arvin is making lemon bread and pumpkin bread for a school bake sale. He needs 4
1
4
 cups of flour for the lemon bread and 1
1
2
 times as much flour for the pumpkin bread. He only has 2
1
8
 cups of flour left in his pantry, so he buys a new bag from the grocery store. How much flour will Marvin use from the new bag?

To find out how much flour Arvin will use from the new bag, we first need to calculate the total amount of flour needed for both the lemon bread and pumpkin bread, and then subtract the flour he already has in his pantry.

### Step 1: Calculate Flour for Lemon Bread
The recipe for the lemon bread requires:

\[
4 \frac{1}{4} \text{ cups of flour}
\]

Convert this mixed number to an improper fraction:

\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}
\]

### Step 2: Calculate Flour for Pumpkin Bread
The pumpkin bread requires \(1 \frac{1}{2}\) times as much flour as the lemon bread. First, convert \(1 \frac{1}{2}\) to an improper fraction:

\[
1 \frac{1}{2} = \frac{3}{2}
\]

Now, multiply this by the flour needed for the lemon bread:

\[
\frac{3}{2} \times \frac{17}{4} = \frac{3 \times 17}{2 \times 4} = \frac{51}{8} \text{ cups}
\]

### Step 3: Total Flour Required
Add the flour needed for both the lemon and pumpkin bread:

\[
\frac{17}{4} + \frac{51}{8}
\]

To add these fractions, find a common denominator (which is 8):

\[
\frac{17}{4} = \frac{17 \times 2}{4 \times 2} = \frac{34}{8}
\]

Now add:

\[
\frac{34}{8} + \frac{51}{8} = \frac{85}{8} \text{ cups}
\]

### Step 4: Subtract Flour Already in the Pantry
Arvin has \(2 \frac{1}{8}\) cups of flour in his pantry, which is:

\[
2 \frac{1}{8} = \frac{2 \times 8 + 1}{8} = \frac{17}{8}
\]

Subtract this from the total flour needed:

\[
\frac{85}{8} - \frac{17}{8} = \frac{68}{8} = 8 \frac{4}{8} = 8 \frac{1}{2} \text{ cups}
\]

### Answer
Arvin will use \(8 \frac{1}{2}\) cups of flour from the new bag.

Would you like more details or have any questions?

Here are some related questions you might find helpful:

1. How do you convert mixed numbers into improper fractions?
2. How can you find a common denominator when adding fractions?
3. How do you multiply fractions?
4. How can you simplify fractions after addition?
5. What are some strategies for solving word problems involving fractions?

**Tip:** When dealing with fractions in word problems, always ensure to convert mixed numbers to improper fractions to simplify calculations!

Learn how to calculate the amount of flour needed for lemon bread and pumpkin bread using fractions. This problem involves converting mixed numbers to improper fractions, adding fractions, and subtracting fractions. Suitable for students in Grades 4-6.

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