Convert 2 2/9 to an improper fraction.
Understand the Problem
The question is asking to convert a mixed number (2 2/9) into an improper fraction. To do this, we will multiply the whole number part by the denominator and add the numerator, placing the result over the original denominator.
Answer
The improper fraction is $\frac{20}{9}$.
Answer for screen readers
The improper fraction for the mixed number $2\frac{2}{9}$ is $\frac{20}{9}$.
Steps to Solve
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Identify the parts of the mixed number The mixed number consists of a whole number part and a fractional part. In $2\frac{2}{9}$, the whole number is $2$, and the fraction is $\frac{2}{9}$.
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Multiply the whole number by the denominator To convert the mixed number to an improper fraction, we multiply the whole number $2$ by the denominator $9$: $$ 2 \times 9 = 18 $$
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Add the numerator to the product Next, we add the numerator $2$ to the product obtained in the previous step: $$ 18 + 2 = 20 $$
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Form the improper fraction Now we place the result over the original denominator $9$: $$ \frac{20}{9} $$
The improper fraction for the mixed number $2\frac{2}{9}$ is $\frac{20}{9}$.
More Information
Converting a mixed number to an improper fraction is useful in various mathematical operations, such as addition and subtraction of fractions, because it simplifies calculations.
Tips
One common mistake is forgetting to multiply the whole number by the denominator, and instead just adding the numerator to the denominator, resulting in an incorrect fraction. To avoid this, always remember to perform the multiplication first.
