Arrange the given ratios as indicated:
a. In ascending order:
i. 2:3, 5:7, 5:6, 11:14 ii. 3:5, 2:7, 3:10,9:14

Answer

To solve the problem of arranging the given ratios in ascending order, we will follow these steps:

### Step 1: Convert each ratio to a decimal
To compare the ratios easily, we will convert each ratio into a decimal form by dividing the first number by the second number.

**For Part a:**
1. **2:3** → \( \frac{2}{3} = 0.6667 \)
2. **5:7** → \( \frac{5}{7} = 0.7143 \)
3. **5:6** → \( \frac{5}{6} = 0.8333 \)
4. **11:14** → \( \frac{11}{14} = 0.7857 \)

**For Part b:**
1. **3:5** → \( \frac{3}{5} = 0.6000 \)
2. **2:7** → \( \frac{2}{7} = 0.2857 \)
3. **3:10** → \( \frac{3}{10} = 0.3000 \)
4. **9:14** → \( \frac{9}{14} = 0.6429 \)

### Step 2: List the decimal values
Now we will list the decimal values obtained from the ratios.

**For Part a:**
- \( 0.6667 \) (from \( 2:3 \))
- \( 0.7143 \) (from \( 5:7 \))
- \( 0.8333 \) (from \( 5:6 \))
- \( 0.7857 \) (from \( 11:14 \))

**For Part b:**
- \( 0.6000 \) (from \( 3:5 \))
- \( 0.2857 \) (from \( 2:7 \))
- \( 0.3000 \) (from \( 3:10 \))
- \( 0.6429 \) (from \( 9:14 \))

### Step 3: Arrange the decimal values in ascending order
Now we will arrange the decimal values in ascending order.

**For Part a:**
- \( 0.6667 \) (2:3)
- \( 0.7143 \) (5:7)
- \( 0.7857 \) (11:14)
- \( 0.8333 \) (5:6)

Thus, the ascending order is:
**2:3 < 5:7 < 11:14 < 5:6**

**For Part b:**
- \( 0.2857 \) (2:7)
- \( 0.3000 \) (3:10)
- \( 0.6000 \) (3:5)
- \( 0.6429 \) (9:14)

Thus, the ascending order is:
**2:7 < 3:10 < 3:5 < 9:14**

### Final Answers:
**Part a:** 2:3 < 5:7 < 11:14 < 5:6
**Part b:** 2:7 < 3:10 < 3:5 < 9:14

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