Multiply. Write your answer in simplest form.
$\frac{5}{7} \times \frac{7}{10}$
Answer (2)
To multiply 7 5 and 10 7 , we find the product as 70 35 . It simplifies to 2 1 by dividing the numerator and denominator by their greatest common divisor, which is 35. Therefore, the final simplified answer is 2 1 .
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Multiply the numerators and denominators: 7 5 × 10 7 = 7 × 10 5 × 7 = 70 35 .
Find the greatest common divisor (GCD) of 35 and 70, which is 35.
Divide both the numerator and the denominator by the GCD: 70 ÷ 35 35 ÷ 35 = 2 1 .
The simplified answer is 2 1 .
Explanation
Problem Analysis We are asked to multiply two fractions and simplify the result. The given expression is 7 5 × 10 7 .
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together. So, we have: 7 5 × 10 7 = 7 × 10 5 × 7 = 70 35
Simplifying the Fraction Now, we need to simplify the fraction 70 35 . We can simplify this fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by the GCD. The GCD of 35 and 70 is 35. So, we divide both the numerator and the denominator by 35: 70 35 = 70 ÷ 35 35 ÷ 35 = 2 1
Final Answer Therefore, the simplified form of the product is 2 1 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 2 1 cup of flour, and you want to double the recipe, you would need 2 × 2 1 = 1 cup of flour. Understanding how to multiply and simplify fractions is essential for accurate measurements and successful cooking.
