Question

Calculate the decimal number for each fraction and identify the ascending numerical order of the decimal numbers:

5/8
, 1/4
, 3/8
, 2/3
, 6/7


8/5
, 4/1
, 8/3
, 3/2
, 7/6
Start Fraction 8 over 5 End Fraction , Start Fraction 4 over 1 End Fraction , Start Fraction 8 over 3 End Fraction , Start Fraction 3 over 2 End Fraction , Start Fraction 7 over 6 End Fraction

0.25, 0.375, 0.625, 0.667, 0.857
0.25, 0.375, 0.625, 0.667, 0.857

0.625, 0.25, 0.375, 0.667, 0.857
0.625, 0.25, 0.375, 0.667, 0.857

5/8
, 1/4
, 3/8
, 2/3
, 6/7)

Answer 1

To find the decimal representations of the fractions you provided, let's calculate them one by one.

### First set of fractions:
1. \( \frac{5}{8} \)
\( 5 \div 8 = 0.625 \)

2. \( \frac{1}{4} \)
\( 1 \div 4 = 0.25 \)

3. \( \frac{3}{8} \)
\( 3 \div 8 = 0.375 \)

4. \( \frac{2}{3} \)
\( 2 \div 3 \approx 0.6667 \) (rounded to 4 decimal places)

5. \( \frac{6}{7} \)
\( 6 \div 7 \approx 0.8571 \) (rounded to 4 decimal places)

### Decimal representatives of the first set:
- \( \frac{5}{8} = 0.625 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{3}{8} = 0.375 \)
- \( \frac{2}{3} \approx 0.6667 \)
- \( \frac{6}{7} \approx 0.8571 \)

### Now, let's arrange these decimals in ascending order:
- 0.25
- 0.375
- 0.625
- 0.6667
- 0.8571

### The ascending order is:
1. \( 0.25 \) (which corresponds to \( \frac{1}{4} \))
2. \( 0.375 \) (which corresponds to \( \frac{3}{8} \))
3. \( 0.625 \) (which corresponds to \( \frac{5}{8} \))
4. \( 0.6667 \) (which corresponds to \( \frac{2}{3} \))
5. \( 0.8571 \) (which corresponds to \( \frac{6}{7} \))

### For the second set of fractions:
1. \( \frac{8}{5} \)
\( 8 \div 5 = 1.6 \)

2. \( \frac{4}{1} \)
\( 4 \div 1 = 4.0 \)

3. \( \frac{8}{3} \)
\( 8 \div 3 \approx 2.6667 \)

4. \( \frac{3}{2} \)
\( 3 \div 2 = 1.5 \)

5. \( \frac{7}{6} \)
\( 7 \div 6 \approx 1.1667 \)

### Decimal representatives of the second set:
- \( \frac{8}{5} = 1.6 \)
- \( \frac{4}{1} = 4.0 \)
- \( \frac{8}{3} \approx 2.6667 \)
- \( \frac{3}{2} = 1.5 \)
- \( \frac{7}{6} \approx 1.1667 \)

### Now, let's arrange these decimals in ascending order:
- \( 1.1667 \)
- \( 1.5 \)
- \( 1.6 \)
- \( 2.6667 \)
- \( 4.0 \)

### The ascending order for the second set is:
1. \( 1.1667 \) (which corresponds to \( \frac{7}{6} \))
2. \( 1.5 \) (which corresponds to \( \frac{3}{2} \))
3. \( 1.6 \) (which corresponds to \( \frac{8}{5} \))
4. \( 2.6667 \) (which corresponds to \( \frac{8}{3} \))
5. \( 4.0 \) (which corresponds to \( \frac{4}{1} \))

### Final Results:
1. **First set in ascending order**:
- \( \frac{1}{4}, \frac{3}{8}, \frac{5}{8}, \frac{2}{3}, \frac{6}{7} \)

2. **Second set in ascending order**:
- \( \frac{7}{6}, \frac{3}{2}, \frac{8}{5}, \frac{8}{3}, \frac{4}{1} \)