Question

equivalent expression of 5 1/2/3√125

Answer 1

can you explain in another way please

Answer 2

To find an equivalent expression for \(5 \frac{1}{2} / 3 \sqrt{125}\), we can break this expression down step-by-step.

1. **Convert the mixed number to an improper fraction:**
\[
5 \frac{1}{2} = \frac{11}{2}
\]

2. **Simplify \(3 \sqrt{125}\):**
\[
\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5}
\]
Then:
\[
3 \sqrt{125} = 3 \cdot 5 \sqrt{5} = 15 \sqrt{5}
\]

3. **Set up the expression:**
\[
\frac{11}{2} / (15 \sqrt{5})
\]

4. **Change division to multiplication by the reciprocal:**
\[
\frac{11}{2} \cdot \frac{1}{15 \sqrt{5}} = \frac{11}{2 \cdot 15 \sqrt{5}} = \frac{11}{30 \sqrt{5}}
\]

Therefore, the equivalent expression of \(5 \frac{1}{2} / 3 \sqrt{125}\) is:
\[
\frac{11}{30\sqrt{5}}
\]

If desired, you could also rationalize the denominator:
\[
\frac{11}{30\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{11\sqrt{5}}{30 \cdot 5} = \frac{11\sqrt{5}}{150}
\]

So the fully simplified and rationalized form could be \(\frac{11\sqrt{5}}{150}\).

Answer 3

Sure! Let’s break down the expression \(5 \frac{1}{2} / 3 \sqrt{125}\) into simpler steps, focusing on each part clearly.

### Step 1: Convert the Mixed Number
First, we need to convert the mixed number \(5 \frac{1}{2}\) into an improper fraction.

- The whole number part is 5, and the fractional part is \(\frac{1}{2}\).
- To convert, multiply the whole number (5) by the denominator (2) and add the numerator (1):
\[
5 \times 2 + 1 = 10 + 1 = 11
\]
- Thus, \(5 \frac{1}{2} = \frac{11}{2}\).

### Step 2: Simplify \(3 \sqrt{125}\)
Now we simplify \(3 \sqrt{125}\):

- Start with \(125\):
\[
\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5 \sqrt{5}
\]
- So, \(3 \sqrt{125} = 3 \times 5 \sqrt{5} = 15 \sqrt{5}\).

### Step 3: Set Up the Division
Now we substitute our results back into the expression:
\[
\frac{11}{2} / (15 \sqrt{5})
\]

### Step 4: Change the Division to Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{11}{2} \div (15 \sqrt{5}) = \frac{11}{2} \times \frac{1}{15 \sqrt{5}}
\]

### Step 5: Multiply the Fractions
Now we multiply the two fractions:
\[
\frac{11 \cdot 1}{2 \cdot 15 \sqrt{5}} = \frac{11}{30 \sqrt{5}}
\]

### Step 6: (Optional) Rationalize the Denominator
To rationalize the denominator (if you prefer not to have a square root in the denominator), we can multiply the numerator and denominator by \(\sqrt{5}\):
\[
\frac{11}{30 \sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{11 \sqrt{5}}{30 \cdot 5} = \frac{11 \sqrt{5}}{150}
\]

### Final Result
So the equivalent expression of \(5 \frac{1}{2} / 3 \sqrt{125}\) can be stated as:
\[
\frac{11}{30 \sqrt{5}}
\]
or, if rationalized, as:
\[
\frac{11 \sqrt{5}}{150}
\]

This gives a clear breakdown of each step, making it easier to follow! If you have any further questions or need additional explanations, feel free to ask.