Problem solving for today please!!

Question

an ant was climbing up a 24 - foot tall tree. The first hour it climbed 1/16 of the way up , the second hour it climbed 1/4 of the rest of the way up. The third hour it climbed 1/5 of the remainder of the way up . what fractional part of the trees height was left to climb?

Answer 1

The word “of” usually means multiply.

The ant climbed (1/16)*24 in the first hour.

The ant climbed (1/4)*[ 24 - (1/16)*24) ] the second hour.   (note: “of the rest of the way”

In the third hour:  (1/5)*{ 24 - (1/4)*[ 24 - (1/16)*24) ] }

What was left:    24 - (1/5)*{ 24 - (1/4)*[ 24 - (1/16)*24) ] }

 

Now, we could save some calculations later if we realized that 1-1/16 is 15/16 and 1-1/4 is 3/4 and 1-1/5 is 4/5.  And, since the problem is always stated as a fraction of what is left, we could say that the amount left is (4/5 of 3/4 of 15/16 of 24):

      (4/5)*{ (3/4)*[ (15/16)*24 ] }               (note: work out the 1-X if you have to)

 

You may cancel first to make this:

             (3*3*3)/(2) = 27/2 feet = 13.5 feet

Answer 2

Hi R,

 

How far did the ant climb in the first hour?

 

the tree is 24 ft and the ant climb 1/16 of that distance.

 

so in the first hour the ant climbed 24 * 1/16 = 24/16 or 1.5 ft

 

How far did the ant climb in the second hour?

 

the ant climbed 1/4 of what was left, so 1/4 of (24-1.5).

 

1/4 * (48/2 - 3/2)  = 45/8  or 5.625 ft

 

How far did the ant climb in the third hour?

 

the ant climbed 1/5 of what was remaining.

 

the amount remaining is (24 - 3/2 - 45/8)  

 

lets get a common denominator for these fractions, it will be 8

 

so we have 192/8 - 12/8 - 45/8  = 135/8

 

now the ant climbed 1/5 of this amount

 

so 1/5 * 135/8  = 27/8   

 

but the question asks for what is left to climb

 

so it would be 135/8 - 27/8 = 108/8 or 27/2 or 13.5 ft.

 

 

if we add up all the parts that he climbed it should equal 10.5 ft since the amount climbed plus the amount remaining must equal 24 ft

 

lets add the parts he climbed to check our work

 

3/2 + 45/8 + 27/8   get a common denominator of 8

 

12/8 + 45/8 + 27/8 = 84/8 or 10.5 ft  and that checks with what we expected.

 

Hope this helps.