# Multiply subtract multiply subtract

Posted on September 29, 2016

Fortunately, for this student that’s not spewing him into Overwhelm.

It’s an ALEKS word problem type;  “There were N houses on sale.   x/y of them were sold one week.   Of the ones remaining, a/b were sold the next week. How many are left?”

He’s a ‘sense maker’ — so he wanted to know why they were explaining it like they were… why was 1/3 of 42 14.   I did my “example with easy numbers so that you can focus on the language” explanation (*why* don’t math materials do this?  Because it actually works???) …. “1/3 of 30 would be 10”   … spelling out how 1/3 0f 30  is the language of multiplying… and it translates into 30 divided by 3.

“So 1/3 of 42 is 14 because 14 + 14 + 14 is 42?”

We have liftoff 🙂

…. 3/8  was confusing, though… but rather than write out the algorithm, we talked through that if 1/8 of 64 was 8… the 3/8 must be 24, and *then* “divide by the bottom, multiply by the top,”   and later on we’ll get to Just Multiplying Ridiculous Random Sized Fractions and we’ll go to algorithm land.