Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.
Answer (2)
To calculate the product of the fractions 6 5 and 3 7 , multiply the numerators and denominators to get 18 35 . This fraction is already in simplest form. Therefore, the answer is 18 35 .
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Multiply the numerators: 5 × 7 = 35 .
Multiply the denominators: 6 × 3 = 18 .
Write the result as a fraction: 18 35 .
The fraction 18 35 is already in its simplest form, so the final answer is 18 35 .
Explanation
Understanding the problem We are asked to multiply two fractions, 6 5 and 3 7 , and give the answer in its simplest form.
Multiplying the fractions To multiply fractions, we multiply the numerators together and the denominators together. So, we have: 6 5 × 3 7 = 6 × 3 5 × 7
Calculating numerator and denominator Now, we calculate the numerator and the denominator: 5 × 7 = 35 6 × 3 = 18 So, the fraction becomes: 18 35
Simplifying the fraction Now, we need to check if the fraction 18 35 can be simplified. To do this, we find the greatest common divisor (GCD) of 35 and 18. The factors of 35 are 1, 5, 7, and 35. The factors of 18 are 1, 2, 3, 6, 9, and 18. The only common factor is 1, so the GCD of 35 and 18 is 1. Since the GCD is 1, the fraction is already in its simplest form.
Final answer Therefore, the answer is 18 35 .
Examples
Fractions are used in everyday life, such as when baking, measuring ingredients, or splitting a pizza. For example, if you have 6 5 of a pizza and you want to share it with two friends, you would need to divide 6 5 by 3. Understanding how to multiply and simplify fractions is essential for solving these types of real-world problems.
