What is Solving Proportions?

S3-SA1-0411

Grade Level:

Class 7

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

Definition

What is it?

Solving proportions means finding a missing value in two equivalent ratios. When two ratios are equal, they form a proportion, and we use this equality to find an unknown part.

Simple Example

Quick Example

Imagine you can buy 2 packets of Maggi for 40 rupees. If you want to buy 4 packets, how much will it cost? Here, the ratio of packets to cost (2:40) should be the same as (4:?). We need to find the missing cost.

Worked Example

Step-by-Step

Let's say a car travels 150 km in 3 hours. How much distance can it cover in 5 hours if it travels at the same speed?

Step 1: Set up the proportion. Let 'x' be the unknown distance.
Distance / Time = Distance / Time
150 km / 3 hours = x km / 5 hours

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Step 2: Write it as an equation.
150/3 = x/5

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Step 3: Simplify the known ratio (optional but helpful).
50 = x/5

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Step 4: Cross-multiply to solve for x (or multiply both sides by 5).
50 * 5 = x

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Step 5: Calculate the value of x.
x = 250

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Answer: The car can cover 250 km in 5 hours.

Why It Matters

Understanding proportions is super useful! Data scientists use it to scale datasets, engineers use it to design structures proportionally, and physicists use it to understand relationships between quantities. It's a foundational skill for many exciting careers, from building rockets at ISRO to developing AI.

Common Mistakes

MISTAKE: Mixing up the units in a proportion (e.g., putting distance in the numerator on one side and in the denominator on the other). | CORRECTION: Always keep the same units in the same position (numerator or denominator) on both sides of the equals sign.

MISTAKE: Not cross-multiplying correctly, or only multiplying one side. | CORRECTION: Remember that if a/b = c/d, then a*d = b*c. Multiply the numerator of one ratio by the denominator of the other.

MISTAKE: Forgetting to write down the units in the final answer. | CORRECTION: Always include the correct units (like km, rupees, kg) with your final numerical answer to make it meaningful.

Practice Questions

Try It Yourself

QUESTION: If 5 pens cost 50 rupees, how much will 7 pens cost? | ANSWER: 70 rupees

QUESTION: A recipe for 4 people needs 2 cups of rice. How many cups of rice are needed for 10 people? | ANSWER: 5 cups

QUESTION: A train travels at a constant speed. It covers 180 km in 2 hours and 30 minutes. How much time will it take to cover 360 km? (Hint: Convert minutes to hours first) | ANSWER: 5 hours

MCQ

Quick Quiz

If 3 kgs of onions cost Rs. 60, how much will 5 kgs of onions cost?

Rs. 80

Rs. 90

Rs. 100

Rs. 120

The Correct Answer Is:

The ratio of kgs to cost is 3/60 = 1/20. So, for 5 kgs, the cost will be 5 * 20 = Rs. 100. Options A, B, and D are incorrect calculations.

Real World Connection

In the Real World

When you're comparing mobile data plans, say 2 GB for Rs. 199 vs. 5 GB for Rs. 449, you're using proportions to find out which plan offers more data per rupee. Even when scaling up a recipe for a big family gathering or calculating fuel efficiency for your bike, proportions are key!

Key Vocabulary

Key Terms

RATIO: A comparison of two quantities | PROPORTION: An equation stating that two ratios are equal | CROSS-MULTIPLICATION: A method to solve proportions by multiplying the numerator of one ratio by the denominator of the other | UNKNOWN VALUE: The missing quantity in a proportion that we need to find

What's Next

What to Learn Next

Great job understanding proportions! Next, you can explore 'Direct and Inverse Proportions' to learn how quantities relate in different ways. This will make you even better at solving real-world problems!