Question

Arrange the following in descending order of magnitude
$\sqrt[8]{90}$
$\sqrt[4]{10}$
$\sqrt{6}$


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Answer 1

Answer:

Due to the complex nature of fractions unlike whole numbers you can’t get your answer by only applying the ascending and descending order rule you’ll have to either take all the fractions to percentage or decimals before arranging accordingly.

Example 1; Arrange the following in descending order of magnitude: 5/9, 7/15, 11/20, 3/8.

Solution

Before arranging these fractions in descending order, let’s first convert it to percentage!

5/9 × 100 = 55.6%

7/15 × 100 = 46.7%

11/20 × 100 = 55%

3/8 × 100 = 37.5%

Now, let’s arrange in descending order (remember highest to lowest percentage) according to the instruction given in the question.

The highest should be 5/9 because it has the highest percentage followed by 11/20 and so on. Ok!

Therefore, the arrangement should be; 5/9, 11/20, 7/15, 3/8 respectively.

Example 2; Arrange the following in ascending order of magnitude: 3/4, 2/3, 1/2, 5/8, 5/12.

Solution

Let’s convert these fractions to decimals before arranging them in ascending order. You can either use long division or calculator to get your decimal number.

3/4 = 0.75

2/3 = 0.67

1/2 = 0.5

5/8 = 0.63

5/12 = 0.42

The lowest value should be 5/12 because it has the lowest decimal followed by 1/2 and so on.

Now, let’s arrange;

5/12, 1/2, 5/8, 2/3, 3/4. (Answer)

Note;

Ascending order is also the same thing as increasing order while descending order is the same thing as decreasing order.

Practice these questions below for further understanding;

1. Arrange the following in descending order of magnitude:

(a) 4/7, 3/5, 11/10, 14/15.

(b) 5/6, 11/18, 7/12, 8/9, 2/5.

(c) 4/9, 11/24, 8/15, 12/20.

(d) 2/3, 3/4, 15/19, 10/11, 7/8.

2. Arrange the following in increasing order of magnitude:

(a) 11/13, 8/15, 6/8, 1/3.

(b) 12/17, 7/34, 2/3, 5/6.

(c) 5/8, 5/6, 11/16, 3/4.

(d) 11/15, 5/12, 19/23, 7/18.

3. Find the greatest of 5/61/3, 2/71/6 and 11/21/4.