Answer

Verified

382.5k+ views

**Hint:**Here in this question, we have to arrange the given numbers from the smallest to the largest. The numbers are in the form of fraction by simplifying the fraction into its simplest form with the help of division or by the table of multiplication. Then we arrange the numbers from the smallest to the largest number.

**Complete step-by-step solution:**

the number is in the form of fraction. The fraction number has two parts numerator and denominator. In the fraction we have 3 kinds

Proper fraction: the value of the numerator is less than the value of the denominator.

Improper fraction: the value of the numerator is greater than the value of the denominator.

Mixed fraction: the combination of a whole number and the fraction term.

While arranging any kind of number we have two kind of arrangements namely,

Ascending order: The numbers are arranged from least to the greatest.

Descending order: The numbers are arranged from greatest to the least.

Now consider the set in the question \[\left\{ {\dfrac{{18}}{9},\dfrac{{32}}{{24}},\dfrac{{25}}{{20}},\dfrac{{33}}{{12}}} \right\}\]

First we simplify each term of the set.

Consider \[\dfrac{{18}}{9}\]

On simplifying we get \[\dfrac{{18}}{9} = 2\]

Consider the second term \[\dfrac{{32}}{{24}}\]

The number 8 is the common factor for the both 32 and 24. Dividing the both numbers by 8 we get \[\dfrac{4}{3}\]. On simplifying we get \[\dfrac{4}{3} = 1.33\]

Consider the third term \[\dfrac{{25}}{{20}}\]

The number 5 is the common factor for the both 25 and 20. Dividing the both numbers by 5 we get \[\dfrac{5}{4}\]. On simplifying we get \[\dfrac{5}{4} = 1.25\]

Consider the fourth term \[\dfrac{{33}}{{12}}\]

The number 3 is the common factor for the both 33 and 12. Dividing the both numbers by 3 we get \[\dfrac{{11}}{4}\]. On simplifying we get \[\dfrac{{11}}{4} = 2.75\]

Therefore the numbers are written as

2, 1.33, 1.25, 2.75.

The ascending order of these numbers is

1.25, 1.33, 2, 2.75.

\[ \Rightarrow \left\{ {\dfrac{{25}}{{20}},\dfrac{{32}}{{24}},\dfrac{{18}}{9},\dfrac{{33}}{{12}}} \right\}\]

This also written as

\[ \Rightarrow \left\{ {\dfrac{{25}}{{20}} < \dfrac{{32}}{{24}} < \dfrac{{18}}{9} < \dfrac{{33}}{{12}}} \right\}\]

**Note:**To simplify the fraction the table of multiplication is needed. The common factor is the number which can divide the both numbers. For the ascending arrangement we use the symbol < and for the descending arrangement we use > symbol. In a proper fraction if the numerator value is less then it will be least and vice versa in the improper fraction.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE