## Monday, September 3, 2012

### Scary fractions

On a social forum, an acquaintance related a story about the meat counter.

She had a conversation with the man about what the smallest amount of meat she could buy.

The guy points to the digital scale and says, "It has to read 0.12 on here."

She says, "Ok, that's about an eighth of a pound."

Counter guy says, "No, it's half of a quarter-pound."

She says, "Yes, an eighth of a pound."

At this point, my acquaintance was very frustrated and stopped arguing.

So, who's right?

Let's start with the counter guy's assertion that, "It's half of a quarter-pound."

$$1/2 * 1/4 = (1*1)/(2*4)$$ $$=1/8$$ So, half of a quarter pound is one-eighth of a pound. How does that come out on a digital scale? Well, 1 divided by 8 is 0.125. So, both the counter guy and my aquaintence were correct.

She made a general complaint for math teachers to make certain that students know half of one-quarter is one-eighth.

The problem is, in our digital world, students are becoming more isolated from fractions. People who sew, cook or do carpentry still deal with fractions quite often, but many other people are just using calculators and computers to do digital computations.

When I work with students, I find that many of them try to just completely skip over problems with fractions.

It's as though they think, "OMG! It's a FRACTION! I can't DO fractions!"

The problem is, there are skills you learn when manipulating fractions that come into play later in math. If you didn't learn it when it used numbers and was fairly easy like $$1/3 + 1/2$$, how are you going to deal with $$(x+3)/(x-3) + x^2/(x+2)$$ towards the end of an algebra course?

This relies on knowing the skills of adding fractions with different denominators and extrapolating that out to something more abstract. Knowing the skill that is concrete, that is the one with numbers, will help you see the connection to the more abstract problem. If you do NOT have the concrete skill, learning the abstract one is much more difficult.

This is yet another area where math teachers are making you do stuff so you can apply the information later on. There really is a reason for most of what we do.