Question

Define associativity of addition, subtraction, multiplication and division for whole numbers.

Answer 1

Associativity for addition:

a + (b + c) = (a + b) + c;

For whole number, addition is associative.

For example: a = 1, b = 2 and c = 3,

a + (b + c) = 1 + (2 + 3) = 6

(a + b) + c = (1 + 2) + 3 = 6

So, we can say that a + (b + c) = (a + b) + c

Associativity for subtraction:

a - (b - c) = (a - b) – c

For whole number, subtraction is not associative.

For example: a = 5, b = 7 and c = 3,

a - (b - c) = 5 -(7 – 3) = 5 – 4 = 1

(a - b) – c = (5 – 7) – 3 = -2 -3 = -5

a - (b - c) ≠ (a - b) – c

Associativity for Multiplication:

a × (b × c) = (a × b) × c

For whole number, multiplication is associative.

For example: a = 5, b = 7 and c = 3

a × (b × c) = 5 × (7 × 3) = 5 × 21 = 105

(a × b) × c = (5 × 7) × 3 = 35 × 3 = 105

a × (b × c) = (a × b) × c

Associativity for Division:

a ÷ (b ÷ c) = (a ÷ b) ÷ c

For whole number, multiplication is associative.

For example: a = 5, b = 7 and c = 3

5 ÷ (7 ÷ 3) = 5 ÷ ($\frac{7}{3}$) = 5 × $\frac{3}{7}$= $\frac{15}{7}$

(5 ÷ 7) ÷ 3 = ($\frac{5}{7}$) × ($\frac{1}{3}$) = $\frac{5}{21}$

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

associative is not valid for division