Work out $\frac{2}{5} \times \frac{8}{9}$. Give your answer in its simplest form.
Answer (2)
To multiply the fractions 5 2 and 9 8 , we get 45 16 . This fraction is already in its simplest form. Thus, the final answer is 45 16 .
;
45 16
Explanation
Problem Analysis We are asked to multiply two fractions, 5 2 and 9 8 , and give the answer in its simplest form. This means we need to multiply the numerators together and the denominators together, and then simplify the resulting fraction if possible.
Multiplying Numerators First, we multiply the numerators: 2 × 8 = 16 .
Multiplying Denominators Next, we multiply the denominators: 5 × 9 = 45 .
Forming the Fraction So, the product of the two fractions is 45 16 .
Checking for Simplification Now, we need to check if this fraction can be simplified. To do this, we look for common factors between the numerator (16) and the denominator (45). The factors of 16 are 1, 2, 4, 8, and 16. The factors of 45 are 1, 3, 5, 9, 15, and 45. The only common factor is 1, which means the fraction is already in its simplest form.
Final Answer Therefore, the answer is 45 16 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 5 2 of a cup of flour and you want to double the recipe, you would need to multiply 5 2 by 2. Similarly, if you are calculating the area of a rectangular garden that is 5 2 meters wide and 9 8 meters long, you would multiply these two fractions to find the area. Understanding how to multiply fractions is essential for many practical applications.
