Properties of Division Division is the inverse operation of multiplication, meaning that a division operation can be used to undo a multiplication operation...
Properties of Division
Division is the inverse operation of multiplication, meaning that a division operation can be used to undo a multiplication operation. The properties of division allow us to use this property to simplify division problems and solve them more efficiently.
Property 1: Division is commutative.
This means that the order in which we perform division does not affect the result. For example, 5 ÷ 2 = 2 ÷ 5.
Property 2: Division is associative.
This means that we can add the dividend and the divisor before dividing by the same quotient. For example, (5 + 2) ÷ 3 = 5 ÷ (2 + 3).
Property 3: Division is distributive over addition.
This means that we can distribute the divisor to the sum of the dividend and the divisor. For example, 5(2 + 3) ÷ 3 = 5 × 2 + 5 × 3.
Property 4: Division is a multiple of factors.
The factors of a quotient are all the possible factors of the numerator divided by the divisor. For example, the factors of 12 ÷ 3 are 1, 2, 3, 4, and 6.
Using these properties, we can simplify division problems in a variety of ways. For example, 12 ÷ 3 = 4 because 4 × 3 = 12. Additionally, 15 ÷ 3 = 5 because 5 × 3 = 15