Which of the following ratios is not equal to `3:8` in its simplest forrm ?

Options

A. `207:552`
B. `261:696`
C. `141:392`
D. `153 :408`

Answer

To determine which of the following ratios is not equal to \(3:8\) in its simplest form, we will evaluate each option step by step.

### Step 1: Evaluate the first option \(207:552\)

1. **Divide both numbers by their GCD (Greatest Common Divisor)**:
- First, we can divide \(207\) by \(3\):
\[ 207 \div 3 = 69 \]
- Now, divide \(552\) by \(3\):
\[ 552 \div 3 = 184 \]
- So, we have:
\[ 207:552 = 69:184 \]

2. **Check if \(69:184\) can be simplified further**:
- Now, we can check if \(69\) and \(184\) can be divided by any common factors. The GCD of \(69\) and \(184\) is \(23\):
\[ 69 \div 23 = 3 \quad \text{and} \quad 184 \div 23 = 8 \]
- Thus:
\[ 69:184 = 3:8 \]
- This ratio is equal to \(3:8\).

### Step 2: Evaluate the second option \(261:696\)

1. **Divide both numbers by their GCD**:
- First, we can divide \(261\) by \(3\):
\[ 261 \div 3 = 87 \]
- Now, divide \(696\) by \(3\):
\[ 696 \div 3 = 232 \]
- So, we have:
\[ 261:696 = 87:232 \]

2. **Check if \(87:232\) can be simplified further**:
- The GCD of \(87\) and \(232\) is \(29\):
\[ 87 \div 29 = 3 \quad \text{and} \quad 232 \div 29 = 8 \]
- Thus:
\[ 87:232 = 3:8 \]
- This ratio is equal to \(3:8\).

### Step 3: Evaluate the third option \(141:392\)

1. **Divide both numbers by their GCD**:
- The GCD of \(141\) and \(392\) is \(1\) (they have no common factors):
- Thus:
\[ 141:392 \text{ cannot be simplified further.} \]

2. **Check if \(141:392\) is equal to \(3:8\)**:
- To check if \(141:392\) is equal to \(3:8\), we can cross-multiply:
\[ 141 \times 8 \quad \text{and} \quad 3 \times 392 \]
- Calculate:
\[ 141 \times 8 = 1128 \quad \text{and} \quad 3 \times 392 = 1176 \]
- Since \(1128 \neq 1176\), the ratio \(141:392\) is not equal to \(3:8\).

### Conclusion:
The ratio that is not equal to \(3:8\) in its simplest form is **\(141:392\)**.

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