Evaluate.
$-\frac{1}{5}-\left(-\frac{1}{8}\right)$
Write your answer in simplest form.
Answer (1)
Rewrite the subtraction of a negative fraction as addition: − 5 1 − ( − 8 1 ) = − 5 1 + 8 1 .
Find the least common denominator (LCM) of 5 and 8, which is 40.
Convert both fractions to have the common denominator: − 5 1 = − 40 8 and 8 1 = 40 5 .
Add the fractions: − 40 8 + 40 5 = 40 − 3 . The final answer is − 40 3 .
Explanation
Understanding the problem We are asked to evaluate the expression − 5 1 − ( − 8 1 ) and write the answer in simplest form. This involves subtracting a negative fraction from a negative fraction.
Rewriting the expression First, we rewrite the expression as an addition problem: − 5 1 − ( − 8 1 ) = − 5 1 + 8 1 To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5 and 8 is 40.
Finding a common denominator Now, we rewrite each fraction with the common denominator of 40: − 5 1 = − 5 × 8 1 × 8 = − 40 8 8 1 = 8 × 5 1 × 5 = 40 5
Adding the fractions Substitute the equivalent fractions back into the expression: − 40 8 + 40 5 = 40 − 8 + 5 = 40 − 3 So, the result is − 40 3 .
Simplifying the fraction Since 3 and 40 have no common factors other than 1, the fraction is already in its simplest form. Therefore, the final answer is − 40 3 .
Examples
Fractions are used in everyday life, such as when calculating proportions in recipes, determining discounts while shopping, or understanding probabilities. For example, if you are baking a cake and need to halve a recipe that calls for 4 1 cup of sugar, you need to calculate 2 1 × 4 1 , which equals 8 1 cup. Understanding how to add, subtract, multiply, and divide fractions is essential for accurate measurements and successful outcomes in various real-world scenarios.
