102 LearnersLast updated on September 4, 2025
Arithmetic
By studying arithmetic, we understand how numbers relate, how to spot numerical patterns, and how to calculate in terms of solving problems. The operation of arithmetic forms the basis of studying mathematics and is applied largely in everyday life.
What is Arithmetic?
Arithmetic is a branch of mathematics that deals with the study of numbers. Arithmetic is primarily concerned with four operations: addition, subtraction, multiplication, and division. They are the simplest tools to use in solving issues of quantities, and thus arithmetic is a significant aspect of academic and everyday life, such as budgeting, cooking, and measurement. Students learn to solve mathematics problems accurately and confidently by being skilled in arithmetic. It also sets you up to study higher mathematics in the future.
Difference Between Arithmetic and Mathematics
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Arithmetic |
Mathematics |
| Arithmetic is the most basic aspect of mathematics, dealing with the numerical operations such as addition, subtraction, multiplication, and division. | Mathematics is a large curriculum with numerous areas, including arithmetic, algebra, geometry, trigonometry, and calculus. |
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It emphasizes direct numerical calculations and basic number properties. |
It is the study of patterns, relationships, shapes, structures, and logical reasoning. |
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Arithmetic is confined to fundamental numerical tasks and simple calculations. |
Mathematics, on the other hand, explores a wide range of areas that go well beyond simply adding and subtracting numbers. |
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It is useful in everyday life, such as managing money, shopping, and solving small difficulties. |
It incorporates abstract concepts such as logical proofs, algebraic equations, measurements, and complex problem-solving methodologies. |
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Arithmetic is often very easy to learn because it deals with fundamental number manipulation. |
Mathematics can be far more complex, requiring more advanced reasoning and abstract thought. |
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It covers a variety of number types, including whole numbers, decimals, fractions, percentages, square roots, and exponents. |
On the other hand, mathematics frequently necessitates mastering complicated topics such as algebra, geometry, and calculus, which involve more analytical thinking. |
What Are the Basic Arithmetic Operations?
Arithmetic operations form the foundation of mathematics and are four fundamental operations: addition, subtraction, division, and multiplication. They are applied to solve everyday problems and are utilized to construct other more advanced mathematical concepts.
1. Addition
- Definition: Adding two or more numbers to get their sum is what addition is all about. It is represented by the '+' sign.
- Key Property: The Four most significant characteristics of addition are commutative property (addition order doesn't change the outcome), associative property (regrouping or grouping doesn't change the sum), identity property (adding zero doesn't change the number), and closure property (real number sum is always real).
- Example: If you add 756 and 876, you have a total of 1632. This indicates how addition happens in everyday life.
2. Subtraction
- Definition: Subtraction involves determining the difference between two numbers by taking the smaller value away from the larger one. It is indicated by the ‘−’ sign.
- Key Property: Subtraction is closed (difference of real numbers is real) but not associative and commutative (order is reversed and order of brackets changes the result with it) or possesses an identity element, as no number would leave another intact if subtracted from it.
- Example: Subtracting 864 from 984 gives you a difference of 120. This shows how subtraction helps compare quantities.
3. Multiplication
- Definition: Multiplication is merely placing a number on top of itself a specific number of times in order to obtain a product. It is indicated by the '×' symbol.
- Key Property: Multiplication possesses the commutative, associative, and identity properties whereby order and structure do not exist. It possesses the zero property (anything multiplied by zero equals zero), the distributive property, and the closure property (product remains real).
- Example: 90 multiplied by 9 is a product of 810. This shows how the multiplication allows repeated addition.
4. Division
- Definition: Division splits a number into an equal amount by dividing one number by another to obtain a quotient and, if any, a remainder. It is symbolized by '÷' or '/'.
- Key Property: Division is non-associative and non-commutative because grouping and order matter. It is an identity property (division by 1 does not change the number), a zero property (division of zero by any number is zero), and non-closed (division by zero is undefined).
- Example: When you divide 66 by 11, the result is 6. This demonstrates how division comes in handy when sharing amounts evenly.
Real-Life Applications of Arithmetic
Understanding the importance of arithmetic helps us handle numbers and perform calculations in everyday life with ease. Here are some real-world applications of arithmetic:
1. Managing Personal Finances
Tracking Spending: Keeping an eye on how much money you spend each week requires adding up different costs, like groceries, bills, and transport fares.
Planning Savings: Figuring out how much to save monthly to reach a financial goal involves subtraction and division.
Comparing Prices: When deciding between products or brands, arithmetic helps compare unit prices (e.g., price per kg or per item).
2. Health and Fitness
Calorie Counting: People use arithmetic to track their daily calorie intake and how much they've burned during workouts.
Dosage Calculations: Arithmetic ensures accurate medication dosage based on weight or age (e.g., mg per kg).
Heart Rate Monitoring: Calculating your average heart rate during exercise or recovery uses basic addition and division.
3. Workplace Applications
Retail and Sales: Cashiers and salespeople often calculate discounts, total bills, or change using arithmetic on the spot.
Inventory Management: Keeping track of stock levels, restocking, and sales performance involves adding, subtracting, and forecasting quantities.
Time Management: Employees often split tasks over available work hours and calculate productivity using arithmetic.
4. Transportation and Commuting
Estimating Travel Time: Dividing distance by speed helps calculate how long a journey will take.
Fuel Planning: Drivers often calculate how much fuel is needed for a trip based on mileage (e.g., kilometers per liter).
Route Optimization: Comparing distances and travel times between different routes helps choose the fastest or most efficient option.
Common Mistakes and How to Avoid Them in Arithmetic
Understanding the basic concepts of arithmetic helps students perform calculations and solve everyday math problems with confidence. However, students often make mistakes when working with operations like addition, subtraction, multiplication, and division. Below are some common arithmetic errors and practical tips to help avoid them.
Mistake 1
Incorrect Use of Multiplication Facts
Practice using multiplication tables regularly. Use strategies such as repeated addition (4+4+4+4+4+4+4+4) or breaking the numbers into parts (6×8 = (6×5) + (6×3) to strengthen understanding.
Mistake 2
Misreading the Word Problems
Teach the students to slow down and highlight the keywords such as each, altogether, total, left, fewer, etc. Also, practice translating words into operations. For example, 3 bags with 4 apples each → 3×4 = 12 apples.
Mistake 3
Overlooking the Zero’s Role in Division and Multiplication
Strengthen the rule that any number multiplied by 0 equals zero, and division by 0 is undefined. For example,
0 × 25 = 0
100 ÷ 0 = undefined
Mistake 4
Misinterpreting Negative Numbers
Confusing the rules for adding and subtracting negative numbers. For example, getting −3 − (−5) wrong as −8 rather than reducing it to −3 + 5 = 2.
To prevent this error, the students will be employing a number line to visualize positive and negative motion.
Keep in mind, adding a negative number takes you left on the number line, while subtracting a negative number takes you to the right.
Mistake 5
Skipping Steps Causes Mistakes
Skipping intermediate steps in multistep problems leads to errors in the final result. For instance, solving 123 + 45 directly without breaking it into smaller steps may result in mistakes.
To avoid this mistake, break down problems into smaller parts (e.g., add hundreds, tens, and ones separately).
Show all your work clearly so you can review it if needed, especially when performing mental math or solving word problems.
Solved Examples of Arithmetic Operations
Problem 1
Find the sum of 453 and 289.
742
Explanation
Let us consider A = 453 and B = 289.
In the next step, we need to add A = 453 and B = 289. This means we have to calculate A + B, that is, 453 + 289 = 742.
So, by following the steps below, we can further break the calculations:
In the units place: 3 + 9 = 12.
We write down 2 and carry 1 to the tens place.
In the tens place: 5 + 8 = 13, plus the carried 1 equals 14.
We write down 4 and carry 1 to the hundreds place.
Lastly, in the hundreds place: 4 + 2 = 6, plus the carried 1 equals 7. We write down 7.
So, the final answer will be 453 + 289 = 742.
Problem 2
Determine the difference between 657 from 943.
286
Explanation
We have A = 943 and B = 657. So, now we need to calculate A − B, that is 943 − 657 which will be 286. How?
We will look at this by calculating each digit starting from the unit's place.
For the units place: We can't subtract 7 from 3, as 3 is smaller than 7, so we borrow from the tens place. The 4 in the tens place becomes 3, and the 3 in the units place turns into 13. This gives us 13 − 7 = 6.
For the tens place: After borrowing, we still can't subtract 5 from 3, so we borrow from the hundreds place.
The 9 in the hundreds place turns into 8, and the 3 in the tens place becomes 13. This results in 13 − 5 = 8.
For the hundreds place: After borrowing, we get 8 − 6 = 2.
Therefore, 943 − 657 = 286.
Problem 3
Calculate the product of 34 and 56.
1904
Explanation
A equals 34 and B equals 56. We need to find A × B. 34 × 56 = 1904.
To start, split 56 into 50 + 6, and use the distributive property:
A × (50 + 6) = (A × 50) + (A × 6).
This gives us: 34 × 50 = 1700 and 34 × 6 = 204.
To finish, add the following to get the results, 1700 + 204 = 1904
Therefore, 34 × 56 = 1904.
Problem 4
Divide 784 by 8.
98
Explanation
A equals 784 and B equals 8. We need to find A ÷ B. 784 ÷ 8 = 98 Begin by dividing the leftmost digits.
78 ÷ 8 = 9 (because 9 × 8 = 72).
Take away the product from the dividend: 78 − 72 = 6.
Move the next digit (4) down, creating the new number 64.
Divide 64 ÷ 8 = 8 (because 8 × 8 = 64).
Take away the product from the remaining dividend: 64 − 64 = 0.
Therefore, 784 ÷ 8 = 98.
Problem 5
Solve the expression (6 × 4) ÷ 12 + (72 ÷ 8) −9.
2
Explanation
Follow the order of operations:
First, multiply 6 by 4 (6 × 4) to get 24, then divide by 12 to get 2.
Next, divide 72 by 8 to get 9.
Finally, combine these results by adding and subtracting: 2 + 9 − 9 = 2.
FAQs on Arithmetic
1.What are the basic arithmetic operations?
2. Why are Arithmetic operations important?
3.What is the correct order of operations?
4. Are addition and subtraction inverse operations?
5.How do you multiply two-digit numbers quickly?
6.How can children in Canada use numbers in everyday life to understand Arithmetic?
7.What are some fun ways kids in Canada can practice Arithmetic with numbers?
8.What role do numbers and Arithmetic play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Arithmetic skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
