Find the product. 17/5 ×5/3
The Correct Answer and Explanation is:
To find the product of ( \frac{17}{5} \times \frac{5}{3} ), we will use the rules for multiplying fractions. The process involves multiplying the numerators together and the denominators together.
Step 1: Multiply the Numerators
First, we multiply the numerators of both fractions:
[
17 \times 5 = 85
]
Step 2: Multiply the Denominators
Next, we multiply the denominators:
[
5 \times 3 = 15
]
Step 3: Form the New Fraction
Now, we can form a new fraction with the results from Step 1 and Step 2:
[
\frac{85}{15}
]
Step 4: Simplifying the Fraction
To simplify ( \frac{85}{15} ), we need to find the greatest common divisor (GCD) of 85 and 15. The prime factorization of these numbers helps:
- The prime factorization of 85 is ( 5 \times 17 ).
- The prime factorization of 15 is ( 3 \times 5 ).
The GCD is 5, as it is the largest number that divides both 85 and 15. Now we can divide both the numerator and the denominator by their GCD:
[
\frac{85 \div 5}{15 \div 5} = \frac{17}{3}
]
Final Result
Thus, the product of ( \frac{17}{5} \times \frac{5}{3} ) simplifies to:
[
\frac{17}{3}
]
Conclusion
The final answer is ( \frac{17}{3} ).
In conclusion, multiplying fractions involves straightforward steps: multiply the numerators to get the new numerator and the denominators to get the new denominator. If possible, the resultant fraction should be simplified to its lowest terms. In this example, simplifying revealed that both numbers shared a common factor, allowing for a more compact representation of the fraction. Understanding how to multiply fractions and simplify them is a fundamental skill in mathematics, applicable in various fields, including cooking, construction, and finance, where precise calculations are necessary.