David W. answered • 08/06/15
Tutor
4.7
(90)
Experienced Prof
Students often ask a very reasonable question: “Why do we need to learn this stuff?”
In this problem, “half of” and “third of” and “fourth of” are used instead of simple terms like “8 jelly beans” because the goal is to be able to “subdivide” quantities by multiplying fractions – and “of” usually means multiply. So, finding an answer is not the main goal; learning to multiply fractions is the goal.
The use of parentheses (remember them in PEMDAS?) really help you to understand the process. And –understanding the process is the goal (not getting the right answer).
So, learning that “one half of” translates to (1/2)(X) in math terms is where we start. Now, what is X?
We assign X to represent the number of jelly beans that Maria started with because the problem asks us, “how many did Maria start with?” When we find that answer, the process is almost (I’ll explain later) complete.
Let’s use more parentheses (please follow the words of the problem):
(1/4)( (1/3)( (1/2)(X) ) ) = 2
Also, please notice that we could modify any value inside of a set of parentheses (for example, if one of the people had eaten 2 of the jelly beans before giving a fraction of the remaining jelly beans away.
O.K., now we have an equation that becomes
(1/24)(X) = 2
and we solve for X so we can report that value.
Multiplying both sides of the equation by 24 (this is legal because multiplying equals by equals produces equals), we get:
X = 48
- - - - - - - -
NOW (the part that I said I’d explain later), CHECK THIS ANSWER:
Is one fourth of one third of one half of 48 equal to 2? Yes!
Carefully read 48 in place of Maria’s jelly beans, 24 in place of Carl’s jelly beans, 8 in place of Austin’s jelly beans and 2 in place of Carmen’s jelly beans in order to verify the words of the problem, “If Carmen received two jelly beans ,,,”
Even though we have an answer, we are not finished the problem solving process until we have checked that answer for accuracy!
In this problem, “half of” and “third of” and “fourth of” are used instead of simple terms like “8 jelly beans” because the goal is to be able to “subdivide” quantities by multiplying fractions – and “of” usually means multiply. So, finding an answer is not the main goal; learning to multiply fractions is the goal.
The use of parentheses (remember them in PEMDAS?) really help you to understand the process. And –understanding the process is the goal (not getting the right answer).
So, learning that “one half of” translates to (1/2)(X) in math terms is where we start. Now, what is X?
We assign X to represent the number of jelly beans that Maria started with because the problem asks us, “how many did Maria start with?” When we find that answer, the process is almost (I’ll explain later) complete.
Let’s use more parentheses (please follow the words of the problem):
(1/4)( (1/3)( (1/2)(X) ) ) = 2
Also, please notice that we could modify any value inside of a set of parentheses (for example, if one of the people had eaten 2 of the jelly beans before giving a fraction of the remaining jelly beans away.
O.K., now we have an equation that becomes
(1/24)(X) = 2
and we solve for X so we can report that value.
Multiplying both sides of the equation by 24 (this is legal because multiplying equals by equals produces equals), we get:
X = 48
- - - - - - - -
NOW (the part that I said I’d explain later), CHECK THIS ANSWER:
Is one fourth of one third of one half of 48 equal to 2? Yes!
Carefully read 48 in place of Maria’s jelly beans, 24 in place of Carl’s jelly beans, 8 in place of Austin’s jelly beans and 2 in place of Carmen’s jelly beans in order to verify the words of the problem, “If Carmen received two jelly beans ,,,”
Even though we have an answer, we are not finished the problem solving process until we have checked that answer for accuracy!
