Here is the first one.

Question

The first wave knocked into the water,

a gold coin, which sank to −12 foot below the surface.

a bronze cup, at −14 foot.

a silver necklace, at −58 foot.

a copper coin, at −78 foot.

 

Meg needs to recover the deepest treasure first. Can you help her locate the treasures on the number line? Which one is deepest?

Answer 1

Convert to eighths:

1/2=4/8

1/4=2/8

Now we have everything in eighths: -4/8, -2/8, -5/8, -7/8.

The surface of the water is 0, and all the treasure is underwater. The deepest is the biggest negative number: -7/8, where the copper coin is. On a number line we have zero at the right hand end of the line. To the left of zero we have eight subdivisions and the number -1. We can label divisions to the left of zero at -2/8, -4/8, -5/8, -7/8 that is, 2, 4, 5, 7 small divisions to the left of zero. The leftmost is where the copper coin is. Label this division copper, then necklace at 5 divisions to the left of zeros, then gold at 4, then bronze at 2.