Write $\frac{7 x+13}{2}+\frac{4 x+5}{2}$ as a single fraction in its simplest form.
Answer (1)
To add the two fractions, we combine the numerators since the denominators are the same. Then, we simplify the resulting expression by combining like terms. The final simplified fraction is 2 11 x + 18 .
Explanation
Understanding the Problem We are asked to add two fractions that have the same denominator. This makes the addition straightforward, as we only need to add the numerators and keep the denominator the same.
Adding the Fractions To add the fractions 2 7 x + 13 and 2 4 x + 5 , we add the numerators and keep the common denominator: 2 7 x + 13 + 2 4 x + 5 = 2 ( 7 x + 13 ) + ( 4 x + 5 )
Simplifying the Numerator Now, we simplify the numerator by combining like terms: 2 7 x + 13 + 4 x + 5 = 2 ( 7 x + 4 x ) + ( 13 + 5 ) = 2 11 x + 18
Final Simplification The fraction 2 11 x + 18 is now in its simplest form, as there are no common factors between the numerator and the denominator that can be cancelled out.
Examples
Fractions are a fundamental concept in mathematics and are used in various real-life situations. For example, when baking, you might need to combine fractions of ingredients, such as flour and sugar. If a recipe calls for 2 7 x + 13 grams of flour and 2 4 x + 5 grams of sugar, where x represents a variable affecting the quantity, adding these fractions helps determine the total amount of dry ingredients needed. Simplifying the resulting fraction ensures you have the most concise representation of the total quantity, making it easier to measure and manage the ingredients.
