NCERT Solutions for Class 8 Mathematics Ganita Prakash Part 1 Chapter 7
NCERT solutions for Class 8 Mathematics Chapter Proportional Reasoning-1 – complete answers & explanations
In this chapter of Class 8 Mathematics, titled "Proportional Reasoning-1," students are introduced to the concept of proportional reasoning, where relationships between quantities are explored through ratios and proportions. The chapter explains how to compare two ratios and determine if they are proportional. Proportions are an essential concept in solving real-world problems, from determining quantities in recipes to measuring distances and areas. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. Introduction to proportional reasoning, where
ratios are used to compare quantities.
2. Understanding how to check if ratios are proportional using cross multiplication.
3. Learning how to solve problems involving proportions in real-life scenarios, like mixing ingredients, calculating speed, and dividing resources.
4. Solving "Rule of Three" problems, a method for solving problems involving proportionality.
5. Applying proportional reasoning to both theoretical and practical problems, such as determining the cost of items, calculating distances, and working with ratios in geometry.
How to use these NCERT solutions?
1. Students should first attempt the
questions on their own and then refer to the solutions to check their work.
2. After checking the solutions, students should focus on understanding the proportional relationships used in each example.
3. Teachers and parents can use the solutions to guide students through the process of solving proportional problems, ensuring they understand the underlying concepts.
4. The solutions follow the worksheet’s structure exactly, making it easy for students to find the corresponding answers to each question.
Important tips & tricks for students
1. Pay attention to the units involved in the ratios and ensure they match before comparing.
2. When solving proportional problems, first simplify ratios to their lowest form for easier comparison.
3. For "Rule of Three" problems, remember that the fourth term can be calculated using cross multiplication.
4. Always check if the ratio remains the same when scaling up or down the quantities involved.
5. Practice solving a variety of real-life problems to get comfortable with applying proportional reasoning in different contexts.
NCERT solutions – complete answer key
7.1 Observing Similarity in Change
1. Which images look similar and which ones look different?
Answer: Images A, C, and D look similar, while B and E look different.
7.2 Ratios
1. The ratio of width to height of image A is 60 : 40.
2. The ratio of width to height of image C is 30 : 20.
3. The ratio of width to height of image D is 90 : 60.
7.3 Ratios in their Simplest Form
1. The ratio of image A simplifies to 3 : 2.
2. The ratio of image D simplifies to 3 : 2.
3. The ratio of image B simplifies to 2 : 1.
4. The ratio of image E simplifies to 1 : 1.
7.4 Problem Solving with Proportional Reasoning
Example 1: Are the ratios 3 : 4 and 72 : 96 proportional?
Answer: Yes, the ratios are proportional, as both simplify to 3 : 4.
Example 2: How many spoons of sugar should Kesang add?
Answer: Kesang should add 30 spoons of sugar to maintain the same sweetness for 18 glasses of lemonade.
7.5 Sharing, but Not Equally!
1. If you divide 12 counters equally, the ratio of counters with each person is 6 : 6, or 1 : 1.
2. If the ratio of counters is 3 : 1, your partner gets 9 counters and you get 3.
7.6 Unit Conversions
1. Anagh mixes 600 mL of orange juice with 900 mL of apple juice. The ratio of orange juice to apple juice is 2 : 3.
2. For the school trip, 204 students require 3 buses. The new ratio of buses to students is 1 : 68.
3. The population density of Delhi is higher than that of Mumbai, as it has more people per square kilometre.
Figure it Out
1. The Earth travels approximately 940 million kilometres around the Sun in a year. It will travel 18 million kilometres in a week.
2. The mason needs to calculate the total area to build the walls based on the size of the plot and the wall’s height.
Why NCERT solutions help students?
NCERT solutions are tailored to the syllabus and provide clear, step-by-step guidance on solving problems. By following the solutions, students gain a better understanding of proportional reasoning, improve their problem-solving skills, and enhance their ability to tackle various types of proportional problems confidently.
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