Mathematics, 30.01.2021 01:00 kevinmoore2884
The whole numbers a and b are divisible by c. Is a+b divisible by c? Is b−a divisible by c? Explain your reasoning.
Answers: 3
is divisible by 
since 
and 
are also whole numbers. 
is divisible by 
, 
whole number that are divisible by 
and 
, which are also whole numbers. We proceed to prove that 
is divisible by 
Given
Compatibility with addition
Definition of division
Commutative and distributive properties
Commutative properties
Definition of division/Result
Compatibility with multiplication
Compatibility with addition 
Definition of division![e + d\cdot (-1) = b\cdot c^{-1} + [a\cdot (-1)]\cdot c^{-1}](/tpl/images/1079/1532/ffc19.png)
Associative and commutative properties![e + d\cdot (-1) = c^{-1}\cdot [b+a\cdot (-1)]](/tpl/images/1079/1532/45065.png)
Commutative and distributive properties.![e+d\cdot (-1) = [b+a\cdot (-1)]\cdot c^{-1}](/tpl/images/1079/1532/9ca0c.png)
Commutative properties.
Definition of division
/Definition of subtraction
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The whole numbers a and b are divisible by c. Is a+b divisible by c? Is b−a divisible by c? Explain...
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