7 Math Mistakes to be Aware Of

April is Math Awareness Month, and some things to be aware of this month — as well as the whole year through — are common math errors. Here are seven that show up frequently.

Incorrect Addition of Fractions. It’s common for kids to add fractions as follows:

$\frac{a}{b} + \frac{c}{d} = \frac{a + c}{b + d}$

And while that algorithm works for batting averages in baseball, it doesn’t work in most other places. More importantly, this mistake is often unaccompanied by reasoning. For example, a student who claims that 2/3 + 4/5 = 7/9 doesn’t realize that with each addend greater than 1/2, then the sum should be greater than 1. That lack of thought bothers me.

Cancellation of Digits, Not Factors. While it’s true that 16/64 = 1/4 and 19/95 = 1/5, students who think the algorithm involves cancelling digits may also argue that 13/39 = 1/9, and that just ain’t right.

Incorrect Distribution. This one takes a lot of forms. In middle school, kids will say that 4(2 + 3) = 8 + 3. As they get older, they apply the distributive property to exponents and claim that (3 + 4)2 = 32 + 42 or, more generally, that (a + b)2 = a2 + b2.

The Retail Law of Close Numbers. A large portion of the population will buy a shirt for $19.99 that they’d pass up if it had a price tag of$20.00. Even though the amounts only differ by one cent, a lesser digit in the tens place makes the price feel much lower. Crazy, but true.

Ignoring the Big Picture. If you are a driver who is interested primarily in speed (and less concerned with price, looks, fuel efficiency, or other factors), would you rather have a vehicle with 305 horsepower or one with 470 horsepower? If you chose the latter option, congratulations! While the owner of a sweet 305-hp Ford Mustang will be sitting at home and sipping a mint julep on his front porch, you’ll still be doing 30 mph on the highway in your Sherman tank.

Correlation Implies Causation. As ice cream sales increase, the number of drowning deaths increases, too. But that doesn’t mean that having an ice cream cone willl make you less likely to swim safely, even if you failed to heed your mother’s advice to wait 30 minutes after eating. It’s just that ice cream sales and swimming-related deaths increase in summer, both of which are to be expected.

Just because two things happen to coincide doesn’t mean that one is the direct (or even indirect) result of the other.

Percents Don’t Work That Way. A 20% decrease followed by a 20% increase does not return you to the initial value. If you invest $100 in a company, and it loses 20% the first year, your investment will then be worth$80. If it gains 20% the next year, you’ll now have $96. Uh-oh. What common math error do you see frequently, and which one bothers you the most? Entry filed under: Uncategorized. Tags: , , , , , , , , . 2 Comments Add your own • 1. xander | April 4, 2013 at 1:32 pm Maybe it is a bit higher level, but $\frac{d}{dx} \frac{f(x)}{g(x)} \ne \frac{f'(x)}{g'(x)}$. 😦 • 2. venneblock | April 4, 2013 at 7:48 pm Quite all right, Xander… around these parts, we like high-level math, too! (And just so you know, if you use LaTeX in a post, you have to put the word “latex” inside the left dollar sign; e.g., you’d enter$latex xxxxx\$ to display xxxxx in $\LaTeX$.)

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