Whole numbers are distributive and not distributive under?with example.
integers are distributive and not distributive under?with examples.
rational numbers are distributive and not distributive under? with examples.
Answers
Answer:
Step-by-step explanation:
The distributive property of multiplication over addition is a×(b+c)=a×b+a×c.
Example 1: 3×(2+5) = 3×2+3×5 because,
3×(2+5) = 3×7 = 21
3×2+3×5 = 6+15 = 21
The distributive property of multiplication over subtraction is a×(b−c)=a×b−a×c.
Example 2: 3×(5−2) = 3×5−3×2 as,
3×(5−2) = 3×3 = 9
3×5-3×2 = 15-6 = 9
To conclude, let us look at the chart of properties of whole numbers given below to understand which property is applicable to which operation.
properties of whole numbers
Distributive Property of Multiplication Over Addition:
In case of any three integers x, y and z, x × (y + z) = (x × y) + (x × z).
Ex: – 3 (4 + 5) = –3 (9) = –27
= (– 3 × 4) + (– 3 × 4)
= (– 12) + (– 12)
= – 24.
Distributive Property of Multiplication Over Subtraction:
In case of any three integers, x, y and z, x × (y - z) = (x × y) – (x × z).
Ex: – 3 (5 – 4) = – 3 (1) = – 3
= (–3 × 5) – (– 3 × 4)
= (– 15) – (– 12)
= – 3.
The distributive property of multiplication over the addition and subtraction holds true in the case of integers.
Distributive property states that for any three numbers x, y and z we have
x × ( y + z ) = (x × y) +( x × z)