$-\frac{6}{7}+\left(-\frac{4}{7}\right)$
Answer (2)
To add the fractions − 7 6 and − 7 4 , we combine the numerators since they share the same denominator, resulting in − 7 10 .
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Add the numerators since the denominators are the same: 7 − 6 + ( − 4 ) .
Simplify the numerator: − 6 + ( − 4 ) = − 10 .
The result is 7 − 10 .
Therefore, the final answer is − 7 10 .
Explanation
Understanding the Problem We are asked to evaluate the sum of two negative fractions: − 7 6 and − 7 4 . Both fractions have the same denominator, which is 7.
Adding the Numerators Since the fractions have the same denominator, we can add the numerators directly: − 7 6 + ( − 7 4 ) = 7 − 6 + ( − 4 )
Simplifying the Numerator Now, we simplify the numerator: − 6 + ( − 4 ) = − 10
Final Result So, the result is: 7 − 10 = − 7 10
Examples
Understanding how to add and subtract fractions, especially those with common denominators, is crucial in many real-life situations. For instance, if you're baking a cake and need to combine different amounts of flour from two open bags, knowing how to add fractions helps you determine the total amount of flour you have. Similarly, in construction, when measuring lengths of materials, you often need to add or subtract fractional measurements to ensure accurate cuts and fits. This skill is also essential in personal finance when budgeting and tracking expenses, as you might need to calculate the total of several small transactions that are represented as fractions of a dollar.
