What is Solving Problems based on Numbers?

S6-SA1-0142

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Solving problems based on numbers means using mathematical operations like addition, subtraction, multiplication, and division, along with logical reasoning, to find solutions to real-world situations described using numerical data. It involves converting a problem from words into a mathematical expression or equation and then calculating the answer.

Simple Example

Quick Example

Imagine you have Rs. 50 and want to buy a packet of biscuits for Rs. 15 and a small juice box for Rs. 20. To find out how much money you have left, you would subtract the cost of the items from your total money. Rs. 50 - Rs. 15 - Rs. 20 = Rs. 15. So, you have Rs. 15 remaining.

Worked Example

Step-by-Step

PROBLEM: A delivery driver covers 25 km in the first hour, 30 km in the second hour, and then takes a 15-minute break. After the break, he covers another 40 km. What is the total distance covered by the driver?

STEP 1: Identify the distances covered. These are 25 km, 30 km, and 40 km.
---
STEP 2: Notice that the 15-minute break is a time factor and doesn't directly add to the distance. We need to focus only on distances.
---
STEP 3: Add the individual distances together.
---
STEP 4: Total distance = 25 km + 30 km + 40 km
---
STEP 5: Total distance = 95 km.

ANSWER: The total distance covered by the driver is 95 km.

Why It Matters

Solving problems based on numbers is fundamental to nearly every field, from designing rockets at ISRO to developing medicines in biotechnology. It helps engineers build stronger bridges, AI/ML scientists train smarter algorithms, and doctors understand patient data. Mastering this skill opens doors to exciting careers in technology, science, and even finance.

Common Mistakes

MISTAKE: Not reading the question carefully and missing key information or including irrelevant details. For example, using the break time in the total distance calculation. | CORRECTION: Always read the problem twice, underline the numbers and keywords, and identify exactly what the question is asking you to find.

MISTAKE: Using the wrong mathematical operation (e.g., multiplying instead of adding). | CORRECTION: Understand what each operation means. 'Total', 'sum', 'altogether' usually mean addition. 'Difference', 'left', 'how much more' usually mean subtraction. 'Times', 'product', 'of' often mean multiplication. 'Share', 'per', 'each' often mean division.

MISTAKE: Making calculation errors, especially with larger numbers or multiple steps. | CORRECTION: Break down complex problems into smaller, manageable steps. Double-check your arithmetic, perhaps by doing the calculation in reverse or using estimation to see if your answer is reasonable.

Practice Questions

Try It Yourself

QUESTION: A baker made 150 laddoos. He sold 85 laddoos in the morning. How many laddoos are left? | ANSWER: 65 laddoos

QUESTION: If a train travels at an average speed of 60 km/hour, how much distance will it cover in 3.5 hours? | ANSWER: 210 km

QUESTION: A fruit seller buys 20 kg of apples for Rs. 1200. He sells them at Rs. 80 per kg. If 2 kg of apples spoil, what is his total profit or loss? | ANSWER: Profit of Rs. 240

MCQ

Quick Quiz

Which operation would you use to find the total cost of 5 items, each costing Rs. 75?

Addition

Subtraction

Multiplication

Division

The Correct Answer Is:

Multiplication is used when you need to find the total of a repeated addition, like adding the cost of 5 identical items. You would multiply 5 by Rs. 75 to get the total cost.

Real World Connection

In the Real World

From managing your daily pocket money to calculating the fuel efficiency of your family's scooter, solving problems based on numbers is everywhere. When you check your mobile data usage, calculate the ingredients for a recipe, or even compare prices for groceries online on apps like JioMart or BigBasket, you are constantly using this skill.

Key Vocabulary

Key Terms

OPERATION: A mathematical action like addition, subtraction, multiplication, or division. | NUMERICAL DATA: Information represented by numbers. | REASONING: Using logic and thought to arrive at a conclusion. | EQUATION: A mathematical statement showing two expressions are equal. | QUANTITY: An amount or number of something.

What's Next

What to Learn Next

Once you're comfortable solving problems with basic numbers, you can explore concepts like 'Algebraic Expressions' and 'Linear Equations'. These build on your number skills by introducing variables and more complex problem-solving methods, which are crucial for advanced mathematics.