PROBLEMS WITH
FRACTIONS
By Lucretia Gabriel
Grades 9-12/Math Lab
Academy of the Holy Names
Upper School
By
participating in this online activity, you will find some helpful hints for
solving problems or equations involving fractions, mixed numbers or improper
fractions.
Before
you begin, print out a copy of this activity.
As you work, write you information and solve the problems in the spaces
provided.
1.
Go
to http://www.mathleague.com/help/fractions/fractions.htm
Use the information at this site to define and give
an example of a/an:
- fraction - include in your answer an
identification of the numerator and denominator.
- mixed number
- improper fraction
To
solve an equation containing a fraction or a mixed number, first notice whether
addition, subtraction, multiplication or division is involved.
Addition
or Subtraction
Sometimes you have to add or subtract fractions with
different denominators. (If you do not remember what a denominator is be sure
to go back to your definition of a fraction.)
2. Example:
X + 1 ¾ = 12
Recall that the opposite of 1 ¾ must be added to
both sides of the equation. The
opposite of 1 ¾ is –1 ¾. Thus:
X
+ 1 ¾ = 12
-1 ¾ = -1 ¾
X = 12 – 1 ¾
To see how to solve 12 – 1 ¾ go to http://www.coolmath4kids.com
Click
on “fraction lessons”; then click on “Adding and Subtracting Fractions with
Whole or Mixed Numbers”.
3. Example:
d – 7 = 2 ¾
9
In
this example, the opposite of - 7
is + 7 which must be added to both sides of the
9
9
equation.
D – 7 = 2 ¾
9
+ 7 = + 7
9
9
Go
back to http://coolmath4kids.com and identify the
steps to add 2 ¾ + 7.
9
4.
Using
the information you have found, solve these other practice problems. If you need more help, go back to one of the
sites you used or go to http://www.mathXpert.com
and have the problem solved for you. Be
sure to write down the steps and know how the problem was solved.
5 5/6 = 2 ¼ + Y
X - 7/8 = 2 ¼
Multiplication
and Division
5. Example:
2 1/5K = 4 ½
To solve this problem, both mixed numbers must be
changed to improper fractions. If you
need help in remembering how to do this go to http://aaamath.com/fra.html and click on “Converting from
Mixed Numbers”.
Rewrite the equation using improper fractions.
The number in front of the variable K is called the
coefficient. Now multiply both sides of
the equation by the reciprocal of
the coefficient. If you need to find
out what a reciprocal is go to http://mathwizz.com/fractions/index.htm and click on “What
is a reciprocal?”
The product of multiplying reciprocals is the number
1. Thus, multiplying the coefficient by
its reciprocal leaves one variable.
Thus on the left hand side of the equation is K.
(5/11)
11/5 K = 9/2 (5/11)
This means that on the other side of the equation
you must multiply the two fractions together.
If you need help in multiplying fractions go to the Math for Morons Like
Us site at http://library.thinkquest.org/20991/prealg/frac.html
and click on the “Math for Morons Like Us” site. Then click on “Multiplication of Fractions”.
K
=
Division
problems are actually multiplication problems.
6. Example h/9 = 6
Another way of writing this problem is 1/9 h = 6
Now this equation can be solved by multiplying both
sides by the reciprocal of 1/9.
Solve: h/9 =
6
7.
More practice problems. Using the information
you have found, solve these other practice problems. If you need more help, go back to one of the sites you used or go
to http://www.mathXpert.com and have the
problem solved for you. Be sure to
write down the steps and know how the problem was solved.
8/9 P = 136
H/14 = 15
(graphic –
blackboard)
Now
it is time to apply these ideas to some practical problems. If you have trouble setting up the equations
for word problems go to http://www.cut-the-knot.org/arithmetic/WProblem.shtml and read the information contained in this
site. You can also go back to the Math
for Morons Like Us site at http://library.thinkquest.org/20991/alg/word.html and use the information there.
8. James uses 1 ½ cups milk and 3 cups flour
for his favorite cookie recipe. This
makes five dozen cookies. How much milk
and flour would he need to make half as many cookies? (Hint: You will need to
multiply everything by ½ .)
9.
You have a job and earn ten dollars an hour for your services. What would your overtime income be if you
earned time and a half for each hour you worked overtime? (Hint: How much would you earn an hour when you
worked overtime if you earned ten dollars plus half of ten dollars for every hour
you worked?)
10.One month a doctor had 72 patients with type O positive blood. That was three sevenths of her patients. How many patients did she have? (Hint: Write and solve an equation to find the total number of the doctor’s patients.) Show all your work and explain how you found the solution.