Multiply. Write your answer as a fraction in simplest form
The Correct Answer and Explanation is:
The correct answer is 9/10.
Explanation:
Objective:
To multiply the fractions 3/4 and 6/5 and write the final answer in its simplest form.
Understanding the Method
Multiplying fractions is a straightforward process. There are two main steps:
- Multiply the numerators (the top numbers) of the fractions to get the new numerator.
- Multiply the denominators (the bottom numbers) of the fractions to get the new denominator.
- Finally, simplify the resulting fraction if possible.
Step-by-Step Calculation
Step 1: Multiply the Numerators
First, we take the numerators from each fraction, which are 3 and 6, and multiply them together.
3 × 6 = 18
This value, 18, becomes the numerator of our new fraction.
Step 2: Multiply the Denominators
Next, we take the denominators from each fraction, which are 4 and 5, and multiply them together.
4 × 5 = 20
This value, 20, becomes the denominator of our new fraction.
Step 3: Write the Resulting Fraction
Combining the results from the first two steps, we get the fraction:
18/20
Step 4: Simplify the Fraction
The instruction asks for the answer in its “simplest form.” This means we must reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both numbers evenly.
To find the GCD of 18 and 20, we can list their factors:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 20: 1, 2, 4, 5, 10, 20
The greatest factor they have in common is 2. Therefore, we divide both the numerator and the denominator by 2.
18 ÷ 2 = 9
20 ÷ 2 = 10
This gives us the simplified fraction 9/10. Since 9 and 10 have no common factors other than 1, this is the fraction in its simplest form.
Final Answer
The product of 3/4 and 6/5 is 9/10.
