Ascending and Descending Order of Fractions

The reading material provided on this page for Ascending and Descending Order of Fractions is specifically designed for students in grades 5 and 6. So, let's begin!

Ascending Order

Ascending numbers refer to a sequence of numbers arranged in increasing order from left to right. This means that each number in the sequence is greater than the previous one and the sequence continues to increase as you move from left to right.

Descending Order

Descending numbers refer to a sequence of numbers arranged in decreasing order, from the largest to the smallest. This means that each number in the sequence is smaller than the previous one and the sequence continues to decrease as you move from left to right.

Ascending and Descending Order of Fractions

1. Ascending order of fractions means arranging the fractions in increasing order from smallest to largest.

For example, the ascending order of the fractions 1/2, 3/4, and 1/3 would be 1/3 < 1/2 < 3/4.

2. Descending order of fractions means arranging the fractions in decreasing order from largest to smallest.

For example, the descending order of the fractions 1/2, 3/4, and 1/3 would be 3/4 > 1/2 >1/3.

Ordering Fractions with same Denominators

For the fractions having the same denominator, the fraction with the smallest numerator is the smallest.

Example: Arrange 17/13, 11/13, 15/13, 7/13 in ascending order.
Comparing the numerators, we get 7 < 11 < 15 < 17

Therefore, 7/13 < 11/13 < 15/13 < 17/13

Ordering Fractions with same Numerators

When the fractions have the same numerator, the fraction with the highest denominator is the smallest.

Example: Arrange 3/7, 3/8, 3/5, 3/4 in ascending order.
Here, the numerator is 3 in all the fractions. So, we compare the denominator.
On comparing the denominators, we get: 4 < 5 < 7 < 8

Therefore, 3/8 < 3/7 < 3/5 < 3/4

Ordering Fractions with Different Numerators and Denominators

Convert the fractions to the like denominators (or numerators) and then compare and order them.

Example: Arrange 2/5, 4/6, 3/5 and 1/3 in ascending order.
Here, the denominators are 5, 6 and 3.
LCM of 3, 5 and 6 is 30.
So, we find equivalent fractions.

The equivalent fractions are:
12/30, 20/30, 18/30 and 10/30
On comparing, we get
10/30 < 12/30 < 18/30 < 20/30

Therefore, 1/3 < 2/5 < 3/5 < 4/6

Summary:

To determine the ascending or descending order of fractions, you need to compare their values and arrange them accordingly. Here's how you can do it:

1. Find a common denominator: To compare fractions, they should have the same denominator. If the fractions already have a common denominator, you can skip this step. Otherwise, find the least common multiple (LCM) of the denominators and convert the fractions to have the same denominator.

2. Compare the numerators: Once the fractions have the same denominator, compare their numerators. For ascending order, start with the fraction with the smallest numerator. For descending order, start with the fraction with the largest numerator.

3. Arrange the fractions: Arrange the fractions in ascending or descending order based on the comparison of their numerators. If the numerators are the same, compare the denominators. The fraction with the smaller denominator should come first in ascending order, while it should come later in descending order.

4. Simplify if necessary: If possible, simplify the fractions once they are arranged in order. Reduce them to their simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

Let's go through an example to illustrate the process:

Example: Arrange the fractions 3/5, 2/3, and 4/7 in ascending order.

Step 1: Find a common denominator. The least common multiple (LCM) of 5, 3, and 7 is 105. Convert the fractions:

3/5 = 63/105
2/3 = 70/105
4/7 = 60/105

Step 2: Compare the numerators. We have:
63/105, 70/105, 60/105

Step 3: Arrange the fractions:
Ascending order: 60/105, 63/105, 70/105

Step 4: Simplify if necessary:
The fractions 60/105, 63/105, and 70/105 can be simplified by dividing the numerator and denominator by their GCD, which is 3:
20/35, 21/35, 30/35

Final result: The fractions 20/35, 21/35, and 30/35 are in ascending order.

Similarly, you can follow these steps to arrange fractions in descending order by starting with the fraction that has the largest numerator and following the same process.

Remember to convert the fractions to a common denominator, compare the numerators, arrange them accordingly, and simplify if possible.