Simplify.
$\frac{\frac{15}{16}}{\frac{3}{5}}$
Answer (1)
Multiply the numerator by the reciprocal of the denominator: 16 15 ⋅ 3 5 .
Cancel common factors: 16 5 ⋅ 3 ⋅ 3 5 = 16 5 ⋅ 1 5 .
Multiply the remaining fractions: 16 5 ⋅ 1 5 = 16 25 .
The simplified expression is 16 25 .
Explanation
Understanding the Problem We are asked to simplify a fraction divided by another fraction. The expression is 5 3 16 15 .
Rewriting the Expression To simplify the expression, we can multiply the numerator by the reciprocal of the denominator. That is, 5 3 16 15 = 16 15 ⋅ 3 5 .
Simplifying the Fraction Then, we can simplify the fraction by canceling common factors. 16 15 ⋅ 3 5 = 16 5 ⋅ 3 ⋅ 3 5 = 16 5 ⋅ 1 5 = 16 25 .
Final Answer Therefore, the simplified expression is 16 25 .
Examples
Understanding how to simplify fractions is essential in many real-life situations, such as cooking, where you might need to adjust ingredient quantities based on a recipe. For example, if a recipe calls for 5 3 of a cup of flour, but you only want to make 16 15 of the recipe, you would use the simplified fraction 16 25 to determine the adjusted amount of flour needed. This ensures that the proportions remain correct, and the dish turns out as expected. Simplifying fractions also helps in calculating proportions in construction, finance, and other fields where accurate scaling is necessary.
