What is the Unitary Method?

S1-SA2-0316

Grade Level:

Class 5

Maths, Physics, Finance, Economics, AI

Definition

What is it?

The Unitary Method is a technique used to find the value of a 'unit' (a single item) first, and then use that unit value to find the value of any desired quantity. It helps us solve problems where we need to compare or scale quantities.

Simple Example

Quick Example

Imagine you bought 5 packets of biscuits for ₹50. To know the price of 1 packet, you'd divide ₹50 by 5. Once you know 1 packet costs ₹10, you can easily find the cost of 7 packets by multiplying ₹10 by 7.

Worked Example

Step-by-Step

PROBLEM: If 4 auto-rickshaws can carry 12 passengers, how many passengers can 7 auto-rickshaws carry?

Step 1: Find out how many passengers 1 auto-rickshaw can carry (the 'unit').
Number of passengers carried by 4 auto-rickshaws = 12 passengers.

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Step 2: Divide the total passengers by the number of auto-rickshaws to find the unit value.
Passengers per 1 auto-rickshaw = 12 passengers / 4 auto-rickshaws = 3 passengers.

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Step 3: Now that we know 1 auto-rickshaw carries 3 passengers, we can find out for 7 auto-rickshaws.

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Step 4: Multiply the unit value by the desired number of auto-rickshaws.
Passengers carried by 7 auto-rickshaws = 3 passengers/auto-rickshaw * 7 auto-rickshaws = 21 passengers.

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ANSWER: 7 auto-rickshaws can carry 21 passengers.

Why It Matters

The Unitary Method is super useful in daily life and in many important fields! From calculating the best deal when shopping to understanding how much fuel an airplane needs (Physics) or even managing money (Finance), it's a core skill. Data analysts and business managers use it all the time to make smart decisions.

Common Mistakes

MISTAKE: Multiplying instead of dividing to find the unit value. For example, if 5 pens cost ₹50, multiplying 50 x 5 to find the cost of 1 pen. | CORRECTION: Always divide the total quantity by the number of items to find the value of one unit. (₹50 / 5 pens = ₹10 per pen).

MISTAKE: Forgetting to perform the second step (multiplying by the desired quantity). Students sometimes stop after finding the unit value. | CORRECTION: Remember the problem usually asks for a new total, not just the unit value. After finding the unit, multiply it by the new number of items.

MISTAKE: Mixing up the quantities. For example, dividing the number of items by the total cost instead of cost by items. | CORRECTION: Always ensure you are dividing the 'total value' (like total cost, total distance, total passengers) by the 'number of units' (like number of items, number of hours, number of vehicles) to get the value per unit.

Practice Questions

Try It Yourself

QUESTION: If 3 packets of milk cost ₹60, what is the cost of 1 packet? | ANSWER: ₹20

QUESTION: A car travels 150 km in 3 hours. How far can it travel in 5 hours at the same speed? | ANSWER: 250 km

QUESTION: If a tailor stitches 8 shirts in 2 days, how many shirts can he stitch in a week (7 days)? | ANSWER: 28 shirts

MCQ

Quick Quiz

If 6 notebooks cost ₹120, how much will 9 notebooks cost?

₹150

₹180

₹200

₹100

The Correct Answer Is:

First, find the cost of 1 notebook: ₹120 / 6 = ₹20. Then, multiply this unit cost by 9 notebooks: ₹20 * 9 = ₹180. So, option B is correct.

Real World Connection

In the Real World

Next time you are at a market buying vegetables, say you see 2 kg of tomatoes for ₹40. Using the Unitary Method, you can quickly figure out that 1 kg costs ₹20, and then decide if buying 3 kg for ₹60 is a good deal. Even delivery apps like Swiggy or Zomato use this idea to calculate delivery charges based on distance.

Key Vocabulary

Key Terms

UNIT: A single item or quantity. | VALUE: The cost, amount, or measure of something. | QUANTITY: How much of something there is. | PER: For each single unit. | PROPORTION: A part, share, or number considered in relation to a whole.

What's Next

What to Learn Next

Great job understanding the Unitary Method! This skill is a building block for many advanced topics. Next, you can explore 'Ratio and Proportion' and 'Percentage' because they often use the Unitary Method as a core part of their calculations. Keep practicing!