Question 1 - Page 116 - Parity of Arithmetic & Algebraic Expressions - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 1 - Page 116 Write a few algebraic expressions which always give an even number.We simply need to create expressions where every term is a multiple of 2 (or another even number). Here is the "recipe" for creating them, followed by examples you can use. The Golden Rule In algebra, the definition of an even number is 2𝑛. If you can multiply any variable part by 2 (or 4, 6, 8 etc.), the result is guaranteed to be even. Let’s look at 3 Ways to Write these expressions Option 1: The "Simple Multiplier" (Easiest) Just pick any letter and put an even number in front of it. 2𝑛 4𝑥 10𝑦 100𝑘 Why it works: Any integer multiplied by an even number becomes even. (3×2=6, which is even). Option 2: The "Sum of Evens" Add or subtract two terms that already have even numbers in front of them. 2𝑎+4𝑏 6𝑚−2𝑛 8𝑥+12𝑦 Why it works: An Even number + An Even number is always Even. Option 3: The "Consecutive Number Trick" (Advanced/Impressive) 𝑛(𝑛+1) Why it works: If you take any number (𝑛) and multiply it by the next number (𝑛+1), one of them must be even. Test: If 𝑛=3, then 𝑛+1=4.3×4=12 (Even). Test: If 𝑛=4, then 𝑛+1=5.4×5=20 (Even). Sample Examples Sample examples can be 6𝑥 (Because it is a multiple of 6 , which is even). 2𝑎+2𝑏 (Because the sum of two even numbers is always even). 4𝑛−2 (Because the difference of two even numbers is always even)."