What fraction is equivalent to 4 12?
The Correct Answer and Explanation is :
To find a fraction equivalent to (4 \frac{1}{2}), we first convert the mixed number into an improper fraction. A mixed number consists of a whole number and a fractional part. Here’s how to convert (4 \frac{1}{2}):
- Multiply the whole number by the denominator:
[
4 \times 2 = 8
] - Add the numerator:
[
8 + 1 = 9
] - Write it as an improper fraction:
The improper fraction is (\frac{9}{2}).
Now, to express (\frac{9}{2}) as an equivalent fraction, we can multiply both the numerator and the denominator by the same integer. This maintains the value of the fraction while changing its appearance.
For example, if we multiply both the numerator and denominator of (\frac{9}{2}) by 2:
[
\frac{9 \times 2}{2 \times 2} = \frac{18}{4}
]
Here, (\frac{18}{4}) is an equivalent fraction to (4 \frac{1}{2}) or (\frac{9}{2}).
Similarly, if we multiply by 3:
[
\frac{9 \times 3}{2 \times 3} = \frac{27}{6}
]
Thus, (\frac{27}{6}) is another equivalent fraction.
In general, for any fraction (\frac{a}{b}), you can create equivalent fractions by multiplying the numerator and denominator by any non-zero integer (k):
[
\frac{a \times k}{b \times k}
]
In summary, (4 \frac{1}{2}) can be converted to the improper fraction (\frac{9}{2}). This fraction can be expressed in multiple equivalent forms, such as (\frac{18}{4}) or (\frac{27}{6}), demonstrating the concept of equivalence in fractions and the flexibility of representing the same quantity in different forms.