Add.
$\frac{1}{5}+\frac{-1}{2}=$
Answer (2)
Find the least common denominator (LCD) of 5 and 2, which is 10.
Rewrite both fractions with the LCD: 5 1 = 10 2 and 2 − 1 = 10 − 5 .
Add the numerators: 10 2 + 10 − 5 = 10 2 − 5 = 10 − 3 .
The final answer is 10 − 3 .
Explanation
Understanding the Problem We are asked to add two fractions, 5 1 and 2 − 1 . To add fractions, they must have a common denominator.
Finding the Common Denominator The least common denominator (LCD) of 5 and 2 is 10. We need to rewrite both fractions with 10 as the denominator.
Rewriting the Fractions To convert 5 1 to a fraction with a denominator of 10, we multiply both the numerator and the denominator by 2: 5 1 = 5 × 2 1 × 2 = 10 2 To convert 2 − 1 to a fraction with a denominator of 10, we multiply both the numerator and the denominator by 5: 2 − 1 = 2 × 5 − 1 × 5 = 10 − 5
Adding the Fractions Now we can add the fractions: 10 2 + 10 − 5 = 10 2 + ( − 5 ) = 10 − 3
Final Answer The resulting fraction is 10 − 3 , which is already in simplest form. Therefore, the sum of 5 1 and 2 − 1 is 10 − 3 .
Examples
Fractions are a fundamental part of everyday life. For instance, if you are baking a cake and the recipe calls for 5 1 of a cup of sugar and you only have a 2 1 cup measuring spoon, you need to figure out how much to take out to get the correct amount. Adding and subtracting fractions helps in accurately measuring ingredients, managing time, and understanding proportions in various real-life situations.
To add 5 1 and 2 − 1 , we first find a common denominator, which is 10. We rewrite the fractions as 10 2 and 10 − 5 , and their sum is 10 − 3 . Therefore, the final answer is 10 − 3 .
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