Express each of the following as a rattio
(1) 17%
(2) 72%
(3) 12.5%
(4) 225%

Answer

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

### Step-by-Step Solution:

**Step 1: Convert the percentage to a fraction.**
- To convert a percentage to a fraction, we divide the percentage value by 100.

**Step 2: Simplify the fraction (if possible).**
- We will simplify the fraction to its lowest terms.

**Step 3: Express the simplified fraction as a ratio.**
- The simplified fraction can then be expressed in the form of a ratio.

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

### (1) Convert 17% to a ratio:
- **Step 1:** Convert to fraction: \( \frac{17}{100} \)
- **Step 2:** This fraction is already in its simplest form.
- **Step 3:** Express as a ratio: \( 17:100 \)

### (2) Convert 72% to a ratio:
- **Step 1:** Convert to fraction: \( \frac{72}{100} \)
- **Step 2:** Simplify the fraction:
- Both 72 and 100 can be divided by 4.
- \( \frac{72 \div 4}{100 \div 4} = \frac{18}{25} \)
- **Step 3:** Express as a ratio: \( 18:25 \)

### (3) Convert 12.5% to a ratio:
- **Step 1:** Convert to fraction: \( \frac{12.5}{100} \)
- **Step 2:** To eliminate the decimal, multiply both the numerator and denominator by 10:
- \( \frac{12.5 \times 10}{100 \times 10} = \frac{125}{1000} \)
- Now simplify: Both 125 and 1000 can be divided by 125.
- \( \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \)
- **Step 3:** Express as a ratio: \( 1:8 \)

### (4) Convert 225% to a ratio:
- **Step 1:** Convert to fraction: \( \frac{225}{100} \)
- **Step 2:** Simplify the fraction:
- Both 225 and 100 can be divided by 25.
- \( \frac{225 \div 25}{100 \div 25} = \frac{9}{4} \)
- **Step 3:** Express as a ratio: \( 9:4 \)

### Final Ratios:
1. 17% = \( 17:100 \)
2. 72% = \( 18:25 \)
3. 12.5% = \( 1:8 \)
4. 225% = \( 9:4 \)

---