Problem 384 Divide. $$ -3 \div \frac{1}{... [FREE SOLUTION]

Chapter 1: Problem 384

Divide. $$ -3 \div \frac{1}{4} $$

Short Answer

Expert verified

-12

Step by step solution

Understand the operation

Dividing by a fraction is the same as multiplying by its reciprocal. So, this division problem can be transformed into a multiplication problem.

Find the reciprocal

The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. Thus, the reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$.

Rewrite the division as a multiplication

Rewrite the problem $-3 \div \frac{1}{4}$ as $-3 \times \frac{4}{1}$.

Perform the multiplication

Multiplying $-3$ by $\frac{4}{1}$ gives $-3 \times 4 = -12$.

Verify the result

Ensure that all steps have been followed correctly and verify the final answer which is $-12$.

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Key Concepts

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

Reciprocal

To understand fraction division, knowing what a reciprocal is will help immensely. A reciprocal of a number is what you multiply that number by to get 1. For fractions, it's simply flipping the fraction.
For instance:

The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$

Reciprocals are useful because dividing by a fraction is the same as multiplying by its reciprocal. When we see \-3 $\frac{1}{4}$, we change it to \-3 $\times \frac{4}{1}$.
This is the core idea behind fraction division: reciprocal turns division into multiplication.

Multiplication of Fractions

After converting division into multiplication using the reciprocal, the next step is the actual multiplication of fractions. Multiplying fractions is straightforward:

Multiply the numerators (top numbers) together.
Multiply the denominators (bottom numbers) together.

When multiplying a fraction by an integer, think of that integer as a fraction with 1 as the denominator. For example, \-3 $\times \frac{4}{1}$ is the same as multiplying \-3 by 4.
This gives us $-3 \times 4 = -12$.
The rule is:

Keep it simple and multiply across the top and bottom.

Negative Numbers

Understanding negative numbers is crucial for our problem. A negative number is less than zero and is usually presented with a minus sign (-) in front of it.
When multiplying negative numbers by positive numbers, the result always inherits the sign of the negative number. For example, \-3 $\times 4$ will result in \-12.
The general principles are:

A negative times a positive is always negative.
A positive times a negative is also negative.

Therefore, in our exercise, multiplying \-3 by 4 yields \-12, confirming our solution.
Practicing these rules will make solving such problems easy and intuitive.

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91影视

Divide. $$ -3 \div \frac{1}{4} $$

Short Answer

Step by step solution

Understand the operation

Find the reciprocal

Rewrite the division as a multiplication

Perform the multiplication

Verify the result

Key Concepts

Reciprocal

Multiplication of Fractions

Negative Numbers

One App. One Place for Learning.

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