Whed $$ \frac{3}{4} $$ gallons of gas on Saturday and $$ 4 \frac{1}{8} $$ gallons of gas on Sunday. H Write your answer as a mixed number in simplest form.

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UpStudy AI · Accepted Answer

To find the total amount of gas purchased over the weekend, we need to add the two quantities together:

1. Convert the mixed number $$ 4 \frac{1}{8} $$ into an improper fraction.
2. Add the two fractions together.
3. Simplify the result if necessary.

### Step 1: Convert $$ 4 \frac{1}{8} $$ to an improper fraction

To convert a mixed number to an improper fraction, use the formula:

$$
\text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \div \text{Denominator}
$$

For $$ 4 \frac{1}{8} $$:

$$
\text{Improper Fraction} = \left(4 \times 8\right) + 1 = 32 + 1 = 33
$$

So, $$ 4 \frac{1}{8} = \frac{33}{8} $$.

### Step 2: Add the two fractions

Now we need to add $$ \frac{3}{4} $$ and $$ \frac{33}{8} $$. To do this, we need a common denominator. The least common multiple of 4 and 8 is 8.

Convert $$ \frac{3}{4} $$ to have a denominator of 8:

$$
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
$$

Now we can add the two fractions:

$$
\frac{6}{8} + \frac{33}{8} = \frac{6 + 33}{8} = \frac{39}{8}
$$

### Step 3: Convert back to a mixed number

To convert $$ \frac{39}{8} $$ back to a mixed number, divide the numerator by the denominator:

$$
39 \div 8 = 4 \quad \text{(whole number)}
$$
$$
39 - (8 \times 4) = 39 - 32 = 7 \quad \text{(remainder)}
$$

Thus, $$ \frac{39}{8} = 4 \frac{7}{8} $$.

### Final Answer

The total amount of gas purchased over the weekend is:

$$
\boxed{4 \frac{7}{8}}
$$
The total amount of gas purchased over the weekend is $$ 4 \frac{7}{8} $$ gallons.

Whed \( \frac{3}{4} \) gallons of gas on Saturday and \( 4 \frac{1}{8} \) gallons of gas on Sunday. H Write your answer as a mixed number in simplest form.

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