To convert a mixed number into an improper fraction, follow these steps:
1. Identify the components of the mixed number:
- Whole number part: -2
- Fractional part: [tex]\(\frac{4}{9}\)[/tex]
2. Understand the relationship:
- For any mixed number [tex]\( a \frac{b}{c} \)[/tex], where [tex]\( a \)[/tex] is the whole number part, [tex]\( b \)[/tex] is the numerator, and [tex]\( c \)[/tex] is the denominator, you can convert it to an improper fraction.
3. Convert the whole number into a fraction:
- Multiply the whole number by the denominator of the fractional part. In this case, -2 multiplied by 9 equals -18.
4. Add or subtract this result from the numerator of the fractional part:
- When converting a mixed number where the whole number is negative, make sure the numerator reflects the same in the improper fraction. So, you subtract the numerator of the fractional part from the product of the whole number and the denominator.
[tex]\[
\text{Improper numerator} = (\text{Whole number} \times \text{Denominator}) - \text{Numerator}
\][/tex]
Substituting the values, we get:
[tex]\[
\text{Improper numerator} = (-2 \times 9) - 4 = -18 - 4 = -22
\][/tex]
5. Keep the same denominator:
- The denominator remains unchanged, which is 9 in this case.
So, the mixed number [tex]\( -2 \frac{4}{9} \)[/tex] can be written as the improper fraction [tex]\( -\frac{22}{9} \)[/tex].
Thus, the improper fraction equivalent to [tex]\( -2 \frac{4}{9} \)[/tex] is [tex]\( -\frac{22}{9} \)[/tex].
