Arrange the following fractions in ascending order :
$\frac{4}{5},\frac{7}{8},\frac{6}{7},\frac{5}{6}$

Q: Arrange the following fractions in ascending order : $\frac{4}{5},\frac{7}{8},\frac{6}{7},\frac{5}{6}$

To arrange the fractions $\frac{4}{5}, \frac{7}{8}, \frac{6}{7}, \frac{5}{6}$ in ascending order, we need to compare their values. One effective way to compare fractions is to convert them to decimal form or find a common denominator. Here, we'll convert them to decimals for simplicity: 1. $\frac{4}{5} = 0.8$ 2. $\frac{7}{8} = 0.875$ 3. $\frac{6}{7} \approx 0.857$ 4. $\frac{5}{6} \approx 0.833$ Now, let's arrange these decimal values in ascending order: - $0.8$ ($\frac{4}{5}$) - $0.833$ ($\frac{5}{6}$) - $0.857$ ($\frac{6}{7}$) - $0.875$ ($\frac{7}{8}$) Thus, the fractions in ascending order are $\frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$. **Explanation for Option 3:** Option 3 lists the fractions as $\frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$, which matches the ascending order we determined. Therefore, Option 3 is correct. **Explanation for why other options are incorrect:** 1. **Option 1: $\frac{4}{5}, \frac{7}{8}, \frac{6}{7}, \frac{5}{6}$** - This option incorrectly places $\frac{7}{8}$ before $\frac{6}{7}$ and $\frac{5}{6}$, which is not in ascending order. 2. **Option 2: $\frac{5}{6}, \frac{6}{7}, \frac{7}{8}, \frac{4}{5}$** - This option incorrectly places $\frac{4}{5}$ at the end, which is not in ascending order. 3. **Option 4: $\frac{7}{8}, \frac{6}{7}, \frac{5}{6}, \frac{4}{5}$** - This option is in descending order, not ascending order. By following the logical process of converting fractions to decimals and comparing their values, we confirm that Option 3 is indeed the correct choice for arranging the fractions in ascending order.

Question

Accepted Answer

To arrange the fractions $\frac{4}{5}, \frac{7}{8}, \frac{6}{7}, \frac{5}{6}$ in ascending order, we need to compare their values. One effective way to compare fractions is to convert them to decimal form or find a common denominator. Here, we'll convert them to decimals for simplicity:

1. $\frac{4}{5} = 0.8$
2. $\frac{7}{8} = 0.875$
3. $\frac{6}{7} \approx 0.857$
4. $\frac{5}{6} \approx 0.833$

Now, let's arrange these decimal values in ascending order:

- $0.8$ ($\frac{4}{5}$)
- $0.833$ ($\frac{5}{6}$)
- $0.857$ ($\frac{6}{7}$)
- $0.875$ ($\frac{7}{8}$)

Thus, the fractions in ascending order are $\frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$.

**Explanation for Option 3:**

Option 3 lists the fractions as $\frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8}$, which matches the ascending order we determined. Therefore, Option 3 is correct.

**Explanation for why other options are incorrect:**

1. **Option 1: $\frac{4}{5}, \frac{7}{8}, \frac{6}{7}, \frac{5}{6}$**
   - This option incorrectly places $\frac{7}{8}$ before $\frac{6}{7}$ and $\frac{5}{6}$, which is not in ascending order.

2. **Option 2: $\frac{5}{6}, \frac{6}{7}, \frac{7}{8}, \frac{4}{5}$**
   - This option incorrectly places $\frac{4}{5}$ at the end, which is not in ascending order.

3. **Option 4: $\frac{7}{8}, \frac{6}{7}, \frac{5}{6}, \frac{4}{5}$**
   - This option is in descending order, not ascending order.

By following the logical process of converting fractions to decimals and comparing their values, we confirm that Option 3 is indeed the correct choice for arranging the fractions in ascending order.