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 ratio and proportion class 6

Ratios

A ratio is a way to compare two quantities or numbers. It tells us how much of one thing there is compared to another. Ratios can be written in three ways: x to y, x: y, or x/y, but they all mean the same thing.

Example:

If Ram's weight is 40 kgs and Ali's weight is 80 kgs, the ratio of Ram's weight to Ali's weight is 1:2.

Proportions

When two ratios are equal, we say they are in proportion. It's like saying the two comparisons are the same.

Example:

Ratios 2:3 and 6:9 are proportional. We write it like this: 2:3 = 6:9.

Golden Ratio

The golden ratio is a special number, about 1.618. It has interesting properties and appears in various places in art and nature.

Difference Between Fractions and Ratios

• A fraction tells you about a part of a whole thing (like 1/3 means one part out of three parts).
• A ratio tells you how two different things compare (like 10:30 shows the comparison between two numbers).

Working with Ratios

We can use ratios to compare things in different situations, like how many hours one person worked compared to another.

Example:

If Joe worked for 8 hours and James worked for 2 hours, Joe worked four times more than James. The ratio of their working hours is 8:2 or 4:1.

Buildings and Ratios

Architects can use ratios to decide if a building design is possible. If a building's width to height ratio fits a certain rule, then the building is okay to build.

Equivalent Ratios

Some ratios are equal to each other even though they look different. For instance, 10:30 and 1:3 are equivalent ratios because they mean the same thing.

Unitary Method

The unitary method helps us find out how much something costs or how far you can travel based on some information. It first finds the value of one unit and then uses that to find the value of more units.

Example:

If a car runs 150 km on 15 liters of fuel, it will run 100 km on 10 liters of fuel.

Direct and Indirect Variation

• In direct variation, when one thing goes up, the other goes up too (like more people doing a job means more work gets done).
• In indirect variation, when one thing goes up, the other goes down (like if a car goes faster, it takes less time to go somewhere).

Applications of Ratios and Proportions

We use ratios and proportions in everyday life, like when shopping, traveling, or running a business.

Summary

Ratios and proportions help us compare different quantities. They are used in math and in everyday life to understand relationships between things. By learning about them, we can make better decisions and understand the world around us.

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