/*! 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 117 Perform these computations. $$... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 117

Perform these computations. $$-57 \div 19$$

Short Answer

Expert verified
-3

Step by step solution

01

Identify the Operation

The problem requires division. Specifically, the division of -57 by 19.
02

Divide the Numbers

Perform the division \( \frac{-57}{19} \). Calculate the result.
03

Simplify the Result

The division of \( -57 \) by \( 19 \) results in approximately \( -3. \)
04

Consider the Sign

Since a negative number is divided by a positive number, the result will be negative.

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Key Concepts

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

Division of Integers
Division of integers involves breaking down a number into equal parts. If you have two integers, and you need to divide one by the other, it's important to first understand what the operation requires. For example, when dividing -57 by 19, the key steps involve:
  • Identifying the need for division.
  • Performing the actual division, \(\frac{-57}{19}\).
  • Simplifying the result, which is approximately -3.
Make sure to understand the basic concept that division is essentially finding out how many times one number fits into another. This is true even when working with negative numbers.
Negative Numbers
Negative numbers can be tricky when performing mathematical operations like division. When you divide a negative number by a positive number, the result is always negative. Here鈥檚 why:
  • A negative number represents a value less than zero.
  • Dividing by a positive number doesn't change the magnitude but influences the sign.
Considering our example, -57 divided by 19 results in approximately -3. The important thing to remember is that the quotient takes the sign of the numerator (in this case, -57).
Mathematical Operations
Mathematical operations include addition, subtraction, multiplication, and division. Each operation has its own rules and impact on the numbers involved. Let鈥檚 break down division in a detail:
  • Division is the process of determining how many times one number is contained within another.
  • The division of integers follows specific rules regarding the sign of the result.
  • When dividing two positive numbers, the result is positive.
  • When dividing two negative numbers, the result is positive.
  • When dividing a positive number by a negative number, or vice versa, the result is negative.
Understanding these rules helps in correctly solving division problems. For instance, \(\frac{-57}{19}\) simplifies to -3, respecting the rule that a negative divided by a positive is negative.

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