What is 3/5 times 1/3 in fraction form?
The Correct Answer and Explanation is:
To calculate the product of two fractions, such as ( \frac{3}{5} \times \frac{1}{3} ), you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
Step-by-Step Calculation:
- Multiply the numerators:
The numerators of the two fractions are 3 and 1.
[
3 \times 1 = 3
]
So, the numerator of the product is 3. - Multiply the denominators:
The denominators of the two fractions are 5 and 3.
[
5 \times 3 = 15
]
So, the denominator of the product is 15.
Thus, the product of ( \frac{3}{5} \times \frac{1}{3} ) is:
[
\frac{3}{15}
]
- Simplify the fraction:
The next step is to simplify ( \frac{3}{15} ). To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 3 and 15 is 3. Now, divide both the numerator and the denominator by 3:
[
\frac{3}{15} = \frac{3 \div 3}{15 \div 3} = \frac{1}{5}
]
Final Answer:
The simplified product of ( \frac{3}{5} \times \frac{1}{3} ) is ( \frac{1}{5} ).
Explanation:
When multiplying fractions, the process involves multiplying the numerators and denominators directly. However, it’s important to check if the resulting fraction can be simplified. Simplification is possible when the numerator and denominator share a common divisor. In this case, ( \frac{3}{15} ) simplifies to ( \frac{1}{5} ), which is the final and simplest form of the answer.