Question 10 - Figure it out - Page 143, 144 - Chapter 6 Class 7 - Number Play - Ganita Prakash

Transcript

Question 10 (a) Identify the statements that are true. (a) The expression 4m – 1 always gives odd numbers Here, 4m is always even 1 is always odd Now, our equation is Even – Odd = Odd Thus, the expression 4m – 1 always gives odd numbers is true Question 10 (b) Identify the statements that are true. (b) All even numbers can be expressed as 6j – 4 Let’s put different values of j and check Putting j = 0 6j – 4 = 6 × 0 – 4 = 0 – 4 = – 4 Putting j = 1 6j – 4 = 6 × 1 – 4 = 6 – 4 = 2 Putting j = 2 6j – 4 = 6 × 2 – 4 = 12 – 4 = 8 So, the equation gives even numbers –4, 2, 8,… But it misses even numbers like 4, 6, 10 Since 6j – 4 doesn’t give all even numbers, it is not true Question 10 (c) Identify the statements that are true. (c) Both expressions 2p + 1 and 2q – 1 describe all odd numbers. Here, 2p + 1 gives 1, 3, 5, 7, 9, 11, … And, 2q – 1 gives –1, 1, 3, 5, 7, 9, 11, … Thus, both expressions describe all odd numbers So, our statement is true Question 10 (d) Identify the statements that are true. (d) The expression 2f + 3 gives both even and odd numbers. Let’s put different values of f and check Putting f = 0 2f + 3 = 2 × 0 + 3 = 0 + 4 = 3 Putting f = 1 2f + 3 = 2 × 1 + 3 = 2 + 3 = 5 Putting f = 2 2f + 3 = 2 × 2 + 3 = 4 + 3 = 7 Thus, the expression always give odd number So, the given statement is false