Operations with Integers: questions with answers

The pair is -10 and 3. Their sum is -7, and first minus second is -13. Reversing them changes the sign of the difference, so 3 cannot be the first integer here.

5 and -13. Reversing the order preserves the sum -8 and changes the difference from -18 to 18. The pair must satisfy both conditions; matching the sum alone is insufficient.

Subtracting a number means adding its additive inverse. The additive inverse of -14 is 14, so the equivalent addition is 5 + 14.

Add the signed movements: 8 + (-13) = -5. The longer leftward movement takes the coin past zero. Adding the magnitudes gives total distance travelled, not final position.

The downward displacement is 40 × (-3) metres. Add it to the starting position: 25 + 40 × (-3) = -95. The lift finishes 95 metres below ground.

Correct answers contribute 16 × 3 marks. Wrong answers contribute 14 × (-2) marks. Add these signed contributions: 16 × 3 + 14 × (-2) = 20. Subtracting the negative penalty would add marks instead of deducting them.

Add enough zero pairs, each containing one positive and one negative token. Each pair represents zero, so this supplies tokens without changing the initial value. Removing the required positive tokens then leaves a negative total.

There are 2 rounds of 9 positive-token removals, or 18 positive tokens in total. Each zero pair supplies one positive token, so at least 18 pairs are needed. Extra pairs could be added but are unnecessary.

The new product is the old product minus -6. Subtracting this negative number increases the product by 6. The same change occurs for positive, zero and negative values of m.

Decreasing the first factor by 1 subtracts one copy of -7 from the product. Since -7 is negative, the product increases by 7, giving -7.

The quotient of two negative numbers is positive: a negative divisor multiplied by a positive quotient gives the negative dividend. In the chapter terminology, the quotient of two debts is a fortune.

Divisor × quotient must equal dividend: (-6) × 12 = -72. The negative divisor -6 multiplied by positive 12 gives the negative dividend -72. Interchanging divisor and dividend does not check this division.

There are 2 negative factors. Each pair of negative factors has a positive product. All negative factors form pairs, so the product is positive. Positive factors do not change this sign.

Multiply the magnitudes: 6 times 7 is 42. One factor is negative and the other is positive, so the product is negative: -42. The factor order does not change the result.

Multiply each term of the sum by the outside factor, then add the products: (-4) × 11 + (-4) × (-5). Multiplying only the first term leaves out one required multiplication. Replacing the addition with multiplication changes the operation.