Simplify [tex]1 / 3 x+y[/tex]
Answer (2)
Rewrite the expression: 3 1 x + y .
Find a common denominator: y = 3 3 y .
Combine the terms: 3 1 x + 3 3 y = 3 x + 3 y .
The simplified expression is: 3 x + 3 y .
Explanation
Understanding the Expression We are asked to simplify the expression 1/3 x + y . This involves combining two terms, one involving x and the other y , into a single fraction.
Finding a Common Denominator To simplify the expression 3 1 x + y , we need to find a common denominator for both terms. In this case, the common denominator is 3. We can rewrite y as a fraction with a denominator of 3: y = 3 3 y .
Rewriting the Expression Now we can rewrite the original expression with the common denominator: 3 1 x + y = 3 1 x + 3 3 y .
Combining the Fractions Combine the two fractions: 3 1 x + 3 3 y = 3 x + 3 y .
Final Answer The simplified form of the expression 1/3 x + y is 3 x + 3 y .
Examples
In real life, this type of simplification can be useful when dealing with proportions or ratios. For example, if you are mixing a solution that requires 1/3 part of a substance 'x' and a certain amount of another substance 'y', you might want to express the total amount of the mixture as a single fraction to easily calculate the required quantities. If 'x' represents a certain chemical and 'y' represents water, then 3 x + 3 y gives you a simplified way to understand the ratio of chemical to the total solution.
To simplify the expression 3 1 x + y , we first rewrite y as 3 3 y to have a common denominator. This allows us to combine the terms and we end up with the simplified form 3 x + 3 y .
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