Chapter 11: Problem 5
What is the value of
Short Answer
Expert verified
The value of is .
Step by step solution
01
- Simplify the numerator
The numerator of the fraction is . Multiply these two fractions by multiplying their numerators and denominators:
02
- Simplify the fraction
Simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
03
- Set up the division of fractions
The original expression now looks like this:
04
- Divide by multiplying by the reciprocal
To divide by a fraction, multiply by its reciprocal. So divide by by multiplying by :
05
- Simplify the multiplication
Multiply the fractions by multiplying the numerators and denominators: . Next, simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
simplifying fractions
Simplifying fractions means making the fraction as simple as possible. This often involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number.
In the example from the exercise, the fraction was simplified by identifying that both 6 and 44 can be divided by their GCD, which is 2. So, .
Simplifying fractions makes them easier to work with and understand. It’s an essential skill in fraction operations like addition, subtraction, multiplication, and division.
In the example from the exercise, the fraction
Simplifying fractions makes them easier to work with and understand. It’s an essential skill in fraction operations like addition, subtraction, multiplication, and division.
dividing by a fraction
Dividing by a fraction involves multiplying by the reciprocal of the fraction. The reciprocal of a fraction is created by swapping its numerator and denominator.
For example, in the given exercise, we needed to divide by . To do this, we multiply by the reciprocal of , which is . This converts the division problem into multiplication: .
This method works because multiplying by a reciprocal effectively cancels out the original fraction, leaving a simple multiplication operation.
For example, in the given exercise, we needed to divide
This method works because multiplying by a reciprocal effectively cancels out the original fraction, leaving a simple multiplication operation.
multiplying fractions
Multiplying fractions is a straightforward process that involves multiplying the numerators together and the denominators together.
For instance, in the exercise, to multiply by , you multiply the numerators to get 6 and the denominators to get 44, resulting in .
Then, the fraction can be simplified to by dividing both the numerator and the denominator by their GCD, which is 2. This step is essential because it keeps the fraction as simple and as easy to understand as possible.
For instance, in the exercise, to multiply
Then, the fraction