Gujarat Board Class 9 Mathematics — Flashcards

A: Step 1: Recall that any integer can be written as a rational number by placing it over 1. Step 2: Write -25 = -25/1 Answer: -25/1 (where p = -25, q = 1, and q ≠ 0) Verification: -25 ÷ 1 = -25 ✓

A: Method: Write 1 and 2 with denominator 6 → 6/6 and 12/6 Step 1: 1 = 6/6 and 2 = 12/6 Step 2: Numbers between 6/6 and 12/6 are: 7/6, 8/6, 9/6, 10/6, 11/6 Step 3: Simplify if needed: 7/6, 4/3, 3/2, 5/3,

A: Answer: Yes, 1/3 is a rational number. Justification: By definition, a number is rational if it can be written as p/q where p and q are integers and q ≠ 0. For 1/3: p = 1 (integer), q = 3 (integer), a

A: Yes, it is a polynomial. Reason: It contains variables with non-negative integer exponents (x² has exponent 2, x has exponent 1, and 5 is a constant with x⁰). All terms have coefficients and constants

A: No, it is NOT a polynomial. Reason: The term -3/x can be written as -3x⁻¹. Since the exponent of x is -1 (a negative integer, not a whole number), this expression does not qualify as a polynomial. Pol

A: Step 1: Identify all terms: 7x⁵, -3x³, 2x, -8. Step 2: Find the exponents: 5, 3, 1, 0. Step 3: The highest exponent is 5. Step 4: The degree of the polynomial is 5. Answer: 5

A: Answer: (i) 2x + 3y = 5 is a linear equation in two variables. Step 1: Check if equation is in form ax + by + c = 0 where a and b are not both zero. Step 2: For (i): 2x + 3y - 5 = 0. This has variabl

A: Step 1: Start with 3y = 2x - 7 Step 2: Move all terms to one side: 2x - 3y - 7 = 0 (or -2x + 3y + 7 = 0) Step 3: Rearrange in standard form: 2x - 3y - 7 = 0 Step 4: Compare with ax + by + c = 0 Answe

A: Step 1: Substitute x = 2 and y = 1 into the equation 2x + y = 5 Step 2: Left side = 2(2) + 1 = 4 + 1 = 5 Step 3: Right side = 5 Step 4: Since Left side = Right side (5 = 5), the equation is satisfied