How many groups of $$ \frac{3}{4} $$ are in a. $$ \frac{11}{4} $$

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To determine **how many groups of $$ \frac{3}{4} $$** are in **$$ \frac{11}{4} $$**, you can perform the following calculation:

### Step 1: Set Up the Division
You're essentially looking to find out how many times $$ \frac{3}{4} $$ fits into $$ \frac{11}{4} $$. This can be represented as:

$$
\frac{11}{4} \div \frac{3}{4}
$$

### Step 2: Convert Division to Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. So, invert the second fraction and multiply:

$$
\frac{11}{4} \times \frac{4}{3}
$$

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:

$$
\frac{11 \times 4}{4 \times 3} = \frac{44}{12}
$$

### Step 4: Simplify the Fraction
Simplify $$ \frac{44}{12} $$ by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

$$
\frac{44 \div 4}{12 \div 4} = \frac{11}{3}
$$

### Step 5: Interpret the Result
The fraction $$ \frac{11}{3} $$ can also be expressed as a mixed number:

$$
\frac{11}{3} = 3 \frac{2}{3}
$$

### **Conclusion**
There are **$$ 3 \frac{2}{3} $$** groups of $$ \frac{3}{4} $$ in $$ \frac{11}{4} $$.

---

**Visual Representation:**

Imagine you have a length of $$ \frac{11}{4} $$ units and you want to divide it into segments each of $$ \frac{3}{4} $$ units:

1. **First group:** $$ \frac{3}{4} $$
2. **Second group:** $$ \frac{3}{4} $$ (Total so far: $$ \frac{6}{4} $$)
3. **Third group:** $$ \frac{3}{4} $$ (Total so far: $$ \frac{9}{4} $$)
4. **Remaining:** $$ \frac{2}{4} = \frac{1}{2} $$ (This is $$ \frac{2}{3} $$ of a full $$ \frac{3}{4} $$ group)

So, you have **3 full groups** and **$$ \frac{2}{3} $$ of another group**.
There are $$ 3 \frac{2}{3} $$ groups of $$ \frac{3}{4} $$ in $$ \frac{11}{4} $$.

How many groups of \( \frac{3}{4} \) are in a. \( \frac{11}{4} \)

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