Question 13 - Figure it out - Page 102 to 105 - Chapter 4 Class 7 - Expressions using Letter-Numbers (Ganita Prakash)

Transcript

Now, we also have to find expressions for each color Expressions to describe the positions for each colour For any whole number value of k (i.e. k = 0, 1, 2, 3,…) Expressions for color are Red: 4k + 1 (Remainder 1) Green: 4k + 3 (Remainder 3) Yellow: 4k + 2 or 4k (Remainder 0 or 2) So we write, Yellow: 2k Question 13 Have you noticed how the colours change in a traffic signal? The sequence of colour changes is shown below. Find the colour at positions 90, 190, and 343. Write expressions to describe the positions for each colour.First, let’s continue our pattern and make it vertical The sequence of colors shown is Red, Yellow, Green, Yellow, which is a repeating cycle of 4 positions. To find the color at a specific position, we can divide the position number by 4 and check the remainder: Remainder 1: Red Remainder 2: Yellow Remainder 3: Green Remainder 0: Yellow Now, let’s look at the colors at positions 90, 190, 343 Position 90 90/4=22 2/4 Since remainder of 2, ∴ The color is Yellow Position 190 190/4=47 2/4 Since remainder of 2, ∴ The color is Yellow Position 343 343/4=85 3/4 Since remainder of 3, ∴ The color is Green