Algebra Puzzle ~ Climb the Pyramid

Today, I have two algebraic puzzles for all the algebra buffs among you: Climb the Pyramid and Label the Fractions on the number line.

But before we jump into it like to mention May Kacharava who usually writes a post each Monday. Today, May is on her well deserved summer vacation. While she relaxes on the beach, I like to pick up on her article campaign labeled cute geometry she created so masterful back in May and June earlier this year.

Now, let’s have some algebraic puzzle fun!

Climb the Pyramids
In this algebraic puzzle you need to combine the like terms in the pyramid found below:

Start with the empty field on the 2nd row and walk your way all the way to the top.

To give you a hint, the missing field on right-hand side at the 2nd row can be found by combining the 3rd and 4th fields from the bottom row. That is:

(3x-2)  +  (x+2)  =  (3x+x)  +  (-2+2)  =  4x + 0 = 4x

Simple, or what?

Fractions on the Number Line
There are six number lines each missing one label as shown in the picture below:

Your task is to deduce the missing label from the already existing labels. Note the length of the number line is in each case 1, or more precisely the interval from 0 to 1.

Let’s find the missing label on the first number line together. 1/3 is given, there is only one more label in the middle between 1/3 and 1. Thus, the missing label has to be 2/3.

Should these two algebra puzzles be too hard, ask one of our algebra tutor for help. They are smart and good-hearted tutors. Give them a try!