Rational Numbers

-3/5 < -2/5

Step 1: Both fractions have the same denominator (5), so compare numerators. Step 2: The numerators are -3 and -2. Step 3: On a number line, -3 is to the left of -2, which means -3 is smaller than -2. Step 4: Since denominators are equal and -3 < -2, we have -3/5 < -2/5. Think of it this way: owing 3 rupees is worse than owing 2 rupees, so -3/5 is less than -2/5.

1/2

Step 1: We need to subtract 1/3 from 5/6. The denominators are different (6 and 3). Step 2: Find LCM of 6 and 3 = 6. Convert 1/3 to have denominator 6: 1/3 = 2/6. Step 3: Now subtract: 5/6 - 2/6 = (5-2)/6 = 3/6. Step 4: Simplify 3/6 = 1/2. The answer is 1/2. Common mistake: Some students subtract denominators too, getting 4/3, which is incorrect.

-1/6

Step 1: To multiply rational numbers, multiply numerators together and denominators together. Step 2: Numerator: (-3) × 4 = -12. Denominator: 8 × 9 = 72. Step 3: Result = -12/72. Step 4: Simplify by dividing both by HCF(12,72) = 12: -12/72 = -1/6. The answer is -1/6. The sign is negative because we multiplied a negative number by a positive number.

Because 5 can be written as 5/1, where 5 and 1 are integers and 1 ≠ 0

Step 1: A rational number is of the form p/q where p and q are integers and q ≠ 0. Step 2: Any integer, like 5, can be written as 5/1. Step 3: Here p = 5 (an integer) and q = 1 (an integer, not equal to 0). Step 4: So 5 satisfies the definition of a rational number. This is why every integer is a rational number - it can always be expressed with denominator 1.