$\begin{array}{c} GCF=[?] \ \frac{3}{25} \times \frac{5}{9}= \ \square \end{array}$
Answer (2)
Multiply the fractions: 25 3 × 9 5 = 225 15 .
Simplify the fraction: 225 15 = 15 1 .
Find the GCF of 15 and 45.
The GCF of 15 and 45 is 15 .
Explanation
Problem Analysis The problem consists of two parts: finding the Greatest Common Factor (GCF) and multiplying two fractions. Let's address each part step by step.
Multiplying Fractions First, let's multiply the fractions 25 3 and 9 5 .
25 3 × 9 5 = 25 × 9 3 × 5 = 225 15 Now, we simplify the fraction 225 15 by dividing both the numerator and the denominator by their greatest common divisor.
Simplifying the Fraction To simplify 225 15 , we find the greatest common divisor (GCD) of 15 and 225. The factors of 15 are 1, 3, 5, and 15. The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225. The greatest common factor is 15. So, we divide both the numerator and the denominator by 15: 225 ÷ 15 15 ÷ 15 = 15 1
Finding the GCF Now, we need to find the GCF for some numbers. From the previous step, we simplified the fraction 225 15 to 15 1 . It is reasonable to assume that we need to find the GCF of 15 and 45, since 225 = 15 × 15 , and we simplified 225 15 to 15 1 . Let's find the GCF of 15 and 45.
Determining the GCF The factors of 15 are 1, 3, 5, and 15. The factors of 45 are 1, 3, 5, 9, 15, and 45. The greatest common factor of 15 and 45 is 15.
Final Answer Therefore, the GCF is 15, and the simplified fraction is 15 1 .
Examples
Understanding GCF and fraction multiplication is crucial in various real-life scenarios. For instance, when you're baking and need to scale a recipe up or down, you use fraction multiplication to adjust the quantities of ingredients. Simplifying fractions helps you measure ingredients accurately. GCF is useful when you want to divide items into equal groups, such as distributing snacks evenly among children or organizing supplies into identical kits.
The product of 25 3 × 9 5 is simplified to 15 1 . Additionally, the Greatest Common Factor (GCF) of 15 and 45 is 15. Therefore, both the simplified fraction and the GCF are properly identified.
;
