Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.
Answer (1)
Multiply the numerators: 5 × 7 = 35 .
Multiply the denominators: 6 × 3 = 18 .
Form the fraction: 18 35 .
Simplify the fraction (if possible): 18 35 is already in its simplest form. 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 the Numerator and Denominator Now, we perform the multiplication in the numerator and the denominator: 5 × 7 = 35 6 × 3 = 18 So, the fraction becomes: 18 35
Simplifying the Fraction To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. 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 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 multiply 6 5 by 3 1 to find out how much of the whole pizza each person gets. This gives 6 5 × 3 1 = 18 5 , meaning each person gets 18 5 of the whole pizza.
