Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.
Answer (2)
To find 6 5 × 3 7 , we multiply the numerators to get 35 and the denominators to get 18, resulting in the fraction 18 35 . This fraction cannot be simplified further, so the answer remains 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 .
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 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 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 bill with friends. For example, if you are making a cake and the recipe calls for 6 5 of a cup of flour, and you only want to make 3 7 of the recipe, you would need to calculate 6 5 × 3 7 to determine how much flour you need. This problem demonstrates a simple multiplication of fractions, which is a fundamental skill in many practical situations.
