What is a Dash Rule?

S2-SA1-0401

Grade Level:

Class 1

NLP, Law, History, Social Sciences, Literature, Journalism, Communication

Definition

What is it?

A Dash Rule is a special rule in mathematics that helps us solve problems quickly when numbers are related in a simple way. It's like a shortcut for finding a missing number when you have three other numbers that are proportional.

Simple Example

Quick Example

Imagine you buy 2 samosas for ₹20. If you want to know how much 4 samosas would cost, you can use the Dash Rule. Here, 2 samosas cost ₹20, so 4 samosas would cost ₹40.

Worked Example

Step-by-Step

Problem: If 3 pens cost ₹45, how much will 5 pens cost?

Step 1: Write down the known information in a clear way. We have pens and cost.
3 pens --- ₹45
5 pens --- ?

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Step 2: Set up the proportion. We want to find the cost of 5 pens. Let the unknown cost be 'x'.
3/5 = 45/x

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Step 3: Cross-multiply the numbers. Multiply the number of pens by the unknown cost, and the cost by the number of pens.
3 * x = 5 * 45

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Step 4: Calculate the product on the right side.
3x = 225

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Step 5: Isolate 'x' by dividing both sides by 3.
x = 225 / 3

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Step 6: Perform the division.
x = 75

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Answer: 5 pens will cost ₹75.

Why It Matters

The Dash Rule helps us understand how quantities change in relation to each other, which is crucial in many fields. Journalists use it to compare data, businesses use it to calculate profits and losses, and scientists use it for experiments. It's a foundational concept for careers in finance, data analysis, and even running your own small business.

Common Mistakes

MISTAKE: Mixing up the order of numbers in the proportion (e.g., writing 3/45 = 5/x instead of 3/5 = 45/x) | CORRECTION: Always keep the same type of quantity (like 'number of items') on the top or bottom of both fractions.

MISTAKE: Forgetting to cross-multiply and instead just dividing numbers straight across. | CORRECTION: Remember to multiply diagonally (numerator of one fraction by denominator of the other) before dividing.

MISTAKE: Not writing down the units (like ₹ or 'pens') which can lead to confusion. | CORRECTION: Always label your numbers with their units to keep track of what you are calculating.

Practice Questions

Try It Yourself

QUESTION: If 4 movie tickets cost ₹800, how much will 7 movie tickets cost? | ANSWER: ₹1400

QUESTION: A car travels 120 km in 2 hours. How far will it travel in 5 hours at the same speed? | ANSWER: 300 km

QUESTION: A chef uses 2 cups of rice to make biryani for 6 people. If he wants to make biryani for 15 people, how many cups of rice will he need? | ANSWER: 5 cups

MCQ

Quick Quiz

If 5 kg of potatoes cost ₹125, how much will 8 kg of potatoes cost?

₹150

₹200

₹225

₹250

The Correct Answer Is:

To solve this, set up the proportion: 5/8 = 125/x. Cross-multiply to get 5x = 8 * 125, which means 5x = 1000. Dividing by 5 gives x = 200.

Real World Connection

In the Real World

When you see 'sale' signs in a shop, like 'Buy 2, Get 1 Free' or '3 for ₹100', the shopkeeper uses the Dash Rule (or similar proportional thinking) to set prices and calculate discounts. Even when you recharge your mobile data, the amount of data you get is proportional to the money you pay, a concept rooted in the Dash Rule.

Key Vocabulary

Key Terms

PROPORTION: A statement that two ratios are equal | RATIO: A comparison of two numbers | CROSS-MULTIPLY: Multiplying the numerator of one fraction by the denominator of the other | UNIT: A standard quantity for measuring | UNKNOWN: A value that needs to be found

What's Next

What to Learn Next

Great job learning the Dash Rule! Next, you can explore 'Direct and Inverse Proportion'. This will help you understand when quantities increase or decrease together, and when one goes up as the other goes down, building on your Dash Rule knowledge.