. If the total number of bags in the godown is 4,50,000, find the number of bags of rice.
- 1,575 students of a school want to go to Surat by bus. If one bus can carry 50 students, how many buses are required to carry all the students?
- There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
- Lara has 3 bags with the same amount of tiles in them, totalling 12 tiles. Markus has 3 bags with the same amount of marbles in them, totalling 18 tiles. How many more marbles does Markus have in each bag?
- There are 4 chalkboards in a classroom. Each chalkboard has 2 pieces of chalk. This means there are 8 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
- Jasmine went to 16 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?
- There is a group of 10 people who are ordering pizza. If each person gets 3 slices and each pizza has 4 slices, how many pizzas should they order?
- There are 255 books in a library. On Monday, 143 books are taken out. On Tuesday, 52 books are brought back. How many books are there now?
- Melissa buys 2 packs of tennis balls for Rs. 150 in total. Altogether, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?
Arithmetic Operators are used in mathematics to make computations. To assign a value to a property or variable, use the Assignment Operator. Numeric, date, system, time, and text assignment operators are all possible.
The four basic rules of mathematics are addition, subtraction, multiplication, and division. Each of the four arithmetic operations is represented by a different symbol, which are +, -, x, and ÷ respectively.
The acronym PEMDAS, which stands for parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right, can be used to recall the sequence of operations.
Thus, we hope that this blog helped you understand the essential elements of Arithmetic Operations along with some solved questions and practice worksheets. Preparing for standardized tests like GRE or GMAT? Leverage Live offers expert guidance and online live classes for standardised exams to help students achieve their target score and successfully land into their dream university abroad! Book a free online demo session with us today!