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Chapter 10: Problem 59

Subtract. $$ -\frac{4}{7}-\left(-\frac{10}{7}\right) $$

Short Answer

Expert verified
The answer is \frac{6}{7}.

Step by step solution

01

Understand the Problem

The exercise asks to subtract \(-\frac{4}{7}\) by \(-\frac{10}{7}\). This operations involves subtraction of a negative fraction by another negative fraction.
02

Simplify the Expression

Use the rule of double negatives to simplify the expression. Subtracting a negative is the same as adding a positive: \[-\frac{4}{7} - (-\frac{10}{7}) = -\frac{4}{7} + \frac{10}{7}.\]
03

Combine the Fractions

\[-\frac{4}{7} + \frac{10}{7}\] can be combined because they have the same denominator. Simply add the numerators: \[-4 + 10 = 6. \]
04

Write the Final Answer

After combining, the final answer is: \[\frac{6}{7}\]

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Key Concepts

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

negative fractions
Understanding negative fractions is crucial in this exercise. A negative fraction is simply a fraction with a negative sign in front of either the numerator, the denominator, or the whole fraction. For example, \(-\frac{4}{7}\) tells us that we have a fraction, but it is less than zero. This negative sign affects the value of the entire fraction, making it important to recognize and correctly handle them in calculations. When dealing with negative fractions, always watch where the negative sign is placed, as it influences the direction and result of the operation.
double negatives in math
In math, a double negative occurs when two negative signs are used in an operation, particularly in subtraction. According to the rules of arithmetic, subtracting a negative number is the same as adding a positive one. This can be thought of as 'reversing the subtraction' because you're essentially taking away the negative influence. In our exercise, we have \(-\frac{4}{7} - (-\frac{10}{7})\). The double negative becomes: \(-\frac{4}{7} + \frac{10}{7}\). This simplification helps streamline the problem, allowing us to move on to combining the fractions more easily.
combining fractions
Combining fractions is straightforward when the fractions share the same denominator. This shared denominator allows us to directly add or subtract the numerators while keeping the denominator constant. In this example, after eliminating the double negative, we have \(-\frac{4}{7} + \frac{10}{7}\). Both fractions have a denominator of 7, so we focus on the numerators: \(-4 + 10\). Combining these gives us 6. The final combined fraction is \frac{6}{7}\. Always ensure the denominators match before combining fractions, and simplify the result if possible to achieve the final answer.

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