calculate and verify using distributive law over addition 4×(3+8) Rela...
Calculating and Verifying Distributive Law over Addition
Problem Statement
Calculate and verify using distributive law over addition 4×(3+8).
Solution
According to the distributive law over addition:
a × (b + c) = a × b + a × c
Therefore, we can apply this law to 4 × (3 + 8) as follows:
4 × (3 + 8) = 4 × 3 + 4 × 8
12 + 32 = 44
Verification
We can verify our answer using the Closure Property of Integers under Addition and Subtraction. This property states that if a and b are integers, then a + b is also an integer.
In our case, 3 and 8 are integers, so their sum, 11, is also an integer. Therefore, we can rewrite the expression 4 × (3 + 8) as:
4 × (3 + 8) = 4 × 11
44
As we can see, both our calculated answer and verified answer are the same, which confirms the validity of our solution.