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 ↓


Proportion


Ratio is an important concept in mathematics that tells us how two ratios compare to each other. When two ratios are equal, they are said to be in proportion. This concept is fundamental in fields like geometry, physics, economics, and even our daily lives. Let us understand the concept of ratio in depth using simple language and examples for grade 7 students.

What is the ratio?

A proportion is an equation that states that two ratios are equal. It can be expressed as:

a/b = c/d

where a, b, c and d are numbers. Here, a and c are called the extremes, and b and d are called the mean.

Understanding ratios

Before delving deeper into ratios, it is important to have a good understanding of proportions. A ratio is a way of comparing two quantities using division. For example, if a basket contains 2 apples and 3 oranges, the ratio of apples to oranges can be written as:

2 : 3

This means that there are 2 apples for every 3 oranges. The ratio can also be written in fraction form:

2/3

Characteristics of the ratio

When two ratios are in proportion, their cross-products are equal. This means:

a/b = c/d

This implies that:

a*d = b*c

This is known as the cross-multiplication rule, and it is a useful tool for determining whether two ratios form a proportion. Let's look at this with an example.

Example: Checking proportions

Consider two ratios:

4/5 and 8/10

Are these ratios proportionate?

To check, we calculate the cross-products:

4 * 10 = 40
5 * 8 = 40

Since the two cross-products are equal, 40 = 40, the ratios are in proportion:

4/5 = 8/10

Using ratios in word problems

Ratios can help solve many kinds of word problems. Let's see how we can apply ratios in real life:

Example: Recipe adjustments

If a recipe calls for 2 cups of flour to make 10 cookies, how much flour is needed to make 25 cookies?

First, determine the proportions:

2/10 = x/25

Cross-multiply to solve for x:

2 * 25 = 10 * x
50 = 10x

Divide both sides by 10:

x = 5

So, 5 cups of flour will be needed to make 25 cookies.

Graphical representation of ratio

Visualizing ratios can provide an intuitive understanding of the concept. Here is a simple example to explain ratios using visualization:

2:3 4:6

Here, the rectangles represent two ratios: 2 : 3 and 4 : 6. The second rectangle is exactly twice the size of the first rectangle for both width segments, which shows their proportional relationship.

Types of ratios

Ratios may be classified into two basic types:

1. Direct proportion

Two quantities are in direct proportion when an increase in one causes an increase in the other and vice versa.

Example: The more apples you buy, the more money you spend. If 1 apple costs $2, then 5 apples cost $10.

2. Inverse proportion

Two quantities are inversely proportional when an increase in one causes a decrease in the other.

Example: Time taken for a journey and speed. If you increase your speed, the time taken for a journey decreases.

Verification of ratios

Sometimes you may need to verify whether two sets of numbers are in proportion. Here's a step-by-step guide:

  1. Find the ratio.
  2. Determine the proportions.
  3. Find the cross-product by cross-multiplying.
  4. If the cross-products are equal, the numbers are in proportion.

Practical application of ratios

Ratio is not just a theoretical concept. It has practical applications in various fields including finance, engineering and science. Here is an example of it in everyday life:

Example: Currency conversion

If 1 US Dollar is equal to 72 Indian Rupees, then how many Indian Rupees will you get in exchange of 10 US Dollars?

Determine the ratio:

1/72 = 10/x

Cross-multiply to solve for x:

1 * x = 72 * 10
x = 720

You will get 720 Indian Rupees for 10 US Dollars.

Final thoughts

Understanding proportions can not only help students excel in math, but also enhance their problem-solving skills in real-life situations. Whether you're adjusting a recipe, scaling a model, or converting currency, proportions play an incredibly valuable role. Mastering this concept will provide a strong foundation for more advanced mathematical topics and practical work.


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Equivalent Ratios
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Proportion

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