This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses multiplication of fractions. By the end of the module students should be able to understand the concept of multiplication of fractions, multiply one fraction by another, multiply mixed numbers and find powers and roots of various fractions.
Section overview
Fractions of Fractions
Multiplication of Fractions
Multiplication of Fractions by Dividing Out Common Factors
Multiplication of Mixed Numbers
Powers and Roots of Fractions
Fractions of fractions
We know that a fraction represents a part of a whole quantity. For example, two fifths of one unit can be represented by
of the whole is shaded.
A natural question is, what is a fractional part of a fractional quantity, or, what is a fraction of a fraction? For example, what
of
?
We can suggest an answer to this question by using a picture to examine
of
.
First, let’s represent
.
of the whole is shaded.
Then divide each of the
parts into 3 equal parts.
Each part is
of the whole.
Now we’ll take
of the
unit.
of
is
, which reduces to
.
Multiplication of fractions
Now we ask, what arithmetic operation (+, –, ×, ÷) will produce
from
of
?
Notice that, if in the fractions
and
, we multiply the numerators together and the denominators together, we get precisely
.
This reduces to
as before.
Using this observation, we can suggest the following:
The word "of" translates to the arithmetic operation "times."
To multiply two or more fractions, multiply the numerators together and then multiply the denominators together. Reduce if necessary.
Sample set a
Perform the following multiplications.
Thus
This means that
of
is
, that is,
of
of a unit is
of the original unit.
Multiplying fractions by dividing out common factors
We have seen that to multiply two fractions together, we multiply numerators together, then denominators together, then reduce to lowest terms, if necessary. The reduction can be tedious if the numbers in the fractions are large. For example,
We avoid the process of reducing if we divide out common factors
before we multiply.
Divide 3 into 9 and 21, and divide 2 into 10 and 16. The product is a fraction that is reduced to lowest terms.
The process of multiplication by dividing out common factors
To multiply fractions by dividing out common factors, divide out factors that are common to both a numerator and a denominator. The factor being divided out can appear in any numerator and any denominator.
Questions & Answers
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?