Question

There was a 6 square foot piece of wrapping paper for a birthday present. It takes 3 3/8 square feet of the paper to wrap the present. How many pieces of 6 square-foot paper are needed to wrap 3 of these presents?

Answer 1

The answer is 2 pieces of paper.

This can be solved using the proportion.
For one present we need 3 3/8 square feet which is the same as 27/8 square feet:
$3 \frac{3}{8} =3+ \frac{3}{8} = \frac{3*8}{8} + \frac{3}{8}= \frac{24}{8}+ \frac{3}{8}= \frac{27}{8}$

If 27/8 square feet are needed for 1 present, how many square feet are needed for 3 presents:
27/8 : 1 = x : 3
After crossing the products:
x = 27/8 * 3 = 81/8

For 3 presents we need 81/8 square feet.
The second equation should look like this:
If 1 piece of paper is 6 square foot big, how many pieces of paper will be 81/8 square feet big:
1 : 6 = x : 81/8
After crossing the products:
6x= 81/8
⇒ $x = \frac{81}{8} /6 = \frac{ \frac{81}{8} }{ \frac{6}{1} } = \frac{81*1}{6*8} = \frac{81}{48} = \frac{48+33}{48} = \frac{48}{48} +\frac{33}{48}= 1+\frac{33}{48}=1\frac{33}{48}$
$1\frac{33}{48}$ is almost 2, therefore, for 3 presents two 6 square foot pieces of the paper are needed.