Simplify [tex]$1 / 3 x+y$[/tex]

Rewrite the expression as a sum of fractions: 3 1 ​ x + y .
Find a common denominator: The common denominator is 3.
Rewrite y with the common denominator: y = 3 3 y ​ .
Combine the fractions: 3 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 combine the terms, we need to find a common denominator. In this case, the common denominator is 3. We can rewrite the expression as 3 1 ​ x + y .

Rewriting y Now, we rewrite y with the denominator 3: y = 3 3 y ​ .

Combining the Terms Finally, we combine the terms: 3 1 ​ x + 3 3 y ​ = 3 x + 3 y ​ .


Examples
Imagine you are sharing a pizza with two friends. The pizza is cut into 3 slices. You get one slice ( x /3 ) and your friend gets a whole pizza ( y ). To figure out the total amount of pizza you both have, you need to add your slice to your friend's whole pizza. This simplification helps you understand the total fraction of pizzas you and your friend possess.

Answered by GinnyAnswer | 2025-07-03

To simplify 3 1 ​ x + y , we rewrite it as a fraction with a common denominator. The result is 3 x + 3 y ​ .
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Answered by Anonymous | 2025-07-04