Work out $\frac{2}{5} \times \frac{6}{7}$. Give your answer in its simplest form.
Answer (1)
Multiply the numerators: 2 × 6 = 12 .
Multiply the denominators: 5 × 7 = 35 .
The result is 35 12 .
The fraction 35 12 is already in its simplest form, so the final answer is 35 12 .
Explanation
Understanding the Problem We are asked to calculate the product of two fractions, 5 2 and 7 6 , and to give the answer in its simplest form.
Multiplying the Fractions To multiply two fractions, we multiply the numerators together and the denominators together. So, we have: 5 2 × 7 6 = 5 × 7 2 × 6 Multiplying the numerators gives 2 × 6 = 12 , and multiplying the denominators gives 5 × 7 = 35 . Therefore, the result is 35 12 .
Simplifying the Fraction Now we need to check if the fraction 35 12 can be simplified. To do this, we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (35). The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 35 are 1, 5, 7, and 35. The only common factor is 1, so the GCD of 12 and 35 is 1. This means that the fraction 35 12 is already in its simplest form.
Final Answer Therefore, the final answer is 35 12 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or calculating proportions. For example, if a recipe calls for 5 2 of a cup of flour and you want to make 7 6 of the recipe, you would multiply these two fractions to find out how much flour you need. This problem demonstrates a basic but essential skill in mathematics that has many practical applications.
