Algebra Play Exercise 6.2 Class 8 Maths – Chapter 6 NCERT Solutions
Detailed NCERT Solutions for Class 8 Maths Chapter 6, Algebra Play, Exercise 6.2, prepared by the ALLEN faculty team according to the updated syllabus, are provided below. These solutions offer clear explanations of the exercise questions for revision, practice, and exam preparation.Exercise 6.2 The greatest product that can be obtained by arranging the given digits in a two-digit number and a one-digit multiplier. It compares different arrangements and finds the biggest product, using algebraic expressions and place values.
1.0Download Class 8 Maths Chapter 6 Ex 6.2 NCERT Solutions PDF
Get the NCERT Solutions PDF for Class 8 Maths Chapter 6 Exercise 6.2 to refer to the solved questions and verify your answers during practice.
2.0Detailed NCERT Solutions for Algebra Play Exercise 6.2 Class 8 Maths (Ganita Prakash Term 2)
1. Fill the digits 1,3 , and 7 in □□×□ to make the largest product possible.
Sol. There are six ways to place three digits:
The six choices are:
In each pair, the one with the larger multiplicand generates the larger product, so we can reduce the comparison to these three expressions.
7 □ 3 □ 1 , □ 7 □ 1 × □ 3 and 33× □ 7
It is clear that □ 7 □ 1 × □ 3 is greater than □ 7 □ 3 × □ 1 , so we only need to compare □ 7 □ 1 × □ 3 and □ 3 □ 1 × □ 7
71×3=7×10×3+1×3
31×7=3×10×7+1×7
Thus, the first term in both expressions is equal.
The second term shows that □ 3 □ 1 × □ 7
=217 is the largest.
2. Fill the digits 3, 5, and 9 in □□×□ to make the largest product possible.
Sol. There are six ways to place three digits: We can fill the first box with 3,5 , or 9 . For each of these choices, we have 2 ways of filling the remaining 2 digits.
The six choices are:
In each pair, the one with the larger multiplicand generates the larger product, so we can reduce the comparison to these three expressions.
95× □ 3 , 9 □ 3 × □ 5 53× □ 9
It is clear that □ 9 □ 3 × □ 5 is greater than ____ 9 □ 5 × □ 3 , so we only need to compare □ 9 □ 3 × □ 5 and □ 5 □ 3 × □ 9
Let us expand these two:
93×5=9×10×5+3×5
53×9=5×10×9+3×9
Thus, the first term in both expressions is equal.
The second term shows that □ 5 □ 3 × □ 9 =477 is the largest.
3.0Key Concepts of Chapter 6 Algebra Play Exercise 6.2
- Arranging given digits in a two-digit number and a one-digit multiplier.
- Finding the arrangement that gives the largest product.
- Comparing different arrangements of the given digits.
- Expressing the products using algebraic expressions.
- Using place value to compare two-digit numbers.
- Examining how the position of digits affects the product.
4.0Benefits of NCERT Solutions Class 8 Maths Chapter 6 Exercise 6.2
- Forms different two-digit numbers using the given digits.
- Compares possible digit arrangements to find the largest product.
- Represents the products using algebraic expressions.
- Uses place value to compare different arrangements.
- Applies algebraic comparison to determine the greatest product.
- Examines the effect of digit placement on the resulting product.