Math Practice: Solving the Viral Math Problem 100÷4(2+3) using the distributive property

[@bradleyreed8876]

If the problem were written 100 ÷ 4x would you still say the answer was 25x ? if so, why not 25/x ?

[@michealjackson1047]

Love it you explain it very nicely!

[@84com83]

I agree - "A terribly written problem!"

[@greenhornet5186]

I thought what is in the parentheses comes first?

[@mathedupshow]

Yes they do, but a lot of solvers wanted to use the distributive property.

[@LongBeachDragon]

1) Your caption says 110, but your video shows 100. 2) Because multiplication is commutative, the distributive property works. 100 / 4(2+3) using distributive is 100/[(4*2}+(4*3)] = 100 / 8+12 = 100/20 = 5. 3) You are correct, though that you cannot distribute the 100, which is simply because there is an operator between the 100 and other terms. 4) 100 / 4x = 25/x, so that doesn't work that way.

[@mathedupshow]

Thanks for the catch!

[@RealMesaMike]

Well, I'll agree that appealing to the Distributive Property is wrongheaded n this example. But here's my musing on the issue: The issue is a bit bigger than just a number bumped up against parentheses. It's the implied multiplication of any type that is the real issue, which could take several forms, such as a number up against a variable, a number up against a symbolic constant (such as π), two variables against each other , etc. Values arranged in this kind of juxtaposition are generally seen (at least by professionals -- scientists and engineers) as being more tightly bound to each other (thus at a higher operator precedence) than values connected by explicit operator symbols. Yes, I know that grade school math teachers are fairly oblivious to this common usage in the Real World, and that's a shame, and it should not be. If it was really meant that the quantity 100÷4 is to be implicitly multiplied by the contents of the parentheses, then it should be indicated that it is to be treated as a single value with respect to the parenthetical expression by enclosing it within parentheses itself. That makes it really clear. Yes, the example problem is, as you state, "horribly written." It should be rejected outright as nothing but gibberish and one should call attention to that fact rather than trying to insist there is a way to "solve it" using simplistic and rigid "rules.". We're not likely to ever encounter such an expression while trying to solve a real world problem anyway, unless, perhaps, accompanied by some context that makes it clear what the expression actually means and how we came up with it. If there were a Society to Stamp Out PEMDAS and "Order of Operations," I'd be a card-carrying member. There are better ways to teach operator precedence in mathematics.

[@jhines0042]

The thing is that it has been taught both ways and so there is sometimes a generational difference and sometimes just a locality difference. So -- the problem is written ambiguously. I was taught that the 4(2+3) had an IMPLICIT multiplication that was considered to be part of the parenthesis operation for the purpose of PEMDAS priorities. Since it wasn't written 100 / 4 * (2 + 3) but was 100 / 4(2+3) the 4(2+3) was one unit and was resolved at parenthesis priority in the PEMDAS ... then the explicit division happens second. But ultimately it is NOW considered ambiguous or unclear as you said.