Work out $\frac{9}{20} \times 5$
Give your answer as a fraction in its simplest form.
Answer (1)
Multiply the fraction by the whole number: 20 9 × 5 = 20 9 × 5 .
Calculate the numerator: 9 × 5 = 45 , so the fraction becomes 20 45 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 5: 20 ÷ 5 45 ÷ 5 = 4 9 .
The simplified fraction is 4 9 .
Explanation
Understanding the problem We are asked to calculate the product of a fraction and a whole number, and then express the answer as a fraction in its simplest form. The problem is to compute 20 9 × 5 .
Multiplying the fractions To multiply a fraction by a whole number, we can write the whole number as a fraction with a denominator of 1. So, we have 20 9 × 1 5 . Then, we multiply the numerators and the denominators: 20 9 × 1 5 = 20 × 1 9 × 5 = 20 45
Simplifying the fraction Now, we need to simplify the fraction 20 45 . Both the numerator and the denominator are divisible by 5. Dividing both by 5, we get: 20 ÷ 5 45 ÷ 5 = 4 9
Final check The fraction 4 9 is in its simplest form because 9 and 4 have no common factors other than 1.
Final Answer Therefore, the answer is 4 9 .
Examples
Imagine you are baking a cake and the recipe calls for 20 9 of a cup of sugar per serving. If you want to make 5 servings, you need to calculate the total amount of sugar required. This is done by multiplying 20 9 by 5, which equals 4 9 cups of sugar. Converting this improper fraction to a mixed number, you would need 2 4 1 cups of sugar. This example shows how multiplying fractions is useful in everyday cooking and baking scenarios.
