Work out $\frac{8}{11} \times \frac{3}{2}$. Give your answer as a fraction in its lowest terms.
Answer (1)
Multiply the numerators and denominators: 11 8 × 2 3 = 22 24 .
Find the greatest common divisor (GCD) of 24 and 22, which is 2.
Divide both the numerator and the denominator by the GCD: 22 ÷ 2 24 ÷ 2 = 11 12 .
The simplified fraction is 11 12 .
Explanation
Understanding the Problem We are given the expression 11 8 × 2 3 . Our goal is to multiply these fractions and simplify the result to its lowest terms.
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 11 8 × 2 3 = 11 × 2 8 × 3 = 22 24
Finding the Greatest Common Divisor (GCD) Now we need to simplify the fraction 22 24 to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 24 and 22 is 2.
Simplifying the Fraction Divide both the numerator and the denominator by their GCD: 22 ÷ 2 24 ÷ 2 = 11 12
Final Answer The fraction 11 12 is now in its lowest terms, as 12 and 11 have no common factors other than 1. Therefore, the final answer is 11 12 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 4 3 cup of flour and you only want to make half the recipe, you need to multiply 4 3 by 2 1 to find the new amount of flour needed. This gives 4 3 × 2 1 = 8 3 cup of flour. Understanding how to multiply and simplify fractions is essential for accurate measurements and successful cooking.
