Algebra vs Geometry vs Arithmetic: ELI5 The Difference Between These

Math is the basic discipline of counting, measuring, and describing the shapes of objects. It also includes the concrete study of structure, order, and relation. Right from sciences to technical advancements, math calculations are utilized everywhere.  Numerous new fields have developed with the establishment of mathematics, from the primitive number system to the relevant research fields. 

Math is broadly divided into various branches with different usages and applications of each one. Algebra, Geometry, and Arithmetic are 3 branches of math with each focusing on different aspects of calculations. By understanding the difference between these 3, individuals can benefit from a detailed analysis of mathematics. 

Students can better organize their ideas and build a solid foundation after being clear with the fundamentals of math. As these branches of math have real-world applications, students and teachers should know the correct usage to understand them briefly. It is prominent to know what makes them different and how they are interrelated. 

Algebra vs geometry vs arithmetic: Basic difference

While all three branches of math are used in schooling and the real world, there is a difference in each branch. Let’s understand the meaning and application to know the difference between them.

1. Algebra

An algebraic expression is a basic combination of constants and variables related by the signs of the basic procedures of addition, subtraction, multiplication, and division. Variables like x, y, and z are used to solve a word problem. Being capable of comprehending algebra as a topic is more essential than just being able to solve equations. The concepts of algebra are utilized in various branches of math. Algebra helps in the discovery of the missing values in algebraic expressions and equations. 

2. Geometry

A subfield of mathematics called geometry examines objects’ dimensions, placements, angles, and sizes. Geometry involves using different shapes concerning height, area, distance, or other mathematical expressions. It is a math branch specializing in a particular set of objects. While geometry generally deals with shapes, it is commonly used in various science and technology-oriented fields. 

3. Arithmetic

The word “arithmetic” is derived from the Greek word “arithmos,” denoting the study of counting numbers and the attributes of the standard mathematical operations. Mathematical operations involving numbers are the foundation of arithmetic. It serves as the starting point for mastering multiple regions of mathematics. Being the oldest branch of math, Arithmetic includes the following aspects.

• Addition (+)
• Subtraction (-) 
• Multiplication (x) 
• Division ()

Arithmetic also includes the mathematical concepts of square roots, exponentiation, and percentage. Students can also learn the difficult subjects of logarithmic and trigonometric functions. 

Challenges students might face

Math is not a tough subject but students are likely to face difficulties as math deals with numbers, shapes, sizes, units of measurement, and extensive usage of formulas. Check the most common challenges faced by students in the 3 branches of math. 

Difficulties a student might face while studying Algebra

1. Lack of Understanding of Variables and Constants

One challenge students face in Algebra is the difference between variables and constants. The lack of understanding of the basic concept hampers their overall knowledge of the subject matter, suggests research. Students who cannot differentiate between the two face difficulty solving algebraic word problems as sometimes, variables are designated as constants. For example, x, y, and z might be designated as variables but a, b, and c as constants; this creates confusion and misunderstanding in the concept. 

2. Simplification of Fractions

Algebra involves solving and simplifying fractions to get the answer. However, most students do not follow the correct steps due to a lack of understanding of the order of steps to reach the desired answer. Hence, students face difficulty simplifying algebraic fractions even after the correct formula but incorrect steps.

3. Poor Grasp on Arithmetic

Solving Algebra questions and equations requires substantial knowledge of basic math. Students who are poor at arithmetic and number theory suffer while solving complex word problems. This can lead to unreasonable errors while solving equations. 

Difficulties a student might face while studying Geometry

1. Lack of Understanding with Formulas

Geometry involves various formulas and the correct steps to derive the answer. Most students do not understand the reason behind a certain formula and try to memorize it. Students who cannot comprehend why a formula is made are likely to make mistakes while solving questions. As formulas have a mathematical approach, it is important to understand their applicability.

2. Poor Visual Ability

As students deal with different shapes and sizes, they need to have good visual abilities. When students read problems on a circle or a triangle, they find it challenging to imagine the exact shape in their minds. If students do not know how an object looks or analyzes the correct structure, they are likely to make mistakes.

3. Poor Vocabulary

Wondering how vocabulary happens to be one of the challenges faced in geometry? Students have to solve multiple problems to understand the core concepts of geometry. However, most students struggle with the correct vocabulary for an object or a tool. For example, they might have seen a tool but would be unaware of the term bisector. Hence, unawareness of the right vocabulary leads to misconceptions about the correct application of a tool or an object. 

Difficulties a student might face while studying Arithmetic

1. Struggle with Addition and Subtraction

While most students gradually learn the fundamentals of Arithmetic, it can be challenging for some children to understand them. Students with Dyscalculia might also face a problem with basic addition or Subtraction due to their math learning disability. With such students, the challenge can be extremely bothersome as they find it difficult to calculate numbers, count through fingers, or be quick at math.

2. Lack of Understanding of Time and Directions

Arithmetic also involves a basic understanding of time and directions. Students face the challenge of exactly determining the time by observing the clock. It can be confusing to differentiate between the small and big hands of the clock. Similarly, students might not be able to tell which is right and which one is left in the matter of direction. These difficulties arise due to a lack of factual knowledge and grasp of arithmetic concepts.

3. Struggle with Application of Arithmetic 

Arithmetic can be challenging and bothersome to students who lack application skills. Some students are not able to identify which operation will be used in which particular situation and end up counting everything. For example, some students simply forget the applicability of arithmetic operations while grocery shopping. They might start counting the total bill or time taken to reach the store through fingers, leading to mistakes.

Where do we use algebra, geometry & arithmetic: Basic application

Math is used in everyday living right from calculating the timings for daily activities to analyzing the shopping budget, distance to travel, and making financial investments. Hence, here is the opportunity to learn about the basic applications of Algebra, Arithmetic, and Geometry.

1. Algebra

• Algebra is used in sports activities as players mentally calculate the distance, speed, and force required to hit the goal.
• Cooking often involves algebraic calculations to understand the weight of ingredients, the baking temperature, and the time required to complete the meal preparation.
• Scheduling the day also requires good knowledge of Algebra as you are likely to calculate the time to wake up, have breakfast, reach school/office, and the hours required for each.

2. Geometry

• Astronomers use geometry to follow stars and calculate satellite and planet distances.
• Mathematics and art are related in several ways since both involve understanding figures, patterns, and shapes. 
• Geometry is highly used in constructing buildings, monuments, and parks as they comprise distance, multiple angles, shapes, and lines to make them perfect.

3. Arithmetic 

• Arithmetic is used in everyday life for basic calculations in grocery shopping, bills, and saving money, where addition, subtraction, and percentages are used.
• Basic sequence arrangement in theaters, stadiums, or auditoriums is also made through Arithmetic.
• Individuals also use Arithmetic concepts to calculate the amount of work completed in a week, the distance required to reach a destination, and count the minutes required to complete particular footsteps while jogging.

Are these interrelated?

While they complete different branches of math, Algebra, Geometry, and Arithmetic are dependent on each other for various mathematical calculations.

• Algebraic equations are used in graphs to find answers to difficult word problems.
• Ample algebraic skills and lessons are related to finding the area of missing dimensions of geometrical shapes.
• Pythagoras theorem is a classic example where angle triangles represent geometry while equations represent Algebra.
• Arithmetic geometrics is yet another field of math that focuses on number fields, polynomial equations, and height functions with the inclusion of algebraic varieties.
• The basic modes of operations of Arithmetic are nearly used in most branches of math for calculating distance, time, and numbers used for algebraic expressions as well as geometry.

Table of comparison: Algebra, Geometry, and Arithmetic 

Summing up..

The differences between Algebra, Geometry, and Arithmetic can be tricky to teach and learn. However, a basic understanding of differences leads to a better grasp of several mathematical concepts. As mentioned, these branches are interrelated and knowledge of each is prominent to solve real word problems. After a thorough understanding, parents, teachers, and adults can use different math worksheets, online games, applications, and manipulatives to polish the concepts. It is always an added advantage when individuals actively practice the concept through practical learning.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,