Divide Fraction Numbers
Again, there are three methods to use Take your pick.
Method One
Dividing Fractions
When dividing
with integers we learned that dividing 8 by 4 (8 ÷ 4) we need to find how
many size 4 bars will fit in one size 8 bar. We use the same method when
dividing fractions. For example, let's divide 1/2 ÷ 1/4. How many 1/4's can you
fit in 1/2? Or how many quarters can you have in one half? Let's use integer
bars to solve this equation.
The purple bar represents one unit, the red bar represents 1/2
unit, and each white bar represents 1/4 unit. We need to find out how many 1/4
(white) bars will fit into one 1/2 (red) bar. Using the picture above, can you
figure it out? The picture shows that 2 white (1/4) bars fit in one red (1/2)
bar, so the answer is 2.
1/2 ÷ 1/4 = 2
To solve this problem mathematically we use the concept that
division is the opposite of multiplication. Dividing by 1/4 is the same as
multiplying by the inverse of 1/4, which is 4/1. Let's see what our answer will
be if we solve this same problem mathematically:
1/2 ÷ 1/4 = 1/2 x 4/1 = (1 x 4) / (2 x 1) = 4/2 = 2
Voilą! We got the same answer!
Let's try another example:
4/3 ÷ 1/3
How many 1/3's are in 4/3? How will this look using the integer
bars?
The green bar represents one unit and each white bar represents
1/3 unit. On top of the green bar we have a train of 4 white bars which
represents 4/3. Can you tell how many 1/3's are in 4/3? I see 4 white bars,
therefore there are 4 white (1/3) bars in the 4/3 train. Now let's solve this
same problem mathematically:
4/3 ÷ 1/3 = 4/3 x 3/1 = (4 x 3) / (3 x 1) = 12/3 = 4
Voilą! The answer is 4 using either method.
One more example:
4/10 ÷ 6/5
Let's draw the integer bars to solve this problem.
The orange bar represents one unit, the purple bar represents
4/10 unit, and each red bar represents 1/5 unit. Since we need 6/5 we have a red
train of 6 red bars. How many red trains (6/5) will fit into the purple (4/10)
bar? The red train is too big to fit in the purple bar. We can only fit 2 of the
six red bars or 2/6 of the red train in the purple bar. We simplify 2/6 to 1/3
and the answer is 1/3. Let's use the mathematical method again to see if we get
the same answer:
4/10 ÷ 6/5 = 4/10 x 5/6 = (4 x 5) / (10 x 6) = 20/60 = 1/3
Voilą!
Exercises
Problem Number

Problem

Answer

Fraction
Multiplication Problems

1

3/4 x 4/3


2

5/7 x 2/5


3

5/8 x 4/10


4

8/5 x 1/10 x 5/2


5

2 1/4 x 3 1/3


6

2/5 x 1 3/4 x 5/7


7

5/6 x 6/7 x 2 1/3


Fraction
Division Problems

8

3/4 ÷ 2/8


9

9/2 ÷ 3/4


10

7/3 ÷ 7/12


11

4/9 ÷ 8/3


12

5 ÷ 1/2


13

2 3/4 ÷ 1 3/8


14

8 1/4 ÷ 8/11


After you have completed all the problems you can check your answers.
Method Two
Convert each term with a fraction into a decimal number then proceed with the
division. Here is a discussion of this method.
Method Three
A calculator can perform the division by entering the fractions with the a/b
key as you enter the problem to be solved. Here is a discussion of that method.
Convert each term in the expression to a decimal. Numerator divided by
denominator.
Method Three
The Texas Instruments TI30Xa has a wonderful key a b/c which allows chain
calculations of fractions. Read through your instruction booklet that came with
your calculator for further instructions. Here is an overview of the technique.
The Fraction Key Perhaps one of the nicest
features of this particular calculator is its ability to work fraction
arithmetic. When properly entered, the calculator will use fractions correctly
in any calculation. First, you need to know how to enter a fraction.
Single fraction: Enter the numerator (top number), press the fraction
key , then enter the denominator (bottom
number). So the fraction is entered as .
The calculator displays the fraction something like .
Mixed numbers: Use the fraction key twice. The mixed number is
entered as . In short,
simply press the fraction key between each number in a fraction or mixed number.
Your calculator knows the difference. The mixed number is displayed as .
Now you are ready to use fractions in other calculations. Simply enter the
fraction wherever it appears as you continue typing the entire calculation. For
example, try computing by entering the
following sequence:
The answer will be displayed as a fraction or a mixed number (if more than
1). In this case, you should get , which means
.
Find a practice problems HERE.
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Listen to an audio file on this topic HERE.
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