The Ultimate Zero-to-Hero Guide to Pre-Algebra

The Ultimate Guide to pre-algebra 01


Welcome to “The Ultimate Zero-to-Hero Guide to Pre-Algebra,” your comprehensive roadmap for mastering the essential building blocks of mathematics. Whether you’re a student, educator, or lifelong learner, this guide is meticulously designed to transform your understanding of pre-algebra from the ground up. With our step-by-step walkthrough, you’ll explore everything from the very basics of numbers and operations to the complexities of geometry and data analysis. Our aim is not just to teach you pre-algebra but to kindle a love for mathematics that will illuminate your journey through algebra, calculus, and beyond. Prepare to demystify the world of variables, unravel the secrets of ratios, and decode the language of mathematics that shapes the world around us.

For each chapter, the guide includes a set of exercises tailored to reinforce the concepts learned. These exercises range from basic calculations to more complex problem-solving scenarios, ensuring a comprehensive understanding of each topic. With detailed solutions provided, learners can track their progress and gain the confidence needed to excel in pre-algebra and beyond.

Here is the table of contents, having list of topics discussed in this article, please feel free to navigate to this article:

Table of Contents

Chapter 1: Understanding the Basics of pre-algebra

Numbers and Operations in algebra

  • Natural Numbers: These are the numbers we naturally count with. They start from 1 and go on indefinitely (1, 2, 3, …). Example: The number of apples in a basket (assuming there’s at least one) is a natural number.

  • Whole Numbers: Whole numbers include all natural numbers and the number 0. Example: The number of cars in a parking lot, which could be zero or any natural number.

  • Integers: Integers are whole numbers that can be positive, negative, or zero. This includes numbers like -3, -2, -1, 0, 1, 2, 3, … Example: The temperature above or below zero on a thermometer is an integer.

  • Rational Numbers: Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They can be written as fractions. Example: The number 1/2 is rational because it represents one divided by two.

  • Irrational Numbers: Irrational numbers cannot be expressed as a simple fraction; their decimal expansions are non-repeating and non-terminating. Example: The square root of 2 (√2) is an irrational number because it cannot be precisely written as a fraction.

  • Real Numbers: Real numbers include all the rational and irrational numbers. The number line represents real numbers. Example: Pi (π), which is approximately 3.14159, is a real number.

  • Arithmetic Operations: These are the basic operations we perform with numbers:

    • Addition (+): Combining two amounts. Example: If you have 3 apples and get 2 more, you now have 3 + 2 = 5 apples.
    • Subtraction (-): Finding the difference between amounts. Example: If you have 5 apples and eat 2, you have 5 – 2 = 3 apples left.
    • Multiplication (×): Repeated addition of the same number. Example: If you have 4 bags with 3 apples each, you have 4 × 3 = 12 apples.
    • Division (÷): Splitting into equal parts or groups. Example: If 12 apples are divided among 4 friends, each friend gets 12 ÷ 4 = 3 apples.
  • Order of Operations (PEMDAS/BODMAS): This rule helps us remember the sequence to solve operations in a complex expression:

    • Parentheses/Brackets
    • Exponents/Orders
    • Multiplication and Division (from left to right)
    • Addition and Subtraction (from left to right) Example: For 3 + 4 × 2, multiply first (4 × 2 = 8), then add (3 + 8 = 11).

Key Terms in Algebra

  • Variable: A variable is a symbol (usually a letter) that stands for a number that can vary or change. Example: In the expression x + 2, x is a variable.

  • Constant: A constant is a fixed value that does not change. Example: In the expression x + 2, the number 2 is a constant.

  • Coefficient: A coefficient is a number used to multiply a variable. Example: In 3x, 3 is the coefficient of the variable x.

  • Expression: An expression is a combination of variables, numbers, and operations. Example: 2x + 3y – 5 is an expression.

  • Equation: An equation is a statement that two expressions are equal, indicated by the equal sign (=). Example: 2x + 3 = 11 is an equation.

  • Inequality: An inequality is like an equation, but instead of equality, it shows a relationship of less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥). Example: x + 3 > 5 is an inequality.

Understanding these basics is your first step in the journey into pre-algebra, providing the foundational language and concepts that will support your mathematical growth.

Chapter 2: The World of Fractions and Decimals

Steps to master algebra

Simplifying Fractions

To simplify a fraction, you divide the top and bottom by the highest number that divides into both exactly.

Example: Simplify 8/12. Both 8 and 12 can be divided by 4, so (8÷4)/(12÷4) = 2/3.

Common Denominator in algebra

A common denominator is a shared multiple of the denominators of two or more fractions. It’s used to add or subtract fractions.

Example: To add 1/4 and 3/5, find a common denominator, which is 20, so 1/4 = 5/20 and 3/5 = 12/20.

Adding and Subtracting Fractions in algebra

Fractions must have a common denominator to be added or subtracted. Then you add or subtract the numerators and keep the denominator the same.

Example: 5/20 + 12/20 = 17/20.

Multiplying and Dividing Fractions in algebra

To multiply fractions, multiply the numerators and denominators separately. To divide, flip the second fraction and multiply.

Example: 2/3 × 3/4 = 6/12 simplifies to 1/2. For division, 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

Mixed Numbers and Improper Fractions in algebra

A mixed number combines a whole number and a fraction, while an improper fraction has a numerator larger than its denominator.

Example: 3½ is a mixed number. To convert it to an improper fraction: 3 × 2 + 1 = 7, so 3½ becomes 7/2.


Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example: 3/4 becomes 0.75 because 3 ÷ 4 = 0.75.

Adding, Subtracting, Multiplying, and Dividing Decimals

When adding or subtracting decimals, align the decimal points. For multiplication, multiply as with whole numbers, and count the total number of decimal places in both factors for the result. Division is done like whole numbers, but you may need to move the decimal point.

Example: 0.5 + 0.25 = 0.75, and 0.5 × 0.2 = 0.10. For division, 0.75 ÷ 0.5 = 1.5.

Rounding Decimals

Rounding decimals involves shortening a decimal to a certain number of decimal places, based on the next digit.

Example: Round 3.14159 to two decimal places: Since the third decimal is 1, round down to 3.14.

Decimal Places and Significant Figures

Decimal places count the numbers after the decimal point. Significant figures include all the meaningful digits in a number, not just after the decimal.

Example: In 123.45, there are two decimal places and five significant figures.

Chapter 3: The Power of Ratios and Proportions in algebra



Writing and Simplifying Ratios

Ratios compare two quantities by division. When writing ratios, it’s important to keep the order consistent and simplify them as much as possible.

Example: The ratio of 8 oranges to 4 apples can be written as 8:4 and simplified to 2:1.

Equivalent Ratios

Equivalent ratios have the same value when simplified, even though they may look different.

Example: The ratios 2:1 and 4:2 are equivalent because when both are simplified, they result in the same ratio of 2:1.


Setting up Proportions

A proportion is an equation that states two ratios are equal. To set up a proportion, you need to have four related quantities.

Example: If 2 oranges cost $1, how much do 6 oranges cost? The proportion would be 2/1 = 6/x, where x is the cost of 6 oranges.

Solving Proportions

To solve proportions, find the value of the variable that makes the two ratios equal.

Example: To solve 2/1 = 6/x, cross-multiply to get 2x = 6, then divide both sides by 2 to find x = 3. So, 6 oranges cost $3.

Direct Variation

Direct variation occurs when two quantities increase or decrease together at the same rate.

Example: If y varies directly with x and y = 2 when x = 1, then the equation of direct variation is y = 2x.

Inverse Variation

Inverse variation happens when one quantity increases while the other decreases. Their product is a constant.

Example: If y varies inversely with x and y = 1 when x = 2, then the equation of inverse variation is xy = 2.

Chapter 4: Mastering the Art of Percentages in Algebra


Understanding Percentages

Converting Fractions and Decimals to Percentages

Percentages are a way of expressing numbers as a fraction of 100. To convert a fraction or a decimal to a percentage, multiply by 100 and add the percent symbol (%) at the end.

Example: Convert 0.75 to a percentage: 0.75 × 100 = 75%.

Example: Convert 3/4 to a percentage: First convert 3/4 to a decimal which is 0.75, then multiply by 100 to get 75%.

Converting Percentages to Fractions and Decimals

To convert a percentage to a decimal, divide by 100. To convert a percentage to a fraction, write the percentage over 100 and simplify if possible.

Example: Convert 50% to a decimal: 50 ÷ 100 = 0.5.

Example: Convert 50% to a fraction: 50% = 50/100 = 1/2.

Finding Percentages of Numbers

To find a percentage of a number, convert the percentage to a decimal and multiply by the number.

Example: Find 20% of 50: Convert 20% to a decimal (0.20) and multiply by 50 (0.20 × 50 = 10).

Percentage Increase and Decrease

Percentage increase or decrease measures how much a number has gone up or down in percentage terms.

Example: If a shirt was $50 and now is $65, the percentage increase is calculated as: [(65 – 50) ÷ 50] × 100 = 30% increase.

Example: If a stock price drops from $30 to $25, the percentage decrease is: [(30 – 25) ÷ 30] × 100 = approximately 16.67% decrease.

Chapter 5: Unveiling the Mystery of Variables and Expressions in Algebra

Working with Variables

Understanding Variables

Variables are symbols that represent unknown values. They are used to hold a value that can change or vary. In algebra, variables are often represented by letters such as x, y, or z.

Example: In the expression x + 5, x is a variable.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables, and operators (like add, subtract, multiply, and divide).

Example: 3x + 2y – 7 is an algebraic expression.

Simplifying Expressions

Simplifying expressions involves combining like terms and reducing expressions to their simplest form.

Example: Simplify 2x + 3x to get 5x.

Solving Equations

One-step Equations

One-step equations are algebraic equations that can be solved in one step by either addition, subtraction, multiplication, or division.

Example: Solve x + 7 = 10 by subtracting 7 from both sides to get x = 3.

Two-step Equations

Two-step equations require two steps to solve. This often involves a combination of operations.

Example: Solve 2x + 3 = 7 by first subtracting 3 from both sides to get 2x = 4, then dividing both sides by 2 to get x = 2.

Multi-step Equations

Multi-step equations may involve several operations and require multiple steps to solve, including the use of the distributive property and combining like terms.

Example: Solve 3(x + 2) – 4 = 11 by first applying the distributive property, then combining like terms, and finally isolating the variable x.

Solving Inequalities

Graphing Inequalities

Graphing inequalities involves shading a region of the number line or coordinate plane that represents all solutions to the inequality.

Example: To graph x > 3 on a number line, put an open circle at 3 and shade to the right.

Compound Inequalities

Compound inequalities involve two separate inequalities that are joined by either “and” or “or”.

Example: The compound inequality 2 < x and x < 5 means x is greater than 2 and less than 5.

Chapter 6: Measurement and Geometry Foundations

Units of Measurement

Length, Mass, Volume, and Time

Units of measurement are used to quantify physical quantities. Length is measured in meters, centimeters, feet, etc., mass in kilograms or pounds, volume in liters or gallons, and time in seconds, minutes, hours, etc.

Metric and Imperial Units

The metric system uses units like meters, liters, and grams, while the imperial system uses units like feet, gallons, and pounds.

Unit Conversion

Unit conversion involves changing a quantity expressed in one set of units to another set of units using a conversion factor.

Example: Convert 5 kilometers to miles by multiplying 5 by the conversion factor 0.621371 (5 km * 0.621371 = 3.106855 miles).

Introduction to Geometry

Points, Lines, and Angles

Points are locations in space, lines are one-dimensional figures that extend infinitely, and angles are formed by two rays meeting at a point.


Triangles are three-sided polygons characterized by three edges and three vertices. The sum of the interior angles in a triangle is always 180 degrees.


Quadrilaterals are four-sided polygons with various types including squares, rectangles, and parallelograms.


A circle is a round shape where every point on the boundary is the same distance from the center. The distance around a circle is its circumference.

Perimeter and Area

The perimeter of a shape is the distance around it, while the area is the measure of space inside it.

Example: The perimeter of a rectangle is 2*(length + width), and the area is length * width.

Surface Area and Volume

Surface area is the total area that the surface of an object occupies, and volume measures the space an object occupies.

Example: The surface area of a cube is 6 * (edge length)^2, and its volume is (edge length)^3.


Chapter 7: Data Analysis Basics in Algebra

Understanding Data

Collecting Data

Data collection is the process of gathering information from various sources to be used for analysis.

Organizing Data

Data organization involves structuring collected information into a format that is easy to understand and analyze, such as tables, charts, or graphs.

Descriptive Statistics

Mean, Median, Mode

The mean is the average of a set of numbers, the median is the middle value when the numbers are in order, and the mode is the most frequently occurring value.


The range of a data set is the difference between the highest and lowest values in the set.

Interquartile Range

The interquartile range (IQR) is a measure of variability that describes the middle 50% of values when ordered from lowest to highest.


Simple Probability

Simple probability measures the likelihood of a single event occurring, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Compound Events

Compound events involve the probability of two or more events happening at the same time, and can be independent or dependent on each other.


Chapter 8: Pre-Algebra Problem Solving

Strategies for Problem Solving

Understanding the Problem

Understanding the problem involves identifying what is being asked, determining the relevant information, and recognizing the unknowns.

Devising a Plan

Devising a plan includes coming up with a method or strategy to solve the problem, such as drawing a diagram, creating a table, or breaking down the problem into smaller parts.

Carrying Out the Plan

Executing the plan involves applying the chosen strategy and carrying out the necessary steps to arrive at a solution.

Reviewing/Extending the Solution

Reviewing the solution entails checking the results for accuracy and determining if the solution can be applied to other problems or extended in some way.

Strategies for Problem Solving: A Concrete Example

Example Problem

Shamsa is planning a birthday party. She has a budget of $150 and wants to buy party favors that cost $5 each. How many party favors can she buy?

Understanding the Problem

Shamsa needs to calculate the maximum number of party favors she can buy without exceeding her budget.

Devising a Plan

She will divide the total budget by the cost of one party favor to find out the maximum number she can purchase.

Carrying Out the Plan

Shamsa carries out the calculation: $150 divided by $5 per party favor equals 30 party favors.

Reviewing/Extending the Solution

She reviews her calculation to ensure she hasn’t exceeded the budget and considers if there are any discounts for buying in bulk that could allow her to purchase more favors or save money.

Example questions for pre-algebra

Here are few example questions that you need to answer in order to practice your concepts of pre-algeba:

Chapter 1: Understanding the Basics

  1. Identify the smallest natural number.
  2. Write the next five whole numbers after 17.
  3. List all integers between -3 and 3.
  4. Express the fraction 3/4 as a rational number.
  5. Is the square root of 2 a rational or an irrational number?
  6. Solve the arithmetic operation: 8 × (3 + 5) ÷ 2 – 6.
  7. If x = 5, evaluate the expression 2x + 3.
  8. Simplify the equation 2(x – 3) + 4 = 0 and find x.
  9. Graph the inequality y < 2x + 1 on a coordinate plane.
  10. What is the value of the expression 3^2 + 4^2?
  11. Calculate the absolute value of -15.
  12. What is the reciprocal of 1/2?
  13. Perform the operation: 7 − (−2) + 3.
  14. Find the product of −4 and 6.
  15. Determine if the number 0.333… is rational or irrational.

Chapter 2: The World of Fractions and Decimals

  1. Simplify the fraction 15/35.
  2. Find the common denominator for 1/4 and 5/6.
  3. Calculate 2/3 + 4/5.
  4. Multiply 7/8 by 1/2.
  5. Convert the mixed number 3 1/2 to an improper fraction.
  6. Express 0.75 as a fraction.
  7. Subtract 0.9 from 2.5.
  8. Multiply 0.8 by 0.05.
  9. Round 3.14159 to the nearest hundredth.
  10. Identify the decimal place and significant figure for 0.042.
  11. Convert the decimal 0.625 to a fraction.
  12. Add 0.2 to 1/3 after converting them to a common format.
  13. Divide 5 by 0.5 and express the answer as a decimal.
  14. Write 1/8 as a decimal without using a calculator.
  15. Round the number 7.456 to the nearest tenth.

Chapter 3: The Power of Ratios and Proportions

  1. Write the ratio of 8 to 12 in simplest form.
  2. Are the ratios 3/4 and 9/12 equivalent?
  3. Set up a proportion to find the unknown number x if x/3 = 12/4.
  4. If y varies directly with x and y = 10 when x = 2, find y when x = 5.
  5. If y varies inversely with x and y = 8 when x = 4, what is y when x = 2?
  6. Express the ratio of 30 minutes to 1.5 hours in simplest form.
  7. Determine if the following ratios form a proportion: 6/8 and 9/12.
  8. Convert the ratio 5:6 into a fraction.
  9. If a bag contains red and blue marbles in a ratio of 2:3, how many red marbles are there if there are 18 blue marbles?
  10. The ratio of the length to the width of a rectangle is 3:2. If the width is 10 inches, find the length.

Chapter 4: Mastering the Art of Percentages

  1. Convert the fraction 3/5 to a percentage.
  2. Change 40% to a decimal.
  3. What is 25% of 200?
  4. If a dress costs $70 after a 30% discount, what was the original price?
  5. A population of 50,000 increases by 5% per year. What is the population after one year?
  6. Calculate the percentage decrease if a product’s price drops from $200 to $150.
  7. Find 150% of 60.
  8. What percentage of a day is 6 hours?
  9. If you save $20 on a $50 item, what percent discount is that?
  10. A score of 80% is needed to pass a test. If the test has 50 questions, how many questions must you answer correctly?

Chapter 5: Unveiling the Mystery of Variables and Expressions

  1. If x = 7, what is the value of 2x + 3?
  2. Simplify the expression 4x – 2x + x.
  3. Solve the one-step equation x/4 = 3.
  4. Find x in the two-step equation 3x – 4 = 11.
  5. Solve the multi-step equation 2(x + 3) + 4x = 24.
  6. Graph the inequality 2x + 3 > 7 on a number line.
  7. Solve the compound inequality 4 < 2x + 1 < 10.
  8. What is the coefficient of y in the expression 3x + 4y – 5?
  9. Combine like terms: 5a + 2b – 3a + 4.
  10. Isolate x in the equation 2x – 5 = 3x + 7.

Chapter 6: Measurement and Geometry Foundations

  1. Convert 50 centimeters to inches.
  2. What is the perimeter of a rectangle with length 6 units and width 4 units?
  3. Calculate the area of a triangle with base 5 units and height 3 units.
  4. Find the volume of a cube with edges measuring 3 units.
  5. What is the circumference of a circle with a radius of 4 units?
  6. How many milliliters are in 3 liters?
  7. If a room is 12 feet by 15 feet, what is the area in square yards?
  8. Convert a temperature of 95 degrees Fahrenheit to Celsius.
  9. Calculate the area of a trapezoid with bases of 6 and 4 units and a height of 3 units.
  10. A car’s odometer reads 22,300.5 miles. If the car travels another 123.25 miles, what will the odometer read?

Chapter 7: Data Analysis Basics

  1. If the mean of five numbers is 10, what is their total sum?
  2. What is the median of the set 2, 7, 9, 12, 13?
  3. Identify the mode in the data set 3, 4, 4, 5, 6, 6, 6, 7.
  4. Calculate the range of the following numbers: 5, 8, 12, 15, 22.
  5. If the first quartile (Q1) is 5 and the third quartile (Q3) is 15, what is the interquartile range?
  6. Create a frequency table for the data set: 3, 3, 3, 4, 5, 5, 6, 6, 6, 7.
  7. What is the probability of rolling a number greater than 4 on a standard six-sided die?
  8. If a coin is flipped three times, what is the probability of getting exactly two heads?
  9. Draw a bar graph to represent the number of pets owned by a group of seven friends: 1, 0, 2, 3, 1, 2, 1.
  10. Determine the mean, median, and mode of the test scores: 85, 90, 90, 95, 100.

Chapter 8: Pre-Algebra Problem Solving

  1. A recipe calls for 3 cups of flour for every 4 cups of sugar. How much sugar is needed if 6 cups of flour are used?
  2. An art piece is sold for $120, which is a 20% profit over the cost. What was the cost price?
  3. A rectangular garden has a length of 20 meters and a width that is half of its length. What is the area of the garden?
  4. If 3 pencils cost 45 cents, how much would 10 pencils cost?
  5. You have a rope 30 meters long, and you need to cut it into pieces that are 2.5 meters each. How many pieces can you cut?
  6. Mike read twice as many books this year as last year. If he read 5 books last year, how many books did he read this year?
  7. If a car travels 150 kilometers in 2 hours, what is its average speed?
  8. Solve for x in the equation 5x − 6 = 2x + 9.
  9. A box contains red and blue marbles. If the ratio of red to blue marbles is 3:4 and there are 12 red marbles, how many blue marbles are there?
  10. If the price of a jacket after tax is $108 and the tax rate is 8%, what is the original price of the jacket before tax?
  11. Convert a speed of 60 miles per hour to feet per second.
  12. How many different outfits can you make with 4 shirts and 3 pairs of pants?
  13. Calculate the surface area of a cylinder with a radius of 3 units and a height of 5 units.
  14. A bookstore offers a 15% discount on a book that originally costs $35. What is the discount amount?
  15. If you have a square plot of land with an area of 49 square meters, what is the perimeter of the plot?



In “The Ultimate Zero-to-Hero Guide to Pre-Algebra,” you’ve journeyed through the core concepts that form the backbone of mathematical understanding. From the basic building blocks of numbers and operations to the more complex realms of geometry and data analysis, this guide has equipped you with the tools and confidence needed to excel. The strategies and exercises provided are designed to reinforce your learning and prepare you for the next steps in your mathematical education. Carry forward the knowledge and skills you’ve acquired here, and let them guide you as you continue to explore the vast and exciting universe of mathematics.

Websites must try
Powerful Websites

Advancements in website tools 💻 in the digital age provide invaluable resources. From e-commerce giants and social media

Read More »
Google Scholar Kaise Use Karein?

Google Scholar ek powerful search engine hai jo scientific literature ke liye use kiya jata hai. Is article mein hum aapko bataein ge ke Google Scholar ko kaise use karein aur kab kab aapko dusre tools ya databases ko use karna chahiye.

Read More »
Chapter 8: The Future of Sampling in Statistics – Emerging Trends and Innovations

The future of sampling in statistics is vibrant and full of potential, marked by technological innovation and methodological advancements. As we embrace these changes, sampling will continue to be a pivotal tool in unraveling the complexities of the world through data. The journey ahead is not just about statistical techniques; it’s about shaping a future where data is collected, analyzed, and used responsibly and innovatively.

Read More »


  1. This service was fantastic! Best purchase yet! I haven’t experienced any dropped followers at all, through the 2 months I’ve had them. Also, the followers are real people, they are not bots. Helped out a lot would definitely recommend for anyone share with your friends and family!!!

  2. This informative blog clearly explains all pre-algebra concepts using real-world examples, so that anyone can easily understand everything about pre-algebra and data science in Algebra.

  3. After reading this blog and completing all exercise questions I assume that if an unknown value out of three three is required to solve then we can use an expression like 2x = 3. Secondly, if an unknown value out of four values then we can use the Proportion and cross-multiplication method like 2/3 = 4/x

  4. me to reflect on the practical applications of pre-algebra in real-life situations, making the learning experience more meaningful. It also encouraged me to think critically about the connections between different mathematical concepts and their relevance to everyday problems.

  5. Amazing! This post contains theoretical as well as practical knowledge about pre-algebra for mathematical and data science students. For better understanding, I must do these practical exercises.

  6. This informative blog clearly explains all pre-algebra concepts using real-world examples, so that anyone can easily understand everything about pre-algebra.

  7. Chapter 1: Understanding the Basics
    Chapter 2: The World of Fractions and Decimals
    Chapter 3: The Power of Ratios and Proportions
    Chapter 4: Mastering the Art of Percentages
    The above 4 chapters were completed with 100% practice.

    1. The smallest natural number is 1.

      The next five whole numbers after 17 are: 18, 19, 20, 21, 22.

      The integers between -3 and 3 are: -3, -2, -1, 0, 1, 2, 3.

      The fraction 3/4 is already a rational number because it can be expressed as a ratio of two integers.

      The square root of 2 is an irrational number. It cannot be expressed as a fraction or a ratio of two integers.

      Solving the arithmetic operation: 8 × (3 + 5) ÷ 2 – 6:
      First, perform the addition within parentheses:
      8 × 8 ÷ 2 – 6
      Next, perform the multiplication:
      64 ÷ 2 – 6
      Then, perform the division:
      32 – 6
      Finally, perform the subtraction:

      Therefore, the result is 26.

      If x = 5, evaluating the expression 2x + 3:
      2(5) + 3 = 10 + 3 = 13

      Therefore, the value is 13.

      Simplifying the equation 2(x – 3) + 4 = 0 and finding x:
      Distributing the 2:
      2x – 6 + 4 = 0
      Combining like terms:
      2x – 2 = 0
      Adding 2 to both sides:
      2x = 2
      Dividing both sides by 2:
      x = 1

      Therefore, the value of x is 1.

      Graphing the inequality y < 2x + 1 on a coordinate plane:
      To graph this inequality, we first graph the line y = 2x + 1 (which is a straight line with a slope of 2 and a y-intercept of 1). Then, since the inequality is y < 2x + 1, we shade the region below the line.

      The value of the expression 3^2 + 4^2 is calculated by squaring each number and then adding the results:
      3^2 + 4^2 = 9 + 16 = 25

      Therefore, the value is 25.

      The absolute value of -15 is 15.

      The reciprocal of 1/2 is 2/1 or simply 2.

      Performing the operation: 7 − (−2) + 3:
      7 – (-2) + 3 = 7 + 2 + 3 = 12

      Therefore, the result is 12.

      The product of -4 and 6 is calculated by multiplying the two numbers:
      -4 * 6 = -24

      Therefore, the product is -24.

      The number 0.333… is a rational number. It can be expressed as a fraction, specifically 1/3.

  8. Chapter 1: Understanding the Basics
    Chapter 2: The World of Fractions and Decimals
    Chapter 3: The Power of Ratios and Proportions
    Chapter 4: Mastering the Art of Percentages
    I and my two sons (Sibtain and Tayyab) completed the above four chapters with 100% practice.
    and blog is very informative and easy to learn pre-algebra.
    ALLAHA KAREEM aap ko dono jahan ki bhalyean aata kry. AAMEEN

  9. 1) Identify the smallest natural number.
    Ans= 1 (Natural no. start with 1 and continues till infinite)

    2) Write the next five whole numbers after 17.
    Ans: 18,19,20,21,22 (Whole no. start with zero.. and continue till infinite)

    3) List all integers between -3 and 3.
    Ans: -3,-2,-1,0,+1,+2,+3 (Remember your graphs)

    4) Express the fraction 3/4 as a rational number.
    Ans: 3/4 (By definition: Rational numbers are defined as numbers that can be written as a fraction or ratio of two integers)

    5) Is the square root of 2 a rational or an irrational number?
    Ans: square root of 2 is an irrational no. because it cannot be written as p/q

    6)Solve the arithmetic operation:
    8 × (3 + 5) ÷ 2 – 6
    Ans: first bracket 8 * 8 / 2-6
    multiply= 64/2-6
    32-6 =26

    7) If x = 5, evaluate the expression 2x + 3.
    Ans: Remember x=5; 2x=2*5 + 3
    10 + 3 = 13

    8) Simplify the equation 2(x – 3) + 4 = 0 and find x.
    Ans: 2(x – 3) + 4 = 0
    2x-6 + 4 = 0 ;(2*x – 2*3 + 4)
    Add 2 both sides
    2x-2+2=0+2 (-2 and +2 deleted)

    9) Graph the inequality y < 2x + 1 on a coordinate plane.
    10) What is the value of the expression 3^2 + 4^2?
    Ans: 3^2=9 and 4^2=16
    9 + 16 =25

    11) Calculate the absolute value of -15.
    Ans the absolute value of -15 is 15 (calculate as how many distance away from 0, never given in negative)

    12) What is the reciprocal of 1/2?
    Ans: 1/2 = 2/1 = 2 ( Interchange Numerator by Denominator)

    13) Perform the operation: 7 − (−2) + 3.
    Ans: 9 + 3 = 6 ( bcoz minus and minus will became plus, and sign of greater number)

    14) Find the product of −4 and 6.
    Ans: -4 * 6 + -24

    15) Determine if the number 0.333… is rational or irrational.
    Ans: 0.333… is a non terminating rational number bcoz it can be written as 1/3

  10. Chapter 1: Understanding the Basics
    Chapter 2: The World of Fractions and Decimals
    Chapter 3: The Power of Ratios and Proportions
    Chapter 4: Mastering the Art of Percentages
    The above 4 chapters were completed with 100% practice.

  11. Example: Solve 3(x + 2) – 4 = 11 by first applying the distributive property, then combining like terms, and finally isolating the variable x.

    sir please is ko solve kr dain

    1. Apply the Distributive Property:




      Distribute the 3 to both terms inside the parentheses:








      Combine Like Terms:

      Combine the constant terms (6 and -4):



      Isolate the Variable


      Subtract 2 from both sides of the equation:



      Divide both sides by 3 to solve for



      So, the solution to the equation


      3(x+2)−4=11 is


    2. Apply the distributive property by multiplying 3 with both x and 2. This gives us: 3x + 6 – 4 = 11.
      Combine like terms. Here, 6 and -4 are like terms, so we can simplify the left side of the equation to 3x + 2 = 11.
      Isolate the variable x by subtracting 2 from both sides of the equation. This gives us: 3x = 9.
      Finally, divide both sides of the equation by 3 to get the value of x. This gives us: x = 3.

  12. It is a comprehensive article about the pre algebra .
    Thank you so much sir for helping us ones can not afford regular degree for Data Science .
    once again sir a big respect for you by heart.

  13. Your content is amazing and such simplified. I am masters student doing data analysis project but your content and teaching astonished such simplified example .May Allah bless you . Soon i ll enroll your data science course to polish my professional skils.

  14. Amazing !!
    I was looking for such a thing since long where I can find all these concepts explained at one place.
    It is an excellent refresher for pre algebra.

    Thanks for your time and effort.

Leave a Reply

Your email address will not be published. Required fields are marked *