What is the algebraic expression describing the following steps — add any two numbers. Class 8

What is the algebraic expression describing the following steps — add any two numbers. Class 8

Question 1.

What is the algebraic expression describing the following steps — add any two numbers. Multiply this by half of the sum of the two numbers? Prove that this result will be half of the square of the sum of the two numbers. Class 8

Solution:

Let the number be x and y.

Now, (x + y) × [latex]\frac{(x+y)}{2}[/latex] = [latex]\frac{1}{2}[/latex] (x + y)²

= Half of the square of the sum of the two numbers proved.

Question 2.

Which is larger? Find out without fully computing the product. Class 8

(i) 14 × 26 or 16 × 24

(ii) 25 × 75 or 26 × 74

Solution:

(i) 14 × 26 = 14 × (24 + 2)

= 14 × 24 + 14 × 2

16 × 24 = (14 + 2) × 24

= 14 × 24 + 2 × 24

So, from the above 16 × 24 is greater.

(ii) 25 × 75 = 25 × (74 + 1)

= 25 × 74 + 25 × 1

26 × 74 = (25 + 1) × 74

= 25 × 74 + 74 × 1

So, from the above 26 × 74 is greater.