# Find Half a Number's Reciprocal Increased by Half its Reciprocal

• MHB
• karush
In summary, "Find Half a Number's Reciprocal Increased by Half its Reciprocal" is a mathematical expression that involves finding the reciprocal of half of a given number and adding half of that reciprocal to the original reciprocal. The reciprocal of a number is found by dividing 1 by the given number. "Increased by" means to add the specified amount to the original number. An example of solving this expression is finding the answer to be 0.1875 when the original number is 8. This expression showcases basic arithmetic skills and the concept of reciprocals in mathematics. It can also be used in more advanced equations and problem-solving scenarios.
karush
Gold Member
MHB
$\tiny{3.1.2}$
The reciprocal of half a number increased by half the recipical of the number is $\dfrac{1}{2}$
$\begin{array}{rl} n= & \textit{the number} \\ \\ \dfrac{n}{2}= &\textit{half the number}\\ \\ \dfrac{2}{n} = &\textit{the reciprocal of half the number}\\ \\ \dfrac{1}{2n}= & \textit{half the reciprocal of the number}\\ \\ \dfrac{2}{n}+\dfrac{1}{2n} &=\dfrac{1}{2}\\ \\ &\textit{Multiply every term by 6n to cancel denominators}\\ \\ 12+3=15 &=3n\quad\therefore n=5 \end{array}$
hopefully :unsure:

ahhh victory...

karush said:
$\tiny{3.1.2}$
The reciprocal of half a number increased by half the recipical of the number is $\dfrac{1}{2}$
$\begin{array}{rl} n= & \textit{the number} \\ \\ \dfrac{n}{2}= &\textit{half the number}\\ \\ \dfrac{2}{n} = &\textit{the reciprocal of half the number}\\ \\ \dfrac{1}{2n}= & \textit{half the reciprocal of the number}\\ \\ \dfrac{2}{n}+\dfrac{1}{2n} &=\dfrac{1}{2}\\ \\ &\textit{Multiply every term by 6n to cancel denominators}\\ \\ 12+3=15 &=3n\quad\therefore n=5 \end{array}$
hopefully :unsure:
Very good. But why "Multiply every term by 6n"? There is no "3" in any of the denominators. Multiplying by 2n is sufficient:
$2n\left(\frac{2}{n}+ \frac{1}{2n}\right)= 2n\left(\frac{1}{2}\right)$
$4+ 1= n$ so $n= 5$.

## 1. What is the meaning of "Find Half a Number's Reciprocal Increased by Half its Reciprocal"?

"Find Half a Number's Reciprocal Increased by Half its Reciprocal" is a mathematical expression that requires finding the reciprocal of a number, which is the number flipped upside down (e.g. the reciprocal of 2 is 1/2), and then adding half of that reciprocal to the original reciprocal.

## 2. How do you find the reciprocal of a number?

To find the reciprocal of a number, you simply flip the number upside down. For example, the reciprocal of 2 is 1/2, the reciprocal of 5 is 1/5, and so on.

## 3. What is the significance of adding half of the reciprocal to the original reciprocal?

Adding half of the reciprocal to the original reciprocal is a way to increase the value of the original reciprocal. This is because adding half of the reciprocal is equivalent to multiplying the original reciprocal by 1.5, which increases the value.

## 4. Can this expression be simplified?

Yes, this expression can be simplified by first finding the reciprocal of the number, then multiplying it by 1.5. This will give the same result as finding half of the reciprocal and adding it to the original reciprocal.

## 5. How can this expression be applied in real life?

This expression can be applied in various real-life situations, such as calculating the amount of medication needed based on a person's weight, determining the amount of ingredients needed for a recipe, or calculating the amount of time needed to complete a task based on its rate of completion.

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