We Distribute, Yet Things MultiplyClass 8 Mathematics Case Study Questions

A community group manages a rectangular vegetable garden. Initially, its length is $a$ meters and its breadth is $b$ meters. The gardeners decide to expand the plot to grow more vegetables. They increase the length by $m$ meters and the breadth by $n$ meters. The original dimensions of the garden were $a = 20$ m and $b = 15$ m. The planned expansion is to add $m = 5$ m to the length and $n = 3$ m to the breadth. The group wants to use algebraic identities to calculate the new area and understand the increase in size, just like in their mathematics textbook.

An architect is designing a large square park with a side length of $a$ units. Inside this park, she plans to create a smaller square floral garden, also centered, with a side length of $b$ units. The area between the outer park boundary and the inner floral garden will be a paved walkway. The architect wants to find an efficient way to calculate the area of this walkway using algebraic identities. For a specific project, the park has a side length of $a = 55$ meters, and the floral garden has a side length of $b = 45$ meters.

A baker sells muffins for ₹11 each. At the end of the day, he needs to quickly calculate the total revenue from selling a large number of muffins without using a calculator. He remembers a method from his school mathematics class for fast multiplication by 11. The method involves using the distributive property, where multiplying by 11 is the same as multiplying by $(10+1)$. For example, to calculate the revenue from selling 387 muffins, he needs to find the product $387 \times 11$.