Sonal writes 15 ÷ 0 = 0 in her notebook. Why is this wrong?

Class 6Whole NumbersWhole Numbers

ABecause 15 ÷ 0 = 15
BBecause 15 ÷ 0 = 1
CBecause 15 ÷ 0 = 0 only when 15 is replaced by an even number
DBecause no whole number multiplied by 0 gives 15, so 15 ÷ 0 has no value at all

Step-by-Step Solution

Division asks which number, multiplied by the divisor, gives the dividend. Here we would need a number that multiplied by 0 gives 15, but every number multiplied by 0 gives 0. So 15 ÷ 0 is not defined; it does not equal 0, 1 or 15. Sonal has confused 15 ÷ 0 with 0 ÷ 15, which really does equal 0.

Answer: D) Because no whole number multiplied by 0 gives 15, so 15 ÷ 0 has no value at all

Key idea: Properties of whole-number addition and multiplication

**Commutative**: a + b = b + a, and a × b = b × a. Order does not matter for addition or multiplication.

**Associative**: (a + b) + c = a + (b + c), and (a × b) × c = a × (b × c). Grouping does not matter.

**Distributive**: a × (b + c) = a × b + a × c. Multiplication 'distributes over' addition. This is one of the most useful rules in all of maths.

**Identity**: a + 0 = a (zero is the additive identity), and a × 1 = a (one is the multiplicative identity).

**Multiplying by zero**: a × 0 = 0 for every whole number a.

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