Integers — Important Questions

1

Step 1: The multiplicative identity is the number that, when multiplied with any integer, gives the same integer. Step 2: Let us check: 5 × 1 = 5, (-12) × 1 = -12, 0 × 1 = 0. Step 3: In every case, multiplying by 1 gives the number itself. Step 4: The number 0 is the additive identity, not the multiplicative identity. Final Answer: 1 is the multiplicative identity because a × 1 = a for every integer a.

11

Step 1: The expression is 18 ÷ 6 + 4 × 2. Using DMAS, we do Division first, then Multiplication, then Addition, then Subtraction. Step 2: Division: 18 ÷ 6 = 3. Expression becomes: 3 + 4 × 2. Step 3: Multiplication: 4 × 2 = 8. Expression becomes: 3 + 8. Step 4: Addition: 3 + 8 = 11. Final Answer: 11. A common mistake is doing addition before multiplication, which would give a wrong answer.

Negative

Step 1: We need to find the sign when 5 negative integers are multiplied. Step 2: The rule is — the product of an ODD number of negative integers is always NEGATIVE. Step 3: The product of an EVEN number of negative integers is always POSITIVE. Step 4: Since 5 is an odd number, the product of 5 negative integers will be negative. Final Answer: Negative. For example, (-1) × (-1) × (-1) × (-1) × (-1) = -1, which is negative.