A proof problem?

Question

5 * 8 + 8
Exactly how and why does this become (5+1) * 8 ?
Where did the 1 come from?

Answer 1

You know that 8 is 1*8, so 5*8+8 = 5*8+1*8=(5+1)*8

Answer 2

Use the distributive property.

5 * 8 + 8 = (5 * 8 ) + (8 * 1) (identity property of 1)
(5 + 1) *8 (factor out the 8)

Check both sides of the original equation for equality.

40 + 8 = 40 + 8

Quod Erat Demonstratum/Quite Easily Done

Answer 3

8( (5*8)/8 +(8)/8 ) divide by 8 and put on outside of bracket

8(5+1) simplified

b/c you multiply the number on the outside of the brackets to both terms inside
so 5*8 is the same as 8(5) and 8 is the same as 8(1)

Answer 4

5*8 + 8
= 5*8 + 1* 8
= (5+1) * 8

looking otherway

5 * 8 + 8
= 8(5+8/8) or 8*(5+1)

Answer 5

(5 x 8) + (8)------Common factor of 8
= 8.(5 + 1) or (5 + 1).8
= 8 x 6
= 48

Answer 6

look at what you have then look at what you need.

solve what you have for something completely different

40+8=48

now 8*6=48... right? good
now 5+1=6 so 8(5+1)

Answer 7

Proof:
Given variables A and B, which are elements of the real numbers, and the statement (A*B) + B, the B can be factored out of both terms to yield (A+1) * B due to the property of distribution among algebraic terms.

lamens example:
just factor out the 8 from both terms

Answer 8

In structures such as a field, there are two operations defined on the non-empty set. You can call these anything you choose - as Bertrand Russell said, mathematics isn't about anything, but it is consistent. So call the two operations addition and multiplication. In some cases, these two operations 'interact' by exhibiting a property of distribution over the other property. In this case, multiplication is distributed over addition. That's the way it is. So, for a, b, c in R, or I, or Q, for example,
a(b + c) = ab + ac, because multiplication is distributive over addition. QED (Quite Entertainingly Deceptive).