3/8 times 3 in fraction form
The Correct Answer and Explanation is :
The correct answer is: {9}{8}
To multiply the fractions ( \frac{3}{8} ) and ( 3 ), we first need to express the whole number ( 3 ) as a fraction. We can do this by writing ( 3 ) as ( \frac{3}{1} ). Now, we can multiply the two fractions together.
The multiplication of two fractions is done by multiplying the numerators together and the denominators together. So we have:
[
\frac{3}{8} \times \frac{3}{1} = \frac{3 \times 3}{8 \times 1} = \frac{9}{8}
]
Thus, ( \frac{3}{8} \times 3 = \frac{9}{8} ).
Explanation of the Steps
- Understanding Fractions: A fraction consists of a numerator (the top part) and a denominator (the bottom part). The numerator represents how many parts we have, while the denominator indicates how many equal parts the whole is divided into.
- Converting Whole Numbers: To multiply a fraction by a whole number, we first convert the whole number into a fraction. This is crucial because fraction multiplication requires both numbers to be in fraction form. The whole number ( 3 ) can be written as ( \frac{3}{1} ) because it represents three whole parts, which is one complete whole.
- Multiplying the Fractions: When multiplying two fractions, we multiply their numerators together and their denominators together. For our example, we multiply ( 3 ) (the numerator of the first fraction) by ( 3 ) (the numerator of the second fraction) to get ( 9 ). For the denominators, we multiply ( 8 ) (the denominator of the first fraction) by ( 1 ) (the denominator of the second fraction) to get ( 8 ). This gives us ( \frac{9}{8} ).
- Interpreting the Result: The fraction ( \frac{9}{8} ) is an improper fraction, which means the numerator is larger than the denominator. It can also be expressed as a mixed number: ( 1 \frac{1}{8} ), indicating that it contains one whole and one-eighth of another whole.
In summary, the multiplication of ( \frac{3}{8} ) and ( 3 ) results in ( \frac{9}{8} ), showcasing the fundamental principles of fraction operations.