Ascending Order of Fractions

To arrange the given fractions in ascending order, we need to compare the numerators and denominators of each fraction. The numerator is the number above the fraction line, and the denominator is the number below the fraction line.

1. Compare the Denominators
The first step is to compare the denominators of the fractions. The denominator represents the total number of equal parts into which a whole is divided. In this case, we have four fractions: 4/7, 11/15, 8/9, and 5/12.

To compare the denominators, we need to find the least common multiple (LCM) of all the denominators. The LCM is the smallest number that is divisible by all the given denominators.

2. Find the LCM of the Denominators
In this case, the denominators are 7, 15, 9, and 12. The LCM of these numbers is 180.

7 × 25 = 175
15 × 12 = 180
9 × 20 = 180
12 × 15 = 180

Therefore, the LCM of the denominators is 180.

3. Convert the Fractions to Equivalent Fractions
Next, we need to convert each fraction to an equivalent fraction with the same denominator (180).

To convert a fraction to an equivalent fraction, we multiply both the numerator and denominator by the same number.

For the fraction 4/7:
4 × 25 = 100
7 × 25 = 175

Therefore, 4/7 is equivalent to 100/175.

For the fraction 11/15:
11 × 12 = 132
15 × 12 = 180

Therefore, 11/15 is equivalent to 132/180.

For the fraction 8/9:
8 × 20 = 160
9 × 20 = 180

Therefore, 8/9 is equivalent to 160/180.

For the fraction 5/12:
5 × 15 = 75
12 × 15 = 180

Therefore, 5/12 is equivalent to 75/180.

4. Compare the Numerators
Now that we have all the fractions with the same denominator, we can compare the numerators to arrange them in ascending order.

The numerators are 100, 132, 160, and 75.

5. Arrange Fractions in Ascending Order
By comparing the numerators, we can see that the fractions can be arranged in ascending order as follows:

75/180, 100/175, 132/180, 160/180

Therefore, the fractions in ascending order are 75/180, 100/175, 132/180, and 160/180.

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