NCERT Solutions Class 7 Maths Chapter 10 — Integer Operations

Solution:

Step 1: When multiplying two integers with different signs (one positive and one negative), the product is always negative.

Step 2: For example, 5 × (-3) = -15 or (-2) × 7 = -14. The sign of the product is consistently negative.

Solution:

Step 1: When multiplying two negative integers, the product is always positive.

Step 2: First, multiply their absolute values: 9 × 7 = 63.

Step 3: Since both integers are negative, the product is positive. So, (-9) × (-7) = 63.

Solution:

Step 1: The temperature change per hour is -3°C.

Step 2: For 4 hours, the total change will be 4 × (-3°C).

Step 3: Multiplying a positive integer (4) by a negative integer (-3) gives a negative product: 4 × (-3) = -12°C.

Solution:

Step 1: Rohan is correct. When multiplying a negative integer (-8) by a positive integer (6), the product is always negative.

Step 2: The rule 'two negatives make a positive' applies only when multiplying two negative integers. Here, one integer is negative and the other is positive.

Step 3: So, (-8) × 6 = -48.

Solution:

Step 1: When multiplying an even number of negative integers, pairs of negatives cancel out their signs, resulting in a positive product. For example, (-2) × (-3) = 6.

Step 2: When multiplying an odd number of negative integers, there will always be one negative sign left over after pairing, resulting in a negative product. For example, (-2) × (-3) × (-4) = -24.

Step 3: Therefore, if the number of negative integers is even, the product is positive.