Problem 50 Evaluate each expression. $$75... [FREE SOLUTION]

Chapter 1: Problem 50

Evaluate each expression. $$75 \div(-5)(-3) \div \frac{1}{2} \cdot 6$$

Short Answer

Expert verified

The result is 540.

Step by step solution

- Evaluate Division

Start by evaluating the first division. Compute the result of dividing 75 by -5. \[\begin{equation} 75 \div (-5) = -15 \end{equation}\]

- Multiply Negative Numbers

Multiply the result from Step 1 by -3. \[\begin{equation} -15 \cdot (-3) = 45 \end{equation}\]

- Perform Division with a Fraction

Next, divide the result from Step 2 by \frac{1}{2}. Dividing by a fraction is the same as multiplying by its reciprocal.\[\begin{equation} 45 \div \frac{1}{2} = 45 \cdot 2 = 90 \end{equation}\]

- Final Multiplication

Multiply the result from Step 3 by 6.\[\begin{equation} 90 \cdot 6 = 540 \end{equation}\]

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Key Concepts

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

Division of Integers

Let's dive into dividing integers. When you divide integers, you deal with both positive and negative numbers. Here, the exercise asks us to divide 75 by -5. The rule is simple:

If you divide two integers with the same sign, the result is positive.
If you divide two integers with different signs, the result is negative.

So, dividing 75 (positive) by -5 (negative) gives us a negative result. That is, 75 divided by -5 equals -15.
Remember, division by a negative number flips the sign of the result.

Multiplication of Numbers

Next, let's cover multiplying numbers, especially negative ones. In the problem, we multiply -15 by -3. Multiplication rules are:

Positive times positive is positive.
Negative times negative is positive.
Negative times positive is negative.

Here, we have -15 times -3, both negative. According to the rules, multiplying two negatives gives a positive result. So, -15 times -3 equals 45.
This transformation from negative to positive is crucial in simplifying expressions.

Handling Fractions

Now, let's focus on how to handle fractions, particularly in division. The problem step involves dividing 45 by $\frac{1}{2}$. Dividing by a fraction is the same as multiplying by its reciprocal.

The reciprocal of $\frac{1}{2}$ is 2 because flipping the fraction gives us 2.
Therefore, 45 divided by $\frac{1}{2}$ is the same as 45 multiplied by 2.

Performing this multiplication, we get 90.
Finally, multiplying 90 by 6 completes the problem, resulting in 540. Understanding these rules will help you handle fractions with ease.

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91影视

Evaluate each expression. $$75 \div(-5)(-3) \div \frac{1}{2} \cdot 6$$

Short Answer

Step by step solution

- Evaluate Division

- Multiply Negative Numbers

- Perform Division with a Fraction

- Final Multiplication

Key Concepts

Division of Integers

Multiplication of Numbers

Handling Fractions

One App. One Place for Learning.

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