Problem 57 Fill in the blank. Dividing by... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 57

Fill in the blank. Dividing by $-8$ is the same as______ by $-\frac{1}{8}$

Short Answer

Expert verified

Multiplying by $-\frac{1}{8}$.

Step by step solution

Understand the Relationship

We need to figure out what mathematical operation is equivalent to dividing by $-8$.

Determine the Inverse Operation

Division by a number can be expressed as multiplication by its reciprocal. Therefore, dividing by $-8$ is the same as multiplying by the reciprocal of \-8\.

Find the Reciprocal

The reciprocal of \-8\ is $-\frac{1}{8}$.

Combine the Operations

So, dividing by \-8\ is the same as multiplying by $-\frac{1}{8}$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

reciprocal

The term 'reciprocal' refers to the number you get when you flip the numerator and denominator of a fraction. For whole numbers like 8, you understand it as the fraction $\frac{8}{1}$. The reciprocal of 8 is therefore $\frac{1}{8}$. This concept is crucial for solving various mathematical operations efficiently. When the number is negative, such as -8, the reciprocal behaves similarly, giving you $-\frac{1}{8}$. It's often used in division because multiplying by the reciprocal is the same as dividing by the original number.

inverse operation

Inverse operations are mathematical operations that undo each other. For instance, addition and subtraction are inverse operations because adding a number and then subtracting the same number brings you back to the original value. Similarly, multiplication and division are inverse operations. If you multiply a number by another and then divide the result by the same number, you return to the original number. When you encounter a division problem, you can transform it into a multiplication problem by using the reciprocal. This principle is seen in the exercise where dividing by $-8$ converts into multiplying by $-\frac{1}{8}$.

multiplication

Multiplication is one of the basic arithmetic operations. It involves combining equal groups of objects. For example, multiplying 3 by 4 is the same as adding 4 three times: \3 \times 4 = 4 + 4 + 4 = 12\. In terms of the reciprocal and division, multiplication helps us simplify division. Instead of dividing by a number, you can multiply by its reciprocal. In our exercise, dividing by \-8\ equates to multiplication by \-$\frac{1}{8}$. Mathematically, \frac{a}{-8} \) becomes \(a \times -\frac{1}{8}\right\ which makes the calculation easier to handle.

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91影视

Fill in the blank. Dividing by \(-8\) is the same as______ by \(-\frac{1}{8}\)

Short Answer

Step by step solution

Understand the Relationship

Determine the Inverse Operation

Find the Reciprocal

Combine the Operations

Key Concepts

reciprocal

inverse operation

multiplication

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