Sure, let's break down the subtraction [tex]\(1 \frac{2}{9} - \frac{2}{3}\)[/tex]. We'll go through it step by step.
### Step 1: Convert Mixed Number to Improper Fraction
First, we'll convert the mixed number [tex]\(1 \frac{2}{9}\)[/tex] to an improper fraction.
A mixed number consists of a whole number and a fraction. To convert [tex]\(1 \frac{2}{9}\)[/tex] to an improper fraction:
- Multiply the whole number by the denominator of the fraction part: [tex]\(1 \times 9 = 9\)[/tex].
- Add the numerator of the fraction part: [tex]\(9 + 2 = 11\)[/tex].
So, [tex]\(1 \frac{2}{9}\)[/tex] becomes [tex]\(\frac{11}{9}\)[/tex].
### Step 2: Ensure Fractions Have a Common Denominator
Next, we need a common denominator to subtract the fractions. The fractions are [tex]\(\frac{11}{9}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]. The denominators are 9 and 3.
To find a common denominator, we'll use the least common multiple (LCM) of 9 and 3, which is 9.
### Step 3: Adjust the Fractions to Have the Common Denominator
- [tex]\(\frac{11}{9}\)[/tex] already has the denominator 9, so it remains as [tex]\(\frac{11}{9}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] needs to be adjusted to have the denominator 9.
To do this, we multiply both the numerator and the denominator by 3:
[tex]\[
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\][/tex]
So, [tex]\(\frac{11}{9}\)[/tex] and [tex]\(\frac{6}{9}\)[/tex] are the fractions we subtract.
### Step 4: Subtract the Fractions
Now we subtract the two fractions:
[tex]\[
\frac{11}{9} - \frac{6}{9} = \frac{11 - 6}{9} = \frac{5}{9}
\][/tex]
### Step 5: Simplify the Fraction (if needed)
In this case, [tex]\(\frac{5}{9}\)[/tex] is already in its simplest form since the greatest common divisor (GCD) of 5 and 9 is 1.
### Conclusion
The result of subtracting [tex]\(\frac{2}{3}\)[/tex] from [tex]\(1 \frac{2}{9}\)[/tex] is:
[tex]\[
1 \frac{2}{9} - \frac{2}{3} = \frac{5}{9}
\][/tex]
