/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 Evaluate the expression. $$(-4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 87

Evaluate the expression. $$(-4)^{2}-(30 \div 50)$$

Short Answer

Expert verified
The result of the expression \(-4^{2} - \frac{30}{50}\) is 15.4.

Step by step solution

01

Evaluate the Power

To start with, let's first calculate \((-4)^{2}\). The number -4 is being squared, which means multiplying -4 by itself. Hence, \((-4)^{2} = (-4) \times (-4) = 16.
02

Perform the Division

Next, let's perform the division between 30 and 50 to get \(\frac{30}{50}\). You could simply divide them as they are to get 0.6, or reduce the fraction to its simplest form \(\frac{3}{5}\) and then divide to get 0.6.
03

Subtract the Results

Now, subtract the outcome of the division from the outcome of the exponentiation as per the order of operations to get the final result. Result will be \(16 - 0.6 = 15.4\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Order of Operations
When evaluating mathematical expressions, it's crucial to follow a specific order known as the order of operations. This ensures that everyone solves the expression the same way and gets the same result. The commonly remembered acronym for this process is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • Parentheses: Always begin solving inside parentheses first.
  • Exponents: Next, compute any exponents.
  • Multiplication and Division: After exponents, handle multiplication and division. These operations are performed as they appear from left to right.
  • Addition and Subtraction: Lastly, perform addition and subtraction, also from left to right.
In the expression \[(-4)^2 - (30 \div 50)\]we first tackle the exponent \[(-4)^2\]before performing the division \[(30 \div 50).\]Finally, we do the subtraction to finish solving the expression.
Handling Exponents in Expressions
Exponents refer to the number of times a number (called the base) is multiplied by itself. Specifically, \[a^n\]means that the base \[a\]is multiplied by itself \[n\]times. When you see an expression such as \[(-4)^2,\]it means that the negative number \[-4\]should be multiplied by itself.
Here, \[(-4) \times (-4) = 16.\]It's essential to include the negative sign inside the parentheses; otherwise, you might only square the 4 and then apply the negative sign, which gives a different result.
Key points to remember:
  • Positive Results from Even Exponents: Squaring a negative number (an even power) always results in a positive, because two negatives multiplied yield a positive.
  • Correct Placement of Parentheses: Always use parentheses to make sure you square the entire negative number, not just the positive component.
Understanding Fraction Division
Dividing fractions is an essential skill for evaluating expressions. In the exercise, the fraction \[30 \div 50\]can be easily misunderstood, but it's simply division followed by possible simplification. Key steps include:
  • Perform the Division: Directly divide the numbers to obtain a decimal, \[\frac{30}{50} = 0.6.\]
  • Reduce the Fraction: If possible, simplify the fraction \[30\]and \[50\] to their smallest terms using their greatest common divisor. Here, it simplifies to \[\frac{3}{5}.\]
  • Translate to Decimal if Needed: Sometimes, further simplification is about expressing the fraction in decimal form, which is \[0.6.\] in this instance.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve and graph the inequality. $$3(x+1) \geq 2(x+5)$$

Determine whether the statement is true or false. Justify your answer. The statement that \(u\) is at least 10 is equivalent to the inequality \(u \geq 10\).

Solve the proportion. $$\frac{3}{2}=\frac{9}{x}$$

Solve and graph the inequality. $$8(z-2)<4(z+1)$$

Structure Write three equations that are equivalent to \(A=\frac{1}{2}(x+y) h\) by solving for each variable, where \(A\) is the area, \(h\) is the height, and \(x\) and \(y\) are the bases of a trapezoid. Explain when you would use each equation.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.