A Number Is Divided By 3/4. Then The Quotient Is Multiplied By 1/2. The Product Equals 64. What Is 3/4 Of The Number?
Introduction
Mathematics is a subject that deals with numbers and their operations. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In this article, we will discuss a problem that involves division and multiplication of fractions. We will use algebraic methods to solve the problem and find the value of the number.
Problem Statement
A number is divided by 3/4. Then the quotient is multiplied by 1/2. The product equals 64. What is 3/4 of the number?
Step 1: Let's assume the number is x
Let's assume the number is x. We are given that the number is divided by 3/4, which can be written as:
x / (3/4)
Step 2: Simplify the expression
To simplify the expression, we can multiply the numerator by the reciprocal of the denominator:
x / (3/4) = x * (4/3)
Step 3: Multiply the quotient by 1/2
The quotient is then multiplied by 1/2, which can be written as:
(x * 4/3) * (1/2)
Step 4: Simplify the expression
To simplify the expression, we can multiply the numerators and denominators:
(x * 4/3) * (1/2) = (x * 4 * 1) / (3 * 2)
Step 5: Simplify the expression further
We can simplify the expression further by canceling out the common factors:
(x * 4 * 1) / (3 * 2) = (x * 4) / 6
Step 6: The product equals 64
We are given that the product equals 64, which can be written as:
(x * 4) / 6 = 64
Step 7: Multiply both sides by 6
To eliminate the fraction, we can multiply both sides by 6:
x * 4 = 64 * 6
Step 8: Simplify the expression
To simplify the expression, we can multiply the numbers:
x * 4 = 384
Step 9: Divide both sides by 4
To find the value of x, we can divide both sides by 4:
x = 384 / 4
Step 10: Simplify the expression
To simplify the expression, we can divide the numbers:
x = 96
Step 11: Find 3/4 of the number
Now that we have found the value of x, we can find 3/4 of the number:
3/4 * 96 = 72
Conclusion
In this article, we discussed a problem that involved division and multiplication of fractions. We used algebraic methods to solve the problem and find the value of the number. We then found 3/4 of the number, which is 72.
Final Answer
The final answer is 72.
Introduction
In our previous article, we discussed a problem that involved division and multiplication of fractions. We used algebraic methods to solve the problem and find the value of the number. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.
Q: What is the problem asking for?
A: The problem is asking for the value of 3/4 of a number, given that the number is divided by 3/4 and then the quotient is multiplied by 1/2, resulting in a product of 64.
Q: How do we start solving the problem?
A: We start by assuming the number is x and then dividing it by 3/4. This can be written as x / (3/4).
Q: Why do we multiply the numerator by the reciprocal of the denominator?
A: We multiply the numerator by the reciprocal of the denominator to simplify the expression. This is a common technique used in algebra to simplify fractions.
Q: What is the next step in solving the problem?
A: The next step is to multiply the quotient by 1/2. This can be written as (x * 4/3) * (1/2).
Q: How do we simplify the expression?
A: We simplify the expression by multiplying the numerators and denominators. This results in (x * 4 * 1) / (3 * 2).
Q: What is the final simplified expression?
A: The final simplified expression is (x * 4) / 6.
Q: What is the next step in solving the problem?
A: The next step is to set the expression equal to 64, which is the given product. This can be written as (x * 4) / 6 = 64.
Q: How do we eliminate the fraction?
A: We eliminate the fraction by multiplying both sides of the equation by 6. This results in x * 4 = 64 * 6.
Q: What is the next step in solving the problem?
A: The next step is to simplify the expression by multiplying the numbers. This results in x * 4 = 384.
Q: How do we find the value of x?
A: We find the value of x by dividing both sides of the equation by 4. This results in x = 384 / 4.
Q: What is the final value of x?
A: The final value of x is 96.
Q: How do we find 3/4 of the number?
A: We find 3/4 of the number by multiplying 3/4 by the value of x. This results in 3/4 * 96 = 72.
Q: What is the final answer?
A: The final answer is 72.
Additional Tips and Tricks
- When dealing with fractions, it's often helpful to multiply the numerator by the reciprocal of the denominator to simplify the expression.
- When multiplying fractions, it's often helpful to multiply the numerators and denominators separately.
- When setting up an equation, make sure to use the correct notation and to follow the order of operations.
Conclusion
In this article, we provided a Q&A section to help clarify any doubts and provide additional information on the problem. We hope that this article has been helpful in understanding the problem and its solution. If you have any further questions or concerns, please don't hesitate to ask.