Work out $\frac{5}{8} \times \frac{9}{2}$. Answer as a fraction in its simplest form.
Answer (1)
Multiply the numerators: 5 × 9 = 45 .
Multiply the denominators: 8 × 2 = 16 .
Form the fraction: 16 45 .
Simplify the fraction (if possible): 16 45 is already in its simplest form. 16 45
Explanation
Understanding the Problem We are asked to multiply two fractions, 8 5 and 2 9 , and express the answer as a fraction in its simplest form.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together. So, we have: 8 5 × 2 9 = 8 × 2 5 × 9
Calculating Numerator and Denominator Now, we calculate the numerator and the denominator: 5 × 9 = 45 8 × 2 = 16 So, the fraction becomes: 16 45
Simplifying the Fraction Now we need to check if the fraction 16 45 can be simplified. To do this, we look for common factors between the numerator (45) and the denominator (16). The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 16 are 1, 2, 4, 8, and 16. The only common factor is 1, which means the fraction is already in its simplest form.
Final Answer Therefore, the answer is 16 45 .
Examples
In baking, if a recipe calls for 8 5 of a cup of flour and you want to make 2 9 batches, you would multiply these fractions to find the total amount of flour needed. This calculation ensures you have the correct proportions for your recipe, maintaining the desired taste and texture. For example, if a cookie recipe requires 8 5 cup of sugar and you plan to make 4.5 batches, multiplying 8 5 × 2 9 tells you exactly how much sugar you need, which is 16 45 cups or 2 16 13 cups. This ensures the cookies are neither too sweet nor too bland.
