Question

Distributivity of multiplication over Addition ane subtraction

For all rational numbers a, b and c ,

a(b + c ) = ab + ac
a(b - c ) = ab - ac ​

Answer 1

Answer:

Distributive property of multiplication over addition and subtraction for rational numbers

The distributive property of multiplication is:

Over addition: a(b + c) = ab + ac

-3/4 {2/3 + (-5/6)} = -3/4 {(4+(-5))/6} = (-3/4) x (-1/6) = 3/24 = 1/8

-3/4 {2/3 + (-5/6)} = -3/4 x 2/3 + (-3/4) x (-5/6) = -1/2 + 5/8 = (-4+5)/8 = 1/8

Over subtraction: a(b - c) = ab - ac

-3/4 {2/3 - 5/6} = -3/4 {(4-5)/6} = (-3/4) x (-1/6) = 3/24 = 1/8

-3/4 {2/3 - 5/6} = -3/4 x 2/3 - (-3/4) x 5/6 = -1/2 + 5/8 = (-4+5)/8 = 1/8

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Answer 2

The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can subtract the numbers and then multiply, or you can multiply and then subtract as shown below. This is called “distributing the multiplier.”