Fractions in Descending Order: Fractions represent equal parts of the whole number. It contains a numerator and denominator. Ordering fractions is nothing but arranging the fractions in descending order that is from bigger numbers to smaller numbers. Know the methods on how to arrange the fractions in descending order and along with ordering fractions in descending order examples here.
Also, Read:
How to Find Descending Order in Fractions?
There are two methods to arrange the fractions in descending order. They as given in the below section. So, the students are advised to go through the below steps and write the fractions in descending order.
Method 1:
Convert the fractions into decimals and then arrange the numbers in descending order.
Method 2:
1. Take the least common multiples of the denominators of the fractions.
2. As the denominators of the given fractions are the same, start comparing the numerators of the given fractions.
3. Now arrange the fractions in descending order i.e., from bigger number to smaller number.
Putting Fractions in Descending Order Examples
Go through the below-provided examples to understand the concept of arranging the fractions in descending order with the same denominators.
Example 1.
Arrange the fractions \(\frac{2}{7}\), \(\frac{3}{5}\), \(\frac{1}{2}\) in the descending order.
Solution:
Given the fractions,
\(\frac{2}{7}\), \(\frac{3}{5}\), \(\frac{1}{2}\)
Let us use the L.C.M method to arrange the fractions in descending order.
\(\frac{2}{7}\), \(\frac{3}{5}\), \(\frac{1}{2}\)
The multiples of 7 are 7, 14, 21, 28, 35…
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35…
The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
35 × 2 = 70
Thus the L.C.M of 7, 5, and 2 is 70.
Now write the fractions with the common denominators.
\(\frac{2}{7}\) × \(\frac{10}{10}\), \(\frac{3}{5}\) × \(\frac{7}{7}\), \(\frac{1}{2}\) × \(\frac{35}{35}\)
\(\frac{20}{70}\), \(\frac{21}{35}\), \(\frac{35}{70}\)
Now arrange the fractions in descending order \(\frac{35}{70}\), \(\frac{21}{70}\), \(\frac{20}{70}\)
Example 2.
Arrange the fractions \(\frac{5}{6}\), \(\frac{5}{9}\), \(\frac{7}{12}\) in the descending order.
Solution:
Given the fractions,
\(\frac{5}{6}\), \(\frac{5}{9}\), \(\frac{7}{12}\)
Let us use the L.C.M method to arrange the fractions in descending order.
\(\frac{5}{6}\), \(\frac{5}{9}\), \(\frac{7}{12}\)
The multiples of 6 are 6, 12, 18, 24, 30, 36,..
The multiples of 9 are 9, 18, 27, 36,…
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108,….
Thus the L.C.M of 6, 9, and 12 is 36.
Now write the fractions with the common denominators.
\(\frac{5}{6}\) × \(\frac{6}{6}\), \(\frac{5}{9}\) × \(\frac{4}{4}\), \(\frac{7}{12}\) × \(\frac{3}{3}\)
\(\frac{30}{36}\), \(\frac{20}{36}\), \(\frac{21}{36}\)
Now arrange the fractions in descending order \(\frac{30}{36}\), \(\frac{21}{36}\), \(\frac{20}{36}\)
Example 3.
Arrange the fractions \(\frac{10}{17}\), \(\frac{5}{17}\), \(\frac{16}{17}\) in the descending order.
Solution:
Given the fractions,
\(\frac{10}{17}\), \(\frac{5}{17}\), \(\frac{16}{17}\)
Let us use the L.C.M method to arrange the fractions in descending order.
In this case, all the denominators are the same.
So you can write the fractions in descending order directly.
The fractions in descending order are \(\frac{16}{17}\), \(\frac{10}{17}\), \(\frac{5}{17}\)
Example 4.
Arrange the fractions \(\frac{1}{4}\), \(\frac{5}{7}\), \(\frac{9}{19}\) in the descending order.
Solution:
Given the fractions,
\(\frac{1}{4}\), \(\frac{5}{7}\), \(\frac{9}{19}\)
Let us use the L.C.M method to arrange the fractions in descending order.
\(\frac{1}{4}\), \(\frac{5}{7}\), \(\frac{9}{19}\)
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36..
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56…
The multiples of 19 are 19, 38, 57…
Thus the L.C.M of 4, 7, and 19 is 133.
Now write the fractions with the common denominators.
\(\frac{5}{6}\) × \(\frac{6}{6}\), \(\frac{5}{9}\) × \(\frac{4}{4}\), \(\frac{7}{12}\) × \(\frac{3}{3}\)
\(\frac{30}{36}\), \(\frac{20}{36}\), \(\frac{21}{36}\)
Now arrange the fractions in descending order \(\frac{30}{36}\), \(\frac{21}{36}\), \(\frac{20}{36}\)
Example 5.
Arrange the fractions \(\frac{4}{5}\), \(\frac{3}{8}\), \(\frac{1}{2}\) in the descending order.
Solution:
Given the fractions,
\(\frac{4}{5}\), \(\frac{3}{8}\), \(\frac{1}{2}\)
Let us use the L.C.M method to arrange the fractions in descending order.
\(\frac{4}{5}\), \(\frac{3}{8}\), \(\frac{1}{2}\)
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40..
The multiples of 8 are 8,16, 24, 32, 40…
The multiples of 2 are 2, 4, 6, 8, 10,…., 40.
Thus the L.C.M of 5, 8, and 2 is 40.
Now write the fractions with the common denominators.
\(\frac{4}{5}\) × \(\frac{8}{8}\), \(\frac{3}{8}\) × \(\frac{5}{5}\), \(\frac{1}{2}\) × \(\frac{20}{20}\)
\(\frac{32}{40}\), \(\frac{15}{40}\), \(\frac{20}{40}\)
Now arrange the fractions in descending order \(\frac{32}{40}\), \(\frac{20}{40}\), \(\frac{15}{40}\)
FAQs on Fractions in Descending Order
1. How do you write fractions in descending order?
You can write the fractions in descending order by finding the least common multiples (L.C.M) of the denominators and then write the order of the fractions from bigger to smaller numbers.
2. What are the methods to arrange the fractions in descending order?
The two methods to arrange the fraction in descending order is
1. Convert the fraction to decimal and then write the decimals from greater number to the smaller number.
2. The other method is to find the LCM of the given fractions and then arrange the fractions in descending order.
3. What is decreasing order in fractions?
The fractions can be first made like fractions and then be arranged in descending order. Arranging in decreasing order means arranging the fractions from greatest to smallest in the given value.