Express each of the following as a ratio:
(1)`43%`
(2)`36%` :
(3)`7.5%`
(4)`125%`

Answer

To express each percentage as a ratio, we will follow these steps:

### Step-by-Step Solution:

1. **Convert the Percentage to a Fraction**:
To convert a percentage to a fraction, divide the percentage by 100.

2. **Simplify the Fraction**:
If possible, reduce the fraction to its simplest form.

3. **Express as a Ratio**:
Write the simplified fraction in the form of a ratio.

Now, let's apply these steps to each percentage given in the question.

#### (1) Convert `43%` to a Ratio:
- **Step 1**: Convert to fraction:
\[ 43\% = \frac{43}{100} \]
- **Step 2**: Simplify the fraction:
The fraction \(\frac{43}{100}\) cannot be simplified further.
- **Step 3**: Express as a ratio:
\[ 43 : 100 \]

#### (2) Convert `36%` to a Ratio:
- **Step 1**: Convert to fraction:
\[ 36\% = \frac{36}{100} \]
- **Step 2**: Simplify the fraction:
\[ \frac{36}{100} = \frac{36 \div 4}{100 \div 4} = \frac{9}{25} \]
- **Step 3**: Express as a ratio:
\[ 9 : 25 \]

#### (3) Convert `7.5%` to a Ratio:
- **Step 1**: Convert to fraction:
\[ 7.5\% = \frac{7.5}{100} \]
- **Step 2**: Eliminate the decimal by multiplying numerator and denominator by 10:
\[ \frac{7.5 \times 10}{100 \times 10} = \frac{75}{1000} \]
Now simplify:
\[ \frac{75}{1000} = \frac{75 \div 25}{1000 \div 25} = \frac{3}{40} \]
- **Step 3**: Express as a ratio:
\[ 3 : 40 \]

#### (4) Convert `125%` to a Ratio:
- **Step 1**: Convert to fraction:
\[ 125\% = \frac{125}{100} \]
- **Step 2**: Simplify the fraction:
\[ \frac{125}{100} = \frac{125 \div 25}{100 \div 25} = \frac{5}{4} \]
- **Step 3**: Express as a ratio:
\[ 5 : 4 \]

### Final Answers:
1. \(43\% = 43 : 100\)
2. \(36\% = 9 : 25\)
3. \(7.5\% = 3 : 40\)
4. \(125\% = 5 : 4\)