What is the Relationship?

S0-SA3-0527

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A 'relationship' shows how two or more things are connected or depend on each other. It describes how a change in one thing affects another. Think of it as a rule that links different items or values.

Simple Example

Quick Example

Imagine you buy samosas. If one samosa costs ₹10, then two samosas cost ₹20, and three samosas cost ₹30. The relationship here is: Total Cost = Number of Samosas × ₹10. As the number of samosas increases, the total cost also increases.

Worked Example

Step-by-Step

Let's find the relationship between the number of hours an auto-rickshaw runs and the total distance it covers, assuming it travels 20 km every hour.

Step 1: Understand the given information. The auto travels 20 km in 1 hour.
---
Step 2: If it runs for 1 hour, distance = 20 km.
---
Step 3: If it runs for 2 hours, distance = 20 km/hour × 2 hours = 40 km.
---
Step 4: If it runs for 3 hours, distance = 20 km/hour × 3 hours = 60 km.
---
Step 5: Notice the pattern. For every hour, the distance increases by 20 km.
---
Step 6: Formulate the relationship. Total Distance = 20 × Number of Hours.

Answer: The relationship is Total Distance = 20 × Number of Hours.

Why It Matters

Understanding relationships helps us predict outcomes and make smart decisions in many fields. Engineers use relationships to design bridges, doctors use them to understand how medicines affect the body, and economists use them to study how prices change. It's key to problem-solving in science, math, and everyday life.

Common Mistakes

MISTAKE: Assuming all relationships are always 'more means more' (direct). | CORRECTION: Relationships can also be 'more means less' (inverse), like how more workers might mean less time to finish a job.

MISTAKE: Not checking if the relationship holds true for different values. | CORRECTION: Always test your assumed relationship with a few different examples to make sure it's consistent.

MISTAKE: Confusing cause and effect with just a correlation. | CORRECTION: A relationship shows how things are linked, but sometimes one thing doesn't directly 'cause' the other, they just happen together.

Practice Questions

Try It Yourself

QUESTION: If 1 kg of rice costs ₹50, what is the relationship between the amount of rice (in kg) and its total cost? | ANSWER: Total Cost = Amount of Rice (kg) × ₹50

QUESTION: A mobile phone battery drains 10% every hour when in use. If it starts at 100%, what is the relationship between the remaining battery percentage and the hours of use? | ANSWER: Remaining Battery Percentage = 100% - (Hours of Use × 10%)

QUESTION: A chaiwala sells chai for ₹15 per cup. On a special offer, if you buy 5 cups or more, each cup costs ₹12. Describe the relationship between the number of cups bought and the total cost. | ANSWER: If Cups < 5, Total Cost = Cups × ₹15. If Cups >= 5, Total Cost = Cups × ₹12.

MCQ

Quick Quiz

What kind of relationship is it when buying more mobile data (GB) leads to a higher bill?

Inverse relationship

Direct relationship

No relationship

Complex relationship

The Correct Answer Is:

This is a direct relationship because as one quantity (mobile data) increases, the other quantity (bill) also increases. In an inverse relationship, one would increase while the other decreases.

Real World Connection

In the Real World

When you use a food delivery app like Swiggy or Zomato, the app calculates your total bill based on the price of food items, delivery charges, and any discounts. This calculation is based on different relationships between these factors. Even predicting cricket match scores involves understanding relationships between player performance and team totals.

Key Vocabulary

Key Terms

DIRECT RELATIONSHIP: When one thing increases, the other also increases. | INVERSE RELATIONSHIP: When one thing increases, the other decreases. | VARIABLE: A quantity that can change or vary. | CONSTANT: A value that does not change. | PATTERN: A regular, repeated way in which something happens or is done.

What's Next

What to Learn Next

Now that you understand what relationships are, you can move on to 'Functions'. Functions are a special type of relationship where each input has exactly one output. This will help you build stronger mathematical models.