Simplify the following expression: [tex]$\frac{7 k^2}{4 k^3}$[/tex]
Answer (1)
Rewrite the expression as a product: 4 7 ⋅ k 3 k 2 .
Simplify the fraction by canceling common factors: k 3 k 2 = k 1 .
Combine the constant and the simplified fraction: 4 7 ⋅ k 1 = 4 k 7 .
The simplified expression is 4 k 7 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 k 3 7 k 2 . This involves simplifying a rational expression by canceling common factors.
Rewriting the Expression First, we can rewrite the expression as a product of a constant and a fraction involving k : 4 k 3 7 k 2 = 4 7 ⋅ k 3 k 2
Simplifying the Fraction Now, we simplify the fraction k 3 k 2 . Since k 3 = k 2 ⋅ k , we can cancel out the k 2 term from both the numerator and the denominator: k 3 k 2 = k 2 ⋅ k k 2 = k 1
Combining the Terms Finally, we combine the constant 4 7 with the simplified fraction k 1 to get the final simplified expression: 4 7 ⋅ k 1 = 4 k 7
Final Answer Therefore, the simplified expression is 4 k 7 .
Examples
Imagine you are scaling a recipe. If the original recipe calls for 4 k 3 7 k 2 cups of flour, where k depends on the number of servings, simplifying the expression to 4 k 7 helps you quickly determine the amount of flour needed for any number of servings. This kind of simplification is useful in many real-world scenarios where you need to adjust quantities based on a variable factor.
