Answer
Verified
409.8k+ 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.
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
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE