Problem 56 Write a mathematical expression ... [FREE SOLUTION]

Chapter 1: Problem 56

Write a mathematical expression for each and simplify. The quotient of \(-80\) and \(-4\)

Short Answer

Expert verified

The simplified expression for the quotient of \(-80\) and \(-4\) is \(20\).

Step by step solution

Write down the quotient expression

We start by writing down the mathematical expression for the quotient of -80 and -4, which involves a division operation. \[ \frac{-80}{-4} \]

Apply the rules of division

Recall that dividing two negative numbers results in a positive number. Apply this rule to our expression: \[ \frac{-80}{-4} = \frac{80}{4} \]

Simplify the expression

Now, we simplify the expression by dividing 80 by 4: \[ \frac{80}{4} = 20 \] The simplified expression for the quotient of -80 and -4 is 20.

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Key Concepts

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

Division of Integers

Integers are whole numbers that can be positive, negative, or zero. Among various arithmetic operations, division is particularly interesting when dealing with integers.
Division is essentially the process of determining how many times one number is contained within another. In the context of integers, this involves dividing one integer by another.

To express division, we often use the symbol "/" or a fraction bar, for example, \( \frac{a}{b} \).
When dividing integers, the result is not always a whole number. In cases where complete division isn鈥檛 possible, the result can be a repeating or terminating decimal.

When performing division of integers, one important aspect to keep in mind is the result's sign, which leads us to consider the rules for division with negative integers, essential for understanding the whole process.

Simplifying Expressions

Simplifying expressions is about reducing them to their most basic form. This makes it easier to work with numbers and helps consolidate operations into manageable results.
In arithmetic, especially with division, simplifying involves performing basic operations until the expression cannot be reduced further.

Look for common factors: Simplification starts by determining any common factors in the numerator and denominator, although in our context, it focuses on the division itself.
Follow division rules: Perform the division operation to find a clearer, shorter expression or number.

In our specific example, after dividing \(-80\) by \(-4\), the expression simplifies to \(20\). Simplifying helps verify results and maintain accuracy in calculations.

Negative Numbers Division

Dividing negative numbers is a frequent task in mathematics, important for both theoretical and practical applications.
When dividing integers with negative numbers, the key rule is understanding how signs affect the result.

Two negatives make a positive: When both the dividend and divisor are negative, as in our problem with \(-80\) divided by \(-4\), the result is positive. This is because two negatives cancel each other out with respect to sign.
Positive divided by negative: Results in a negative quotient, as the opposite signs do not cancel.
Negative divided by positive: Similarly, this also results in a negative quotient.

Understanding these rules is crucial. It allows precise calculations when handling operations involving negative numbers. This knowledge becomes foundational as you encounter more complex mathematical scenarios.

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91影视

Write a mathematical expression for each and simplify. The quotient of \(-80\) and \(-4\)

Short Answer

Step by step solution

Write down the quotient expression

Apply the rules of division

Simplify the expression

Key Concepts

Division of Integers

Simplifying Expressions

Negative Numbers Division

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