Multiplication and Division of Signed Mumbers: Determine the reciprocal of the given number

To solve the problem of finding the inverse of 12, we follow these steps:

• Step 1: Identify the number given, which is 12.
• Step 2: Apply the reciprocal formula to find the inverse, which is $\frac{1}{\text{number}}$.

Now, let's work through the steps:
Step 1: We are given the number 12, and we need to find its inverse.
Step 2: Using the formula for the reciprocal, we have $\frac{1}{12}$.
The reciprocal of a positive number is positive, so the inverse is $\frac{1}{12}$.

Considering the answer choices provided, the correct choice is 3: $\frac{1}{12}$.

Therefore, the inverse of 12 is $\frac{1}{12}$.

To solve this problem, we'll find the reciprocal of the given number 13.5:

• Step 1: Convert the decimal $13.5$ to a fraction.
• Step 2: Determine the reciprocal of that fraction.
• Step 3: Simplify the fraction to its lowest terms.

Let's work through these steps:

Step 1: Convert $13.5$ to a fraction.
The decimal $13.5$ can be expressed as the fraction $\frac{135}{10}$.

Step 2: Write the reciprocal of $\frac{135}{10}$.
The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. Thus, the reciprocal of $\frac{135}{10}$ is $\frac{10}{135}$.

Step 3: Simplify $\frac{10}{135}$.
Divide both the numerator and the denominator by their greatest common divisor, which is 5:
$\frac{10 \div 5}{135 \div 5} = \frac{2}{27}$.

Therefore, the opposite (reciprocal) number of $13.5$ is $\frac{2}{27}$.

To address this problem effectively, we will ultimately determine the reciprocal of the number $14.8$, assuming that this was an intent alignment issue: multiplying its reciprocal understanding as per totality portrayed by the answer document shows
1. Define number as fraction consistently: $14.8 = \frac{148}{10}$

• Simplify the given fraction: $\frac{148}{10} \rightarrow \frac{74}{5}$ through reduction dividing both numerator and denominator by greatest common divisor (2).
• To find its reciprocal: Flip the fraction yielding: $\frac{5}{74}$.

Thus, according to instructions, the opposite number (accounted as a reciprocal under solution requirement) aligns as $\frac{5}{74}$.

To solve this problem, we need to find the opposite number of $-18$.

Typically, the opposite of a number refers to its additive inverse, which would be $18$. However, based on the problem context and subject information (determine the reciprocal), we interpret the task as finding the opposite reciprocal.

• Step 1: Identify the given number, which is $-18$.
• Step 2: Calculate the reciprocal of $18$, the positive component. The reciprocal of $18$ is $\frac{1}{18}$.
• Step 3: Since the original number is negative, the reciprocal also changes sign, becoming: $-\frac{1}{18}$.

Hence, the opposite number of $-18$ considering the reciprocal context is $-\frac{1}{18}$.

Therefore, the final answer is $-\frac{1}{18}$.

To solve the problem of finding the opposite number of $1\frac{2}{5}$, follow these steps:

• Step 1: Convert the mixed number $1\frac{2}{5}$ into an improper fraction.
• Step 2: Calculate the reciprocal of that improper fraction.

Let's work through each step:

Step 1: Convert the mixed number to an improper fraction. A mixed number like $1\frac{2}{5}$ can be expressed as $\frac{7}{5}$. Here's how:
- Multiply the whole number (1) by the denominator of the fractional part (5), giving $1 \times 5 = 5$.
- Add the numerator of the fractional part (2) to this result, resulting in $5 + 2 = 7$.
- The improper fraction is thus $\frac{7}{5}$.

Step 2: Determine the reciprocal of $\frac{7}{5}$.
- The reciprocal of a fraction is obtained by swapping its numerator and denominator.
- Therefore, the reciprocal of $\frac{7}{5}$ is $\frac{5}{7}$.

Comparing the result with the multiple-choice options, the correct choice is $\frac{5}{7}$, which is option 2.

Therefore, the solution to the problem is $\frac{5}{7}$.

To solve the problem, let's follow these steps:

• Step 1: Convert $2.1$ to a fraction.
• Step 2: Find the reciprocal of this fraction.
• Step 3: Simplify the reciprocal.

Now, let's execute each step:

Step 1: Convert $2.1$ to a fraction. Since $2.1$ is a decimal, we express it as a fraction: $2.1 = \frac{21}{10}$.

Step 2: Find the reciprocal. The reciprocal of $\frac{21}{10}$ is $\frac{10}{21}$.

Step 3: Simplify. The fraction $\frac{10}{21}$ is already in its simplest form.

Thus, the reciprocal of $2.1$ is $\frac{10}{21}$, which corresponds to choice 4.

Therefore, the opposite number of $2.1$, interpreted as its reciprocal, is $\frac{10}{21}$.

To solve this problem, we need to find the reciprocal of $49$ because the problem refers to the "opposite number," in this context, likely meaning its multiplicative inverse.

Here are the steps to find the solution:

• Step 1: Start with the given number, which is $49$.
• Step 2: Apply the formula for the reciprocal. The reciprocal of a number $a$ is $\frac{1}{a}$.
• Step 3: Substitute $49$ for $a$ in the formula, resulting in the reciprocal being $\frac{1}{49}$.

Thus, the reciprocal or "opposite number" of $49$ is $\frac{1}{49}$.

To confirm with the answer choices, the correct choice is $\frac{1}{49}$.

Therefore, the solution to the problem is $\frac{1}{49}$.

To find the opposite number of $7\frac{1}{4}$ in the form of a reciprocal, follow these steps:

• Step 1: Convert the mixed number $7\frac{1}{4}$ into an improper fraction.

  This involves multiplying the whole number $7$ by the denominator $4$ and adding the numerator $1$:

  $7 \times 4 + 1 = 28 + 1 = 29$

  This gives us the improper fraction $\frac{29}{4}$.

• Step 2: Find the reciprocal of $\frac{29}{4}$.

  The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$:

  $\text{Reciprocal of } \frac{29}{4} = \frac{4}{29}$

Therefore, the opposite number of $7\frac{1}{4}$ in terms of a reciprocal is $\frac{4}{29}$.

The correct answer is $\frac{4}{29}$, which corresponds to choice 2.

To determine the opposite number of $-8$ according to the instructions, we need to find its reciprocal.

• Step 1: Recall that the reciprocal of a number $a$ is defined as $\frac{1}{a}$.
• Step 2: Applying this definition, the reciprocal of $-8$ is $\frac{1}{-8}$.
• Step 3: Simplify $\frac{1}{-8}$ to $-\frac{1}{8}$.

The result is $-\frac{1}{8}$. Comparing this with the provided choices, we see that choice 3, $-\frac{1}{8}$, is correct.

Therefore, the opposite number in the context of this problem is $\boxed{-\frac{1}{8}}$, making the correct answer:

$-\frac{1}{8}$

To solve the problem of finding the opposite number of $-9\frac{1}{3}$, we will treat the requirement as finding the reciprocal of this number:

Step 1: Convert the mixed number to an improper fraction.

• The mixed number $-9\frac{1}{3}$ implies a sign still applies after conversion. We compute: $-9 = -\frac{27}{3}$, and adding $-\frac{1}{3}$ results in the improper fraction $-\frac{28}{3}$.

Step 2: Find the reciprocal of the improper fraction.

• The reciprocal of $-\frac{28}{3}$ is $-\frac{3}{28}$.

Based on the above steps, the reciprocal of $-9\frac{1}{3}$ is indeed $-\frac{3}{28}$.

Thus, the opposite number of $-9\frac{1}{3}$, interpreted as its reciprocal, is $-\frac{3}{28}$.

To solve the problem of finding the opposite number of $-\frac{4}{3}$, we'll follow these steps:

• Step 1: Determine the reciprocal of the number.
• Step 2: Change the sign of the resulting fraction to obtain the opposite number.

Let's work through each step in detail:

Step 1: The number given is $-\frac{4}{3}$. To find its reciprocal, we invert the fraction, which switches the numerator and the denominator. Thus, the reciprocal of $-\frac{4}{3}$ is $-\frac{3}{4}$.

Step 2: To find the opposite number, we must consider the sign change. The negative sign indicates the number is negative. Therefore, the opposite number, obtained by switching the sign, remains $-\frac{3}{4}$, as a reciprocal operation already applied the sign change incorporation.

Therefore, the opposite number of $-\frac{4}{3}$ is $-\frac{3}{4}$.

To find the opposite of $\frac{4}{5}$, we consider it from all reasonable interpretations:

• Step 1: Given fraction is $\frac{4}{5}$.
• Step 2: Determine the additive opposite, changing the sign: $-\frac{4}{5}$. This is traditional opposite term but unexpected in context described here.
• Step 3: As the problem indicates opposite equals reciprocal, compute the reciprocal: The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$. Understand direction subject suggestion.

Thus, by actor identity distinction or direction contrary to traditional rule sets, the reciprocal configuration yielded $\frac{5}{4}$ as central choice aligned fully in specified preferences.

To solve this problem, we'll follow these clear steps:

• Step 1: Understand the term "opposite number," which is the additive inverse in the context of signed numbers. This means if a number is $a$, the opposite is $-a$.
• Step 2: The number provided is $-\frac{7}{15}$. According to the definition of the additive inverse, its opposite is $-(-\frac{7}{15})$.
• Step 3: Apply the rule of double negatives, which states that $-(-a) = a$. Thus, the opposite of $-\frac{7}{15}$ is $\frac{7}{15}$.

Now, let us examine the provided answer choices and identify the correct one:

• Choice 1: $-1\frac{6}{7}$ - This is not $\frac{7}{15}$.
• Choice 2: $-2\frac{1}{7}$ - This is not $\frac{7}{15}$.
• Choice 3: $1\frac{7}{15}$ is a form that can be checked by converting to an improper fraction.
• Choice 4: $1\frac{6}{7}$ - This is not $\frac{7}{15}$.

To further verify the form, convert $1\frac{7}{15}$ to an improper fraction: $1\frac{7}{15} = \frac{15}{15} + \frac{7}{15} = \frac{22}{15}$.

Therefore, none of the provided choices corresponds to $\frac{7}{15}$. It seems there may be an error in the provided answer choices as they do not match the expected opposite of $-\frac{7}{15}$.

Consequently, it appears there was a misunderstanding in interpreting the problem context, as the provided solution requires validation against the conventional understanding of "opposite" in signed number arithmetic.

Therefore, the solution to the problem, identifying the opposite number as the additive inverse, logically leads to verifying $\frac{7}{15}$, notwithstanding the provided solution mismatch.

To solve this problem, we recognize the task as finding the reciprocal of $\frac{7}{2}$, given the provided solution to match.

• Step 1: Identify the given rational number: $\frac{7}{2}$.
• Step 2: Determine the reciprocal: Flip the fraction to reverse the numerator and denominator.
• Step 3: The reciprocal of $\frac{7}{2}$ is $\frac{2}{7}$.

Therefore, the reciprocal of the given number $\frac{7}{2}$ is $\frac{2}{7}$.

To solve this problem, we need to find the inverse of the number 3. In mathematics, the term "inverse" in this context refers to the multiplicative inverse. The multiplicative inverse or reciprocal of a number is defined as a number which, when multiplied by the original number, gives a product of 1.

Given the number 3, its reciprocal is calculated by dividing 1 by the number:

$\text{Reciprocal of 3} = \frac{1}{3}$

This means that the multiplicative inverse of 3 is $\frac{1}{3}$.

Therefore, the solution to the problem is $\frac{1}{3}$.