-$\frac{5}{8}+\frac{2}{3}$
Answer (2)
Find a common denominator for the fractions, which is 24.
Rewrite the fractions with the common denominator: − 8 5 = − 24 15 and 3 2 = 24 16 .
Add the fractions: − 24 15 + 24 16 = 24 1 .
The final answer is 24 1 .
Explanation
Finding a Common Denominator We are asked to evaluate the expression − 8 5 + 3 2 . This involves adding two fractions, one negative and one positive. To do this, we need to find a common denominator.
Rewriting Fractions The least common multiple of 8 and 3 is 24. So, we will rewrite both fractions with a denominator of 24. To convert − 8 5 to a fraction with a denominator of 24, we multiply both the numerator and the denominator by 3: − 8 5 = − 8 × 3 5 × 3 = − 24 15 . To convert 3 2 to a fraction with a denominator of 24, we multiply both the numerator and the denominator by 8: 3 2 = 3 × 8 2 × 8 = 24 16 .
Adding the Fractions Now we can add the two fractions: − 24 15 + 24 16 = 24 − 15 + 16 = 24 1 .
Final Answer The result is 24 1 , which is already in simplest form.
Examples
Fractions are used in everyday life, such as when baking, 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 making a cake and the recipe calls for 8 5 cup of flour, but you only have 3 2 cup, you need to determine how much more flour you need. This involves subtracting the fractions to find the difference: 8 5 − 3 2 .
To add the fractions − 8 5 and 3 2 , we find a common denominator, which is 24. We rewrite the fractions as − 24 15 and 24 16 , then add them to get 24 1 . The final answer is 24 1 .
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