There are 7 2/3 pounds of bricks in a bag. Each brick weighs 3 5/6 pounds. How many bricks are in the bag?

Question

 I want to learn this by tomorrow.

Answer 1

Since each brick is 3 5/6 pounds we know that there is more than one brick in each bag.  Wouldn't it be nice if there was an even number per bag? 

 

One way to do this is to change your mixed numbers to improper fractions.  To do this for the bag, take the denominator in 7 2/3 and multiply by 7 (3x7 = 21).  Then add the numerator (2) to get 23.  Finally, the denominator will be 3 (the original denominator).  So 7 2/3 = 23/3.  Do the same thing for the brick.  3 5/6 = 23/6.

 

Now you can divide the pounds of bricks per bag (23/3) by the pounds in each brick (23/6).

23/3 divided by 23/6.  Turn this into a multiplication problem.  23/3 x 6/23.  23 goes into 23 one time.  6/3 = 2 bricks per bag.

Answer 2

Hi Tammy!

 

2 bricks, and here's why:

 

Make the 2 fractions 'talk to each other' by using a common denominator. Change the first weight to 7 4/6.

 

Then, since you can't subtract 4/6 - 5/6, turn both mixed numbers into improper fractions:

 

7 4/6 becomes 46/6 and 3 5/6 becomes 23/6.

 

46/6 - 23/6 = 23/6.

 

In other words, 23/6 + 23/6  (two equal "bricks") = 46/6, or the full weight of 7 4/6, or 7 2/3.

 

Hope this helps!

 

Matt

Answer 3

Tammy,

  You have reached that "teachable moment" that a good tutor/teacher lives for (but, obviously, can't force to happen although there are good approaches).  This is great!!

 

The key to problems like this is simple:  Get the units correct !

 

Here's what the problem gives you:

     7 2/3 pounds per bag.       that is.     (7 2/3) pounds/bag

    3 5/6 pounds per brick.      that is,     (3 5/6) pounds/brick

    How many bricks?

 

    (pounds/bag) / (pounds/brick) will give brick

            To divide by fraction, invert denominator and multiply:

                  (pounds/bag) * (bricks/pound)    gives us bricks/bag   [note: there is 1 bag]

 

Let's do this:

   ( (7 2/3) pounds/bag ) / ( (3 5/6) pounds/brick )

      (7 2/3) / (3 5/6)  bricks

      (23/3) / (23/6)  bricks     

         [note: to change mixed number to improper fraction, multiply the whole number by the denominator of the fraction and then add the numerator of the fraction.  Thus,3*7=21 then add 2 gives 23/3).

     (23/3) * (6/23) bricks             [invert and multiply]

             2 bricks                     [cancel like mad, because teachers make up easy problems]

 

Now, just to build your confidence:

 

If a bag weighs 6 2/3 pounds and each stone weighs 1 1/3 pounds, how many stones are there in the bag?