[tex]\frac{1}{2}+\frac{-3}{5}+\frac{3}{2}[/tex]
Answer (2)
To solve 2 1 + 5 − 3 + 2 3 , first find a common denominator, which is 10. After converting the fractions, we combine them to get 10 14 , which simplifies to 5 7 . The final answer is 5 7 .
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Find a common denominator for the fractions, which is 10.
Rewrite each fraction with the common denominator: 10 5 + 10 − 6 + 10 15 .
Add the numerators: 5 + ( − 6 ) + 15 = 14 .
Simplify the fraction: 10 14 = 5 7 .
The final answer is 5 7 .
Explanation
Understanding the Problem We are given the expression 2 1 + 5 − 3 + 2 3 . Our goal is to evaluate this expression and find its value.
Finding a Common Denominator To add these fractions, we need to find a common denominator. The least common multiple of 2 and 5 is 10. So, we will rewrite each fraction with a denominator of 10.
Rewriting Fractions 2 1 = 2 × 5 1 × 5 = 10 5
5 − 3 = 5 × 2 − 3 × 2 = 10 − 6
2 3 = 2 × 5 3 × 5 = 10 15
Adding the Fractions Now we can add the fractions: 10 5 + 10 − 6 + 10 15 = 10 5 − 6 + 15 = 10 14
Simplifying the Fraction We can simplify the fraction 10 14 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 10 14 = 10 ÷ 2 14 ÷ 2 = 5 7
Final Answer Therefore, the value of the expression is 5 7 .
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 need 2 1 cup of flour and 2 3 cups of sugar for a recipe, you need to add these fractions to determine the total amount of ingredients. In this case, 2 1 + 2 3 = 2 4 = 2 cups of ingredients.
