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Chapter 1: Problem 445

Subtract. $$ -\frac{3}{5}-\left(-\frac{4}{5}\right) $$

Short Answer

Expert verified
The result is \(\frac{1}{5}\).

Step by step solution

01

Identify the Problem

We need to subtract \(-\frac{4}{5}\) from \(-\frac{3}{5}\). The expression is \(-\frac{3}{5}-(-\frac{4}{5})\).
02

Rewrite the Expression

Rewrite the expression by understanding that subtracting a negative is equivalent to adding the positive of that number. Therefore, \(-\frac{3}{5} - (-\frac{4}{5})\) is the same as \(-\frac{3}{5} + \frac{4}{5}\).
03

Combine the Fractions

Since the fractions have the same denominator, combine them directly: \(-\frac{3}{5} + \frac{4}{5} = \frac{-3 + 4}{5}\).
04

Simplify the Fraction

Simplify the numerator: \(-3 + 4 = 1\). Thus, \(\frac{-3 + 4}{5} = \frac{1}{5}\).

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Key Concepts

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

negative numbers in fractions
Subtracting fractions can be challenging, especially when negative numbers are involved.
A negative number simply means it's less than zero.
So, a negative fraction like \(-\frac{3}{5}\) represents a value below zero. When working with negative fractions, keep in mind these key points:
  • Subtracting a negative is the same as adding a positive. For example, \(-\frac{3}{5} - (-\frac{4}{5})\) becomes \(-\frac{3}{5} + \frac{4}{5}\).
  • Negative signs can be tricky. Ensure you're correctly identifying whether a fraction is negative when simplifying expressions.
Understanding these basics makes handling negative fractions less intimidating and ensures you can simplify operations accurately.
simplifying fractions
Simplifying fractions involves reducing them to their simplest form.
This means dividing the numerator and denominator by their greatest common divisor (GCD). However, in this problem, the fractions already share the same denominator. Hence, simplification mainly focuses on the numerator.
Here are easy steps to follow:
  • Combine fractions: For \(-\frac{3}{5} + \frac{4}{5}\), combine the numerators while keeping the denominator the same.
  • Simplify the numerator: Calculate \(-3 + 4 = 1\).
  • Result: The fraction becomes \frac{1}{5}\, which is already simplified.
By focusing on these steps, you can simplify almost any fraction operation efficiently.
fraction operations
Being proficient with fraction operations is essential for solving various math problems.
The operations include addition, subtraction, multiplication, and division.
In our example, the operation was subtraction, but we needed to understand how subtracting a negative number turned it into an addition problem.
  • Addition: When adding fractions with the same denominator, keep the denominator constant and add the numerators.
  • Subtraction: Change the subtraction of a negative to addition and then add as usual.
  • Multiplication: Multiply the numerators and denominators together.
  • Division: Invert (flip) the second fraction and multiply.
Grasping these basic operations and their unique approaches ensures you can handle any fraction problem confidently.

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