Problem 4 Compute the exact value of the g... [FREE SOLUTION]

91影视

Prealgebra

David Arnold

$Math Studyset 91影视 Explanations$ Math

2020 Edition

Chapter 2: Problem 4

Compute the exact value of the given expression. $-6-\frac{-7}{7}$

Short Answer

Expert verified

The exact value of the expression is -5.

Step by step solution

Simplify the Fraction

First, we look at the fraction $-\frac{-7}{7}$. Simplifying this means dividing $-7$ by $7$. This gives us $-1\times\frac{7}{7}$, which further simplifies to $-1\times 1 = 1$. Therefore, $-\frac{-7}{7} = 1$.

Substitute the Simplified Value into the Expression

Now that we have simplified the fraction, substitute $1$ back into the expression. The expression becomes $-6 + 1$.

Perform the Addition

Carry out the addition operation on the expression $-6 + 1$. Adding $1$ to $-6$ results in $-6 + 1 = -5$.

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Key Concepts

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

Simplifying Fractions

Fractions can sometimes look more complicated than they really are. Simplifying a fraction means reducing it to its simplest form. This is very helpful in making calculations easier and faster.

Here's how you simplify fractions:

Divide the numerator by the denominator. The numerator is the number on top, and the denominator is the number below the line.
Check if both the numerator and the denominator have a common factor. If they do, divide both by it to further simplify the fraction.

In our exercise, we had the fraction $-\frac{-7}{7}$. Dividing $-7$ by $7$ results in $-1$.

But because we had two negative signs, they cancel each other out, turning our fraction into $1$. This is a basic rule in arithmetic: a negative divided by another negative is a positive.

Negative Numbers

Negative numbers can sometimes be confusing, but they follow predictable rules that always stay the same.

A negative number is any number less than zero. In the context of adding or subtracting, negatives take away from the total. Here's a simple guide to working with them:

Adding a negative number is like subtracting its positive equivalent.
Subtracting a negative number is actually like adding its positive counterpart.

In our exercise, the expression was $-6 - \frac{-7}{7}$. We simplified this to $-6 + 1$. The negative sign in front of $\frac{-7}{7}$ was removed after simplification, turning subtraction into addition. This led to the calculation of $-6 + 1$.

Basic Arithmetic Operations

Understanding basic arithmetic operations is crucial for prealgebra, especially when dealing with integers and fractions. These operations are addition, subtraction, multiplication, and division.

Let's briefly review them:

Addition combines two numbers to form a total.
Subtraction reduces a number by removing the value of another.
Multiplication adds a number to itself a specified number of times.
Division splits a number into equal parts.

In our problem, we primarily used addition and subtraction. First, we simplified the fraction to $1$. Then the expression became $-6 + 1$. We added $1$ to $-6$, which takes us one step closer to zero, resulting in $-5$.

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91影视

Compute the exact value of the given expression. \(-6-\frac{-7}{7}\)

Short Answer

Step by step solution

Simplify the Fraction

Substitute the Simplified Value into the Expression

Perform the Addition

Key Concepts

Simplifying Fractions

Negative Numbers

Basic Arithmetic Operations

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