/*! 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 51 Perform the indicated operation.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 51

Perform the indicated operation. \(\frac{30}{-2}\)

Short Answer

Expert verified
The result of \( \frac{30}{-2} \) is -15.

Step by step solution

01

Identify the operation

The problem asks for the division of the two numbers: 30 and -2. The division operation is indicated by the fraction bar in \( \frac{30}{-2} \).
02

Divide the numbers

Perform the division by dividing the numerator (30) by the denominator (-2). Divide 30 by -2 to get the quotient.
03

Simplify the result

When dividing 30 by -2, compute \( 30 \div (-2) = -15 \). The quotient is -15 because a positive number divided by a negative number results in a negative number.

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.

Negative Numbers Division
Dividing negative numbers can seem tricky at first, but it's actually quite simple. A basic rule to remember is that when you divide a positive number by a negative number, the result is always a negative quotient. Likewise, dividing a negative number by a positive number will also yield a negative result. This is because positive and negative numbers are considered opposite in sign.
Therefore, the operation becomes straightforward:
  • Positive 梅 Negative = Negative
  • Negative 梅 Positive = Negative
  • Negative 梅 Negative = Positive
  • Positive 梅 Positive = Positive
Understanding these rules helps you predict the sign of the quotient even before completing the math. In our example, \(\frac{30}{-2}\), the quotient will be negative because you are dividing a positive number (30) by a negative number (-2).
Numerator and Denominator
In division expressed as a fraction, such as \(\frac{30}{-2}\), the top number is called the numerator, and the bottom number is the denominator.
The numerator (30 in our example) represents how many parts you have, while the denominator (-2) indicates into how many parts you want to divide the numerator.
Think of the fractional bar as a division sign. When you see \(\frac{30}{-2}\), it simply tells you to divide 30 by -2.
Understanding the role of the numerator and denominator helps clearly frame division problems:
  • Numerator \(\Rightarrow\) Quantity to Divide
  • Denominator \(\Rightarrow\) Dividing Factor
Another key point is that if the negative sign is with the denominator, as in this case, the result will be negative, as explained in the previous section.
Quotient Calculation
After understanding the signs and parts of a fraction, the next step is calculating the quotient. The quotient is the result you get when you divide the numerator by the denominator. In simple terms, it is the answer to the division problem.
For the calculation, you perform a simple division: \[30 \div (-2)\]Calculate as you normally would, ignoring the signs initially:
  • Divide 30 by 2, which gives 15
Now, reintroduce the signs. As division involves a positive number (30) and a negative number (-2), the quotient becomes negative. Thus:
  • The final quotient is -15
The key takeaways are:
  • Divide the numbers as usual
  • Apply the rule of signs to determine if the quotient is positive or negative

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. A woman received a statement of her charge account at Old Navy. She spent \(\$ 93\) on purchases last month. She returned an \(\$ 18\) top because she didn't like the color. She also returned a \(\$ 26\) nightshirt because it was damaged. What does she actually owe on her account?

Evaluate each expression when \(x=-5, y=4,\) and \(t=10\). \(\frac{15-x}{y+2}\)

Subtract. \(16-(-21)\)

Decide whether the given number is a solution of the given equation. \(4=1-x ; 5\)

Simplify each expression. \(-2+[(8-11)-(-2-9)]\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.