Can You do the Math?

by Forrest M. Mims III

Eighth graders in British Columbia back in 1890 were expected to pass a difficult exam if they wished to continue on to high school. Similar exams were given to US high school hopefuls.

Let’s look at the math section of the test. Here’s a question that requires a knowledge of algebra:

“Three men, A, B, and C, start together from the same place to walk around an island 60 miles in circumference; they walk in the same direction, A at the rate of 5 miles per hour, B at 4, and C at 3. In what time will all be together for the first time after starting, and how many miles will each have traveled?”

Two questions concern interest. “Find the compound interest on $500 for 1 year 6 months at 8% per annum, interest payable semi-annually,” and, “What is the present worth of $600 due 8 months 18 days hence at 9% per annum.”

Students could use pencil and paper to answer these and other math questions. The remaining 10 math questions had to be done “mentally” with no pencil and paper.

A few of the mental questions were basic, like, “What is the first prime number below 100?”

A prime number can be divided only by one and itself. This rules out 99 and 98. 97 can be divided only by one and itself, so 97 is the correct answer. No pencil needed.

This mental question is tougher: “If 3/8 of a ton cost $13.50, what will 5/9 of a ton cost?”

One solution is to first find the cost for a full ton by mentally dividing $13.50 by 3 to find that 1/8 ton cost $4.50. Then multiply $4.50 x 8 to find the cost for a full ton: $36.00.

Next, find the price for 1/9 of a ton by dividing $36.00 by 9. The result is $4.00. Finally, multiply 5 x $4.00 to get the answer: $20.00. No pencil needed.

Some of the remaining mental questions are more difficult. Can you mentally figure what 225 hats will cost at $.66 2/3 each? (Hint not in the exam: Each hat costs 2/3 of a dollar.)

Can you mentally determine the simple interest on $1,250 for 2 years and 8 months at 2/3% per month? Can you figure what part of 2/3 of 3 ½ is 5/9 of 4 1/2–-without pencil and paper?

Those who say that calculators make number skills obsolete should look at China and India. Their students score much higher in math than ours, and they are competing for the same high-tech jobs. Students need both number and calculator skills.

Forrest M. Mims III and his science are featured online at www.forrestmims.org and www.sunandsky.org.

This feature was originally published in Forrest Mims's weekly science column in the Seguin Gazette-Enterprise, Seguin, Texas. The column is written for a general audience.