This is a two point question,
where 1 point is given for the answer of yes or
no and then another point for your explanation and
support of your answer.
Let's begin this problem by making sure we understand
what it is we are looking for. You know that Mike
is putting lights around his patio which has 6 sides
of different lengths. He needs the wire to go around
all six sides. He cuts the wire at 50 feet and you
need to find out if 50 feet of wire is enough wire
to install the lights.
The information you are given are the lengths of
the 6 sides, 2 3/4 feet, 10 1/2 feet, 8 1/4 feet,
9 5/8 feet, 12 3/4 feet, and 7 1/4 feet. You also
know that you really only have 50 feet of wire to
go around the this patio.
To better see the solution, it may be easier to
make a simple drawing of the patio.
One way to see if 50 feet is even close is to make
an estimate by doing some rounding of the lengths
of the sides. So, you would end up with:
3 ft + 11 ft + 8 ft + 10 ft
+ 13 ft + 7 ft = 52 ft
With the estimation, it appears Mike may not have
enough wire. But you better finish solving this
one so that Mike knows whether or not to spend his
time putting up the wire or not.
Solving the problem, you need to rewrite the fractions
as equivalent fractions with the common denominator
of 8. Then add the mixed numbers. The six sides
rewritten look like this:
2 6/8 + 10 4/8 + 8 2/8 + 9
5/8 + 12 6/8 + 7 2/8
Add the whole numbers first.
2 + 10 + 8 + 9 + 12 + 7 =
48
Now add the fractions.
6/8 + 4/8 + 2/8 + 5/8 + 6/8
+ 2/8 = 25/8
Rewrite 25/8 as a mixed number.
3 1/8
Now you add 48 + 3 1/8 which equals 51 1/8.
As you look at your answer you
notice that the distance around the patio is 51
1/8 feet. Since Mike cut the wire at 50 feet, he
won't have enough wire to install the lights around
the patio. Looks like Mike should have done some
math first before cutting the wire! |
