Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Ratio and Proportion → Ratios ↓


Simplifying Ratios


Ratios are a simple way to compare two or more numbers. Understanding and simplifying ratios is important in math, especially when dealing with ratios. This guide will help you learn how to simplify ratios in a clear and easy way.

What is the ratio?

A ratio is a comparison between two or more numbers that shows how many times one value contains or is contained in another value. Ratios can be expressed in different forms such as:

1:2
3:5
10:15

Each of these examples shows a different relationship between the numbers. Ratios can also be expressed as fractions. For example, 1:2 is the same as 1/2. When simplifying ratios, we usually try to express them in their simplest form.

Why simplify ratios?

By simplifying a ratio, you make it easier to understand and compare. Simplification helps solve problems more efficiently. For example, a ratio of 20:40 can be simplified to 1:2, making it easier to work with and understand.

Steps to simplify ratios

Let's learn how to simplify ratios with step-by-step examples:

1. Identify the numbers in the ratio

First, identify the numbers you are comparing. Let's take an example where we have a ratio of 8:12.

2. Find the Greatest Common Divisor (GCD)

To simplify a ratio, you need to find the greatest common divisor of the numbers. The GCD is the largest number that can divide both numbers evenly.

Example: The divisors for 8 and 12 are:

  • Divisors of 8: 1, 2, 4, 8
  • Divisors of 12: 1, 2, 3, 4, 6, 12

The largest number that divides both is 4. Therefore, 4 is the GCD of 8 and 12.

3. Divide both numbers by GCD

Now, divide each number in the ratio by the GCD. Here's how you do it for the numbers 8 and 12:

8 ÷ 4 = 2
12 ÷ 4 = 3

Hence the simplified ratio is 2:3.

More examples of simplifying ratios

Example 1: 30:50 Simplification

Step 1: Find the GCD of 30 and 50.

Divisors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Divisors of 50: 1, 2, 5, 10, 25, 50

GCD is 10.

Step 2: Divide both numbers by 10.

30 ÷ 10 = 3
50 ÷ 10 = 5

The simplified ratio is 3:5.

Example 2: 45:60 Simplification

Step 1: Find the GCD of 45 and 60.

Divisors of 45: 1, 3, 5, 9, 15, 45

Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

GCD is 15.

Step 2: Divide both numbers by 15.

45 ÷ 15 = 3
60 ÷ 15 = 4

The simplified ratio is 3:4.

Special cases

Let us discuss some special cases and how to deal with them:

Example 3: When one of the numbers is 1

Suppose we have the ratio 13:1. In this case, 13 cannot be any simpler since it is already a prime number, so we leave the ratio as it is: 13:1.

Example 4: When both the numbers are equal

Consider the ratio 7:7. The GCD of the two numbers is 7.

7 ÷ 7 = 1
7 ÷ 7 = 1

The simplified form is 1:1.

Visualization of ratios

Visual representations can make understanding ratios much easier. Consider the following way to represent ratios:

1 part 2 parts

In the above example, the two parts of red correspond to the larger number in a simplified ratio of 1:2.

Tips for simplifying ratios

  • Always express ratios in whole numbers.
  • If the numbers are not too large, look for common factors.
  • If you can't easily find any common factors, make a list of divisors or use prime factorization.

Practice problems

Try simplifying these ratios yourself:

  1. Simplification 14:28
  2. Simplification 50:100
  3. Simplification 9:27
  4. Simplification 36:60
  5. Simplification 20:25

Closing thoughts

Simplifying ratios is a basic skill in math that provides a clearer perspective when comparing quantities. By practicing these steps and examples, you can master the art of simplifying ratios. Always remember to find the greatest common denominator and simplify to the most easily understood form.


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Understanding Ratios
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Equivalent Ratios

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Simplifying Ratios

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