Malt needs `5 1/9`gallons of hydrochloric acid for an experiment . He has `3 1/3` gallons already . How many more gallons of hydrochloric acid does Matt need ?

Options

A. `2 7/9`
B. `2 2/3`
C. `2 1/8`
D. `1 7/9`

Answer

To find out how many more gallons of hydrochloric acid Matt needs, we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
- For `5 1/9` gallons:
\[ 5 \frac{1}{9} = \frac{5 \times 9 + 1}{9} = \frac{45 + 1}{9} = \frac{46}{9} \]

- For `3 1/3` gallons:
\[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

### Step 2: Set up the equation.
We need to find out how much more Matt needs, which we can represent as \( x \):
\[ 3 \frac{1}{3} + x = 5 \frac{1}{9} \]
Substituting the improper fractions:
\[ \frac{10}{3} + x = \frac{46}{9} \]

### Step 3: Solve for \( x \).
To isolate \( x \), we subtract \( \frac{10}{3} \) from both sides:
\[ x = \frac{46}{9} - \frac{10}{3} \]

### Step 4: Find a common denominator.
The common denominator for 9 and 3 is 9. We convert \( \frac{10}{3} \) to have a denominator of 9:
\[ \frac{10}{3} = \frac{10 \times 3}{3 \times 3} = \frac{30}{9} \]

### Step 5: Perform the subtraction.
Now we can subtract:
\[ x = \frac{46}{9} - \frac{30}{9} = \frac{46 - 30}{9} = \frac{16}{9} \]

### Step 6: Convert back to a mixed number.
To convert \( \frac{16}{9} \) back to a mixed number:
- Divide 16 by 9:
- 9 goes into 16 one time (1) with a remainder of 7.
Thus,
\[ \frac{16}{9} = 1 \frac{7}{9} \]

### Final Answer:
Matt needs \( 1 \frac{7}{9} \) gallons more of hydrochloric acid.

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