Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
[tex]$\frac{7}{4}+\left(-\frac{6}{7}\right)$[/tex]
Answer (2)
Find a common denominator for the fractions, which is 28.
Rewrite the fractions with the common denominator: 4 7 = 28 49 and − 7 6 = − 28 24 .
Add the fractions: 28 49 − 28 24 = 28 25 .
The fraction 28 25 is in simplest form, so the final answer is 28 25 .
Explanation
Understanding the Problem We need to evaluate the expression 4 7 + ( − 7 6 ) . This involves adding a positive fraction to a negative fraction. To do this, we need to find a common denominator.
Finding the Common Denominator The least common multiple (LCM) of 4 and 7 is 28. This will be our common denominator.
Rewriting Fractions Now, we rewrite each fraction with the common denominator of 28: 4 7 = 4 × 7 7 × 7 = 28 49 − 7 6 = − 7 × 4 6 × 4 = − 28 24
Adding the Fractions Next, we add the two fractions: 28 49 + ( − 28 24 ) = 28 49 − 24 = 28 25
Simplifying the Result Finally, we check if the fraction 28 25 can be simplified. The factors of 25 are 1, 5, and 25. The factors of 28 are 1, 2, 4, 7, 14, and 28. The only common factor is 1, so the fraction is already in its simplest form.
Final Answer Therefore, the final answer is 28 25 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add and subtract fractions is essential for accurate calculations in these situations. For example, if you are baking a cake and need to combine 4 7 cups of flour with − 7 6 cups of sugar (representing a reduction from the initial amount), you would perform the calculation above to determine the final amount.
To evaluate 4 7 + ( − 7 6 ) , we first find a common denominator, which is 28. Rewriting the fractions leads to 28 49 − 28 24 = 28 25 . The final answer in simplest form is 28 25 .
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