Break apart and distribute to solve 72÷8 72÷8=(40÷8)+(32÷8) 9=5+4 9=9
2 answers:
Answer:
72 ÷ 8 is equal to 9
Step-by-step explanation:
If we want to solve 72 ÷ 8 by breaking apart and distributing, the first step is to write the number ''72'' as the sum or subtraction of two numbers that are divisible by ''8''.
We can write :
If we replace this last expression in the original one :
72 ÷ 8 = (40 + 32) ÷ 8 (II)
Now in (II) we can use the distributive property of the division :
(40 + 32) ÷ 8 = (40 ÷ 8) + (32 ÷ 8) (III)
Finally, we need to solve the expression (III) :
(40 ÷ 8) + (32 ÷ 8) = 5 + 4 = 9
We find that 72 ÷ 8 is 9 by breaking apart and then distributing.
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Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.