$-\frac{6}{7}+\left(-\frac{4}{7}\right)$
Answer (2)
The problem requires adding two negative fractions with a common denominator.
Add the numerators: − 6 + ( − 4 ) = − 10 .
Write the result as a fraction with the common denominator: − 7 10 .
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: − 6 + ( − 4 ) = − 10 .
Writing the Result Now, we write the result as a fraction with the common denominator: − 7 10 . This fraction is already in its simplest form.
Final Answer Therefore, the final answer is − 7 10 .
Examples
Fractions are used in everyday life, such as when calculating proportions in recipes, determining discounts while shopping, or understanding probabilities in games. For instance, if you are baking a cake and need to halve a recipe that calls for 3 2 cup of flour, you would need to calculate 2 1 × 3 2 , which simplifies to 3 1 cup of flour. Similarly, when splitting a bill among friends or understanding sale percentages, fractions play a crucial role in ensuring fair and accurate calculations.
To evaluate the sum of the fractions − 7 6 and − 7 4 , add the numerators to get − 10 , resulting in the final answer of − 7 10 . Both fractions share a common denominator of 7, making the addition simple. The overall answer is − 7 10 .
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