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


In mathematics, ratio and proportion are essential concepts, especially when dealing with different quantities. Both concepts help us understand the relationship between numbers and are used in various aspects of daily life and the study of mathematics.

Understanding ratios

A ratio is a comparison of two or more numbers that indicates their size in relation to one another. Ratios are often used to describe things like length, weight, volume, or the relationship between any group of comparable quantities.

Simple example of proportion

Suppose you have a basket full of apples and bananas. If there are 4 apples and 6 bananas in it, then the ratio of apples and bananas is as follows:

Apples : Bananas = 4 : 6

This ratio can also be simplified. By dividing both sides by their greatest common divisor, which is 2, we get:

2 : 3

Example: There are 10 boys and 5 girls in a class. Find the ratio of boys and girls.

Solution:

The ratio of boys and girls is:

10 : 5

In a simplified form it is like this:

2 : 1

Visualization of ratios

Ratios can be represented using bars, circles, or other types of visual representations.

For example, consider the ratio of 3:2:

3 parts 2 parts

Understanding ratios

A ratio is an equation that states that two ratios are equal. Ratios are often used when scaling quantities up or down.

Simple example of proportion

Let's say we have a recipe that uses 4 cups of flour to make 8 pancakes. If we want to make 16 pancakes, how much flour do we need? This involves deciding the proportions.

4 cups flour / 8 pancakes = x cups flour / 16 pancakes

Solving the proportion, we get that x = 8 cups of flour.

Example: If 5 meters of cloth costs $20, how much will 12 meters of cloth cost?

Solution:

First, determine the proportions:

5 meters / $20 = 12 meters / x

Cross multiply to solve for x:

5 * x = 12 * 20
5x = 240
x = 48

Therefore, 12 meters of cloth will cost $48.

Visualization of ratios

Ratios can be visualized through diagrams showing equivalent quantities.

Consider the previous example of pancakes and flour. If we double both parts of the ratio, we can see that:

4 cups for 8 pancakes 8 cups for 16 pancakes

Important concepts in ratio and proportion

When working with ratios and proportions, here are some important concepts and steps:

  • Simplifying ratios: Always try to express ratios in their simplest form by dividing both terms by their greatest common divisor.
  • Cross multiplication: Use cross multiplication to solve proportions, as it can help find unknown values easily.

Examples of ratio problems

Example 1: The ratio of sugar to flour in a recipe is 2: 3. If you have 8 cups of sugar, how much flour do you need?

Solution: Determine the proportion and solve:

2/3 = 8/x

Cross multiplication:

2 * x = 3 * 8
2x = 24
x = 12

You will need 12 cups of flour.

Example 2: The ratio of pencils and pens in a box is 7: 3. If it contains 42 pencils, how many pens are there?

Solution: Determine the proportion and solve:

7/3 = 42/x

Cross multiplication:

7 * x = 3 * 42
7x = 126
x = 18

There are 18 pens in total.

Examples of proportion problems

Example 1: If a car travels 300 km in 5 hours, how much distance will it be able to cover in 7 hours at the same speed?

Solution: Determine the proportion and solve:

300 km / 5 hours = x km / 7 hours

Cross multiplication:

5 * x = 300 * 7
5x = 2100
x = 420

This car can travel 420 km in 7 hours.

Example 2: If 10 apples cost $15, how much will 25 apples cost?

Solution: Determine the proportion and solve:

10 apples / $15 = 25 apples / x

Cross multiplication:

10 * x = 15 * 25
10x = 375
x = 37.5

25 apples would cost $37.50.

Conclusion

Ratio and proportion are not just mathematical concepts; they are tools we use in almost every area of life. From cooking recipes to scale modeling, financial calculations to scientific analysis, understanding how to work with ratios and proportions helps us make informed decisions based on the relationships between numbers. By practicing problems and familiarizing yourself with these concepts, you will gain a deeper understanding and mastery over their practical applications.


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Ratio and Proportion

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