Beer saves the day - again. Improper Fractions

21   What do I do with this improper fraction?

 8

You need to change it into a mixed fraction. How do you do this? Well, think of beer. You have 21 bottles but can only carry 8 bottles at a time...

You will make 1 full trip, carrying 8 bottles.

You will make a 2nd full trip carrying another 8 bottles.

You have 5 bottles left.  They do not represent a "full" trip. Your 2 "full trips" become the whole number component of the mixed fraction. 

Your 5 bottles that are "left over" go on the top shelf of the fridge. (That is where all left overs go." Your denominator was 8, so let's keep it at 8. You now have...

2  5

     8    

For a video explanation, start 2 minutes into the video here

S S +, SD - IGNORE the signs!

What is -2 x 3?

When I was taught about multiplying and dividing 2 positive or negative numbers, I was told to remember...

1) A "+" times a "+" is a positive
2) A "+" times a "-" is a negative
3) A "-" times a "+" is a negative
4) A "-" times a "-" is a positive.

The same applies when dividing numbers.

Lots to remember. And statements 2 and 3 are really the same thing. So...

When multiplying or dividing 2 numbers, the first thing to do is...

IGNORE the signs.

They do not exist. For now.

For example... -2 x 3.

Treat this as 2 x 3 = 6. Then remember SS+, SD-

If the signs are the SAME (SS), your answer is positive (+). If the signs are are DIFFERENT (SD), your answer is negative (-). 

In our example, the signs are different so your answer has to be negative. Turn your answer of 6 into -6 and you are done.

Pythagorean Triples - Work Smart, Not Hard!

A lot of triangle questions can be solved without using the Pythagorean Theorem. 

No need to worry about pesky squares and square roots! 

Pythagorean Triples to the rescue!

Some common triples are...

3:	4	:5
5:	12	:13
8:	15	:17
7:	24	:25
9:	40	:41

The first 2 triplets (3:4:5 and 5:12:13) are the most common ones that I have seen on math tests. 

If you have a triangle question that involves two sides being 5 and 12 units in length, then you know the third side is 13 units long. 

Some questions aren't quite so obvious. You might have a triangle with two sides being 6 and 8 units. 

There is no Pythagorean triple with a 6 and 8 in it. 

However, 6 and 8 are just double the 3 and 4 in the 3:4:5 ratio. The third side is double 5... 10! If your triangle question involves 26 and 24, the third side is 10.

Have a Nice Day!

Which one is the numerator and which one is the denominator? A common question, answered easily by "Have a Nice Day." N, D - Nice Day, Numerator, Denominator.