What is the Unitary Method? | Simple Explanation for Class 7

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What is the Unitary Method in Algebra?

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Unitary Method is a technique used in Algebra to find the value of a required quantity by first finding the value of a single unit. It involves two main steps: finding the value of one unit, and then multiplying that unit value by the number of units needed.

Simple Example

Quick Example

Imagine you bought 5 samosas for ₹50. If you want to know how much 1 samosa costs, you'd divide ₹50 by 5. Then, if you want to know the cost of 8 samosas, you'd multiply the cost of one samosa by 8. This is the unitary method in action!

Worked Example

Step-by-Step

QUESTION: If 6 kg of onions cost ₹90, how much will 10 kg of onions cost?

STEP 1: Identify the given information.
Cost of 6 kg onions = ₹90

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STEP 2: Find the cost of 1 kg of onions (the 'unit' value).
Cost of 1 kg onions = Total cost / Total quantity
Cost of 1 kg onions = ₹90 / 6
Cost of 1 kg onions = ₹15

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STEP 3: Now, find the cost of the required quantity (10 kg).
Cost of 10 kg onions = Cost of 1 kg onions × Required quantity
Cost of 10 kg onions = ₹15 × 10
Cost of 10 kg onions = ₹150

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ANSWER: 10 kg of onions will cost ₹150.

Why It Matters

The Unitary Method is a fundamental skill used in many advanced fields like Data Science to compare different data points, in Physics for calculating rates, and in Economics for understanding pricing. It helps engineers estimate material costs and even helps AI/ML models scale calculations. Mastering this helps you think logically and solve complex problems in various careers.

Common Mistakes

MISTAKE: Directly multiplying or dividing without finding the unit value first. | CORRECTION: Always find the value of 'one' unit first, then proceed to find the value of the required quantity.

MISTAKE: Confusing direct and inverse variation. Thinking that if more items cost more, then fewer items must also cost more. | CORRECTION: In direct variation (which the basic unitary method handles), if one quantity increases, the other quantity increases proportionally. In inverse variation (a different concept), if one increases, the other decreases.

MISTAKE: Calculation errors, especially with division and multiplication. | CORRECTION: Double-check your arithmetic in each step. A small error in finding the unit value will lead to a wrong final answer.

Practice Questions

Try It Yourself

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: If 15 workers can build a wall in 4 days, how many workers are needed to build the same wall in 3 days? (Hint: This is an inverse variation problem, but you can still use the unitary method logic to find 'total work' first). | ANSWER: 20 workers

QUESTION: A juice vendor sells 25 glasses of juice for ₹500. If he wants to earn ₹800, how many glasses of juice must he sell? | ANSWER: 40 glasses

MCQ

Quick Quiz

If 4 pens cost ₹60, what is the cost of 7 pens?

₹90

₹105

₹120

₹15

The Correct Answer Is:

First, find the cost of 1 pen: ₹60 / 4 = ₹15. Then, multiply the cost of 1 pen by 7: ₹15 * 7 = ₹105.

Real World Connection

In the Real World

From calculating your monthly mobile data usage based on daily consumption to figuring out how many packets of biscuits you can buy with your pocket money, the Unitary Method is everywhere. Even delivery apps like Swiggy or Zomato use similar logic to estimate delivery times and costs based on distance and average speed.

Key Vocabulary

Key Terms

UNIT: A single item or quantity. | QUANTITY: The amount or number of something. | PROPORTIONAL: When two quantities change at the same rate. | DIRECT VARIATION: When one quantity increases, the other also increases. | INVERSE VARIATION: When one quantity increases, the other decreases.

What's Next

What to Learn Next

Great job understanding the Unitary Method! Next, you can explore Direct and Inverse Proportions, which are extensions of this concept. They will help you solve even more complex problems involving varying quantities and rates.