Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Algebra → Solving Simple Equations ↓


Balancing Equations


Balancing equations is an essential skill in algebra that you will continue to use throughout your math journey. Let's explore what it means to balance an equation and how you can practice this skill using visual and text examples.

What are equations?

The equation is like a balance scale. Imagine you have a scale that has different weights on each side. For the scale to remain balanced, the total weight on each side must be the same. Similarly, in a mathematical equation, the two sides must be equal. Here's what a simple equation looks like:

x + 3 = 7

In this equation, you want to find the value of x that makes the left side equal to the right side.

The concept of balance

Just like with real-life scales, the key to solving the equation is to keep it balanced. Whatever you do to one side, you must do the same to the other. This principle helps you isolate the variable, which in this case is x, to find its value.

Let us understand this with a visual example:

X 3 7

Imagine a rectangle with x written on it and three orange blocks on the left side of the scale. On the right side, there are seven green blocks. The goal is to find the weight (or value) of x that balances the scale.

How to solve simple equations

Here's a step-by-step guide to solving simple equations:

1. Simplify both sides

Start by simplifying both sides of the equation as much as possible. If there are any like terms you can add or subtract, do so.

2. Isolate the variable

The main goal is to bring the variable (such as x) to one side of the equation. We use the principle of balancing equations. For the equation x + 3 = 7, you would subtract 3 from both sides, getting:

x + 3 - 3 = 7 - 3

This makes it simpler:

x = 4

3. Check your work

Always substitute your answer back into the original equation to see if it makes both sides equal. In our example, replacing x by 4 gives:

4 + 3 = 7

Since both sides are equal, x = 4 is the correct solution.

More examples

Example 1

Solve y - 5 = 10.

Phase:

  1. Add 5 to both sides to isolate y.
y - 5 + 5 = 10 + 5

This makes it simpler:

y = 15

Check by substituting 15 for y in the original equation:

15 - 5 = 10

Example 2

Solve 3z = 12.

Phase:

  1. Divide both sides by 3 to isolate z.
3z / 3 = 12 / 3

This makes it simpler:

z = 4

Check by substituting 4 for z in the original equation:

3 * 4 = 12

Example 3

Solve a / 4 = 3.

Phase:

  1. Multiply both sides by 4 to isolate a.
a / 4 * 4 = 3 * 4

This makes it simpler:

a = 12

Check by substituting 12 instead of a in the original equation:

12 / 4 = 3

Visual example for understanding

Here's another visual to help you understand balance:

X , 3 , X

As you can see, when x is the same on both sides and balanced, your statement is true.

Build your skills

The more you practice, the more comfortable you will become solving equations. Try writing some practice problems and solving them using the steps given. Remember, whatever operation you do on one side of the equation, you must do the same on the other side to keep it balanced.

Practice problems

  1. Solve b + 6 = 9
  2. Solve 2q = 14
  3. Solve r / 5 = 2
  4. Solve t - 8 = 4

Try solving these on your own, and check your answers by substituting values into the original equations. Keep practicing, and you'll master the art of balancing equations in no time!


Grade 6 → 2.2.1


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Balancing Equations

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