Find the product.
$\frac{7}{16} \times \frac{4}{49}$
Enter your simplified answer.
Answer (2)
Multiply the numerators and denominators: 16 7 × 49 4 = 16 × 49 7 × 4 .
Factor the numerator and denominator to identify common factors: 4 × 4 × 7 × 7 7 × 4 .
Cancel the common factors: 4 × 4 × 7 × 7 7 × 4 = 4 × 7 1 .
Multiply the remaining factors in the denominator: 4 × 7 1 = 28 1 . The final answer is 28 1 .
Explanation
Understanding the Problem We are asked to find the product of two fractions, 16 7 and 49 4 , and simplify the result.
Multiplying the Fractions To find the product of two fractions, we multiply the numerators and the denominators: 16 7 × 49 4 = 16 × 49 7 × 4
Simplifying the Fraction Now, we simplify the fraction by canceling common factors. Notice that 49 = 7 × 7 and 16 = 4 × 4 . So we can rewrite the fraction as: 16 × 49 7 × 4 = 4 × 4 × 7 × 7 7 × 4 We can cancel a factor of 4 from the numerator and denominator, and a factor of 7 from the numerator and denominator: 4 × 4 × 7 × 7 7 × 4 = 4 × 4 × 7 × 7 7 × 4 = 4 × 7 1
Final Result Finally, we multiply the remaining factors in the denominator: 4 × 7 1 = 28 1 So, the simplified product of the two fractions is 28 1 .
Examples
Fractions are used in everyday life, such as when baking, measuring ingredients, or splitting a bill with friends. For example, if you have 16 7 of a pizza and you eat 49 4 of that remaining amount, you have eaten 28 1 of the whole pizza. Understanding how to multiply and simplify fractions is essential for many practical applications.
The product of 16 7 and 49 4 is 28 1 after simplifying the fraction. We obtained this by multiplying the numerators and denominators, then simplifying by finding the greatest common divisor. Thus, the final answer is 28 1 .
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