Divisibility by 3, Divisibility by 9

During math tutoring, no matter what the level, the front line is arithmetic.

In that spirit, here’s a handy trick to tell if a number is divisible by 3:

Add up the digits.  If the sum is divisible by 3, then so is the original number.

Example:  consider the number 222.  2+2+2=6.  Since 6 is divisible by 3, so is 222.  (Many people might not expect that.)  In fact, 222 ÷ 3 = 74.  (Check for yourself.)

A similar law works for 9:  if the digits add up to something divisible by 9, then the original number is also divisible by 9.

Example:  consider 414.  4+1+4 = 9, so 414 is divisible by 9.  So is 864, since 8+6+4=18, and 18 is of course divisible by 9.

Of all the math tricks I know, these are two of the most useful.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

French: passé composé, imparfait, and plus-que-parfait: when to use them.


Well, today I thought we’d discuss some French:  specifically, the passé composé, the imparfait, and the plus-que-parfait.  In what situation do you use each?

The passé composé is the first way to express the past tense that I learned in high school.  It is the French equivalent to the English verb with -ed (eg., I walked).  The passé composé has two parts:  the auxiliary, followed by the past participle.

The imparfait expresses, as my French teachers always explained, “a state of things that had no particular beginning.  It may not yet be finished.”  For instance, “When I was young ….”  Additionally, “It was raining….”  Both use the imparfait tense.  In French, it’s among the easiest constructions, consisting of a stem with a subject-specific ending.

The plus-que-parfait expresses a completed action that happened before another completed action.  Consider  the sentence:  “I had finished the laundry when you called.”  “I had finished” is the plus-que-parfait tense, whereas “you called” is the passé composé.

Well, there you have it:  the passé composé, the imparfait, and the plus-que-parfait.  My wife (who is French and does our French tutoring) explained them to me.

Have a great day.  Come again.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Simplifying Radicals…part I

Hello.  One of the most dreaded topics in high school math – as you’ll quickly find out if you do math tutoring – is radicals.

Well, here’s our first math post: simplifying radicals. Today, we’ll look at square roots only.

For example, consider the following:

Simplify √90

Well, here’s what we do:

1)  Find the number that divides into 90 and is “square rootable”.

In this case it’s 9, since √9 is exactly 3.

2)  Realize that √90 =  (√9)(√10)

Since 9×10=90.

3)  Replace √9 with 3.

(√9)(√10) = 3√10

So √90 = 3√10.

This is a basic case of simplifying a radical.

Come back for more hints.  Have a great day!

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Testing, testing…

Good afternoon.  This is the first blog entry by Oracle Tutoring, Campbell River, BC.  We tutor math, chemistry, physics, biology 12, English, French, and science.

We will be doing posts that help with specific problems or queries in the subjects above.

Thanks for coming.  Please visit again soon!