4 x 5 (30 / 6) + 5

Question

So, I have had a debate with a few colleagues of mine. Between us all, we’ve came up with two different answers. 105 & 25 being the answers. VERY IMPORTANT... the “/“ *division* symbol between the 30 and the 6 inside the parentheses is and actual division sign (a colon symbol with a horizontal line in between the dots). Not a fraction symbol creating a numerator or denominator. I’ve had it explained by both parties on how they got to their answers. One person solved parentheses first by the 30 divided by 6 = 5. Then finished problem left to right. 4x5x5+5= 105. Then the other solved it by distributing the 5 to each variable inside the parentheses. Therefore 4x(5x30)divided by(5x6)+5. Which he simplified. 4x150divided by30+5. Which = 600divided by30+5. Which of course is 25. Both ways explained makes sense. So what’s the real answer?

Answer 1

You can't "distribute" the 5 that way. To distribute the 5, you would need 5(30+6) or 5(30-6). The correct answer is 105, using order of operations (PEMDAS).

Answer 2

This is a great question!

105 is the correct answer. Yes, you should work in the parentheses first and then work left to right.

Distributing the 5 to both values in the parentheses is incorrect. You would only do this if the terms inside the parentheses were being added or subtracted, not if they are multiplied or divided.

Hope this helps!

Answer 3

I'm not quite sure what you were trying to say with a colon symbol but the first way makes since to me. parenthesis goes first (PEMDAS), left to right for multiplication and division, then addition last:

4 x 5(30/6) + 5

4 x 5 x 5 + 5

20 x 5 + 5

100 + 5

105

The second way pretends that you are multiplying by 5/5 into the parenthesis instead of 5/1 :

4 x 5/5(30/6) + 5

4 x (150/30) + 5

4 x 5 + 5

20 + 5

25

but this was not is not what the problem is, it's really

4 x 5/1(30/6) + 5

4 x (150/6) + 5

4 x 25 +5

100 + 5

105

technically, the first way is the correct order of operations but this helps understand the error of saying 5 is 5/5 when it is 5/1

Answer 4

105 ... there is no "distributive" property of multiplication over multiplication or division. (And any calculator with support for parentheses will get it right.)