What is 2/3 x 6 in simplest form?
The Correct Answer and Explanation is :
To solve ( \frac{2}{3} \times 6 ), we can follow these steps to arrive at the simplest form.
- Understanding the Expression: The expression ( \frac{2}{3} \times 6 ) consists of a fraction and a whole number. The fraction ( \frac{2}{3} ) indicates that we have 2 parts out of a total of 3 equal parts. The number 6 can be thought of as ( \frac{6}{1} ), which allows us to multiply a fraction by a whole number easily.
- Converting the Whole Number: To perform the multiplication, we can rewrite the whole number as a fraction:
[
6 = \frac{6}{1}
]
Now, we can multiply the two fractions together:
[
\frac{2}{3} \times \frac{6}{1}
] - Multiplying the Numerators and Denominators: When multiplying fractions, we multiply the numerators together and the denominators together:
[
\frac{2 \times 6}{3 \times 1} = \frac{12}{3}
] - Simplifying the Fraction: Now, we simplify ( \frac{12}{3} ). To do this, we divide the numerator (12) by the denominator (3):
[
12 \div 3 = 4
]
So, ( \frac{12}{3} ) simplifies to 4. - Conclusion: The result of ( \frac{2}{3} \times 6 ) in its simplest form is 4.
This example demonstrates how to multiply fractions and whole numbers effectively. By converting the whole number into a fraction, we can apply the same rules of multiplication. Additionally, simplifying the result is an essential step in expressing answers in their simplest form, making it easier to understand and communicate numerical results. Thus, the final answer is 4.