## Lesson 1: Integers. Answer to the Tricky Exercise (VI)

October 24, 2011

Isabel was right. Given two numbers, a and b, it is always verified the product

L.C.M(a,b) · H.C.F.(a,b)= a · b

The product of H.C.F and L.C.M. of two numbers is 9072. If one of the numbers is 72, we will find the other applying the result before. If we divide 9072 by 72 we obtain 126.

The question is why?. Because if we want to get L.C.M(a,b) we choose all the factors with the greatest exponent they appear and when we get H.C.F.(a,b) we choose the common factor with the smallest exponent they appear. Multiplying L.C.M(a,b) · H.C.F.(a,b) we find repeated factors but their  product coincides perfectly with a · b where there are the same repeated factors and the factors corresponding to L.C.M(a,b) and  H.C.F.(a,b). Check it with L.C.M(15,45) · H.C.F.(15,45) , for instance

Congratulations Isabel and Lydia! Thanks for your effort Javier. There will be extra points for everybody!

## Lesson 1: Integers. Lyrics and a Tricky Exercise (V)

October 8, 2011

Thanks for your translations. All of them were close to the right translation. There are two points:

Chips, in this context,  are some “little stones or plastic pieces” used to do calculations with integers in an intuitive way. Fried potatoes would not be appropriate.

To mix something up  means confundir con.

Here you are the lyrics and the  rap again

Integers Rap

I-N-T-E-G-E-R

When you know us

you’ll be a star.

I-N-T-E-G-E-R

This is the kind of numbers we are.

Positives, negatives and zero

Positives, negatives and zero

Get to know us

you’ll be a math hero

Use a number line and chips

When you do it so fast

And flips, and flips, and flips.

Multiplying and dividing use the rules

Don’t mix them up

Use the rules.

I-N-T-E-G-E-R

When you know us

you’ll be a star.

I-N-T-E-G-E-R

This is the kind of numbers we are.

Positives, negatives and zero

Positives, negatives and zero

Positives, negatives and zero

Positives, negatives and zero

Get to know us

you’ll be a math hero

Get to know us

you’ll be a math hero

Multiplying and dividing use the rules

Don’t mix them up

Use the rules.

### A tricky exercise

The product of H.C.F and L.C.M. of two numbers is 9072. If one of the numbers is 72, find the other number. Justify your answer.