Practice30Create account

The water level of a check dam near Solapur falls 4 cm on each of 9 dry days, then rises 6 cm on each of 3 rainy days. What is the net change in the level?

Class 7Integers (Extended)Integers
  • A−18 cm
  • B−54 cm
  • C18 cm
  • D2 cm

Step-by-Step Solution

Dry days contribute 9 × (−4) = −36 cm and rainy days 3 × (+6) = +18 cm. The net change is −36 + 18 = −18 cm, so the level ends 18 cm lower than it began. Answering −54 treats the rise as one more fall; 18 cm has the right size but the wrong sign; 2 cm comes from adding the two rates (−4 + 6) without ever multiplying by the numbers of days.
Answer: A) −18 cm

Key idea: Properties — same as for whole numbers, mostly

Integers obey:
- **Commutative** for addition and multiplication: a + b = b + a; a × b = b × a.
- **Associative** for addition and multiplication: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c).
- **Distributive**: a × (b + c) = a × b + a × c — and this is true even when a, b, c are negative.

Subtraction and division are NOT commutative or associative for integers (they aren't for whole numbers either). Order and grouping matter.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Integers (Extended) practice questions

More Class 7 Integers (Extended) practice

Which statement about the integer 0 is FALSE?Six friends jointly ran a food stall at a Diwali mela in Indore and ended with a loss of…What is the value of (−12) × (−7) × (−3) × (8 − 8) × 25?Starting at 0, Kabir makes the equal orange jumps on the number line and stops at the…In this multiplication grid, each cell is the row number times the column number. What…