Answer
Verified
479.1k+ views
Hint: Take LCM of the denominators of each of the given fractions. Suppose the LCM of the denominators is \[x\]. Divide \[x\] by the denominator of each fraction and multiply the numerator and denominator of the fraction by the value you get on dividing \[x\] by the denominator of the fraction. As the denominators of all the fractions are the same now, compare the numerators of the fractions and arrange them in ascending or descending order. Once you arrange the fractions in ascending or descending order, divide the numerator and denominator by the value you got on dividing \[x\] by the denominator.
Complete step-by-step answer:
We have the fractions \[\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}\]. We have to arrange them in ascending or descending order. We will do so by evaluating the LCM of the denominators of each of the fractions.
Thus, we have the numbers \[11,15,18,22,33\].
The LCM of numbers \[11,15,18,22,33\] is \[11\times 2\times 9\times 5=990\].
We can rewrite the fraction \[\dfrac{4}{11}\] as \[\dfrac{4}{11}=\dfrac{4\times 90}{11\times 90}=\dfrac{360}{990}\].
Similarly, we can rewrite the fraction \[\dfrac{10}{15}\] as \[\dfrac{10}{15}=\dfrac{10\times 66}{15\times 66}=\dfrac{660}{990}\].
We can rewrite the fraction \[\dfrac{6}{18}\] as \[\dfrac{6}{18}=\dfrac{6\times 55}{18\times 55}=\dfrac{330}{990}\].
We can rewrite the fraction \[\dfrac{12}{22}\] as \[\dfrac{12}{22}=\dfrac{12\times 45}{22\times 45}=\dfrac{540}{990}\].
We can rewrite the fraction \[\dfrac{15}{33}\] as \[\dfrac{15}{33}=\dfrac{15\times 30}{33\times 30}=\dfrac{450}{990}\].
Thus, we have the fractions \[\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}\] rewritten as \[\dfrac{360}{990},\dfrac{660}{990},\dfrac{330}{990},\dfrac{540}{990},\dfrac{450}{990}\].
Arranging these fractions in ascending order, we have \[\dfrac{330}{990}<\dfrac{360}{990}<\dfrac{450}{990}<\dfrac{540}{990}<\dfrac{660}{990}\].
Hence, the fractions arranged in ascending order are \[\dfrac{6}{18}<\dfrac{4}{11}<\dfrac{15}{33}<\dfrac{12}{22}<\dfrac{10}{15}\].
We can also arrange these fractions in descending order as \[\dfrac{10}{15}>\dfrac{12}{22}>\dfrac{15}{33}>\dfrac{4}{11}>\dfrac{6}{18}\].
Note: A fraction represents a part of a whole. Arranging the fractions in ascending order means arranging them in the increasing order of their value. While, arranging the fractions in descending order means arranging them in decreasing order of their values. Be careful while evaluating the LCM of the denominators as the LCM of any two numbers might not be the same as LCM of five numbers
Complete step-by-step answer:
We have the fractions \[\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}\]. We have to arrange them in ascending or descending order. We will do so by evaluating the LCM of the denominators of each of the fractions.
Thus, we have the numbers \[11,15,18,22,33\].
The LCM of numbers \[11,15,18,22,33\] is \[11\times 2\times 9\times 5=990\].
We can rewrite the fraction \[\dfrac{4}{11}\] as \[\dfrac{4}{11}=\dfrac{4\times 90}{11\times 90}=\dfrac{360}{990}\].
Similarly, we can rewrite the fraction \[\dfrac{10}{15}\] as \[\dfrac{10}{15}=\dfrac{10\times 66}{15\times 66}=\dfrac{660}{990}\].
We can rewrite the fraction \[\dfrac{6}{18}\] as \[\dfrac{6}{18}=\dfrac{6\times 55}{18\times 55}=\dfrac{330}{990}\].
We can rewrite the fraction \[\dfrac{12}{22}\] as \[\dfrac{12}{22}=\dfrac{12\times 45}{22\times 45}=\dfrac{540}{990}\].
We can rewrite the fraction \[\dfrac{15}{33}\] as \[\dfrac{15}{33}=\dfrac{15\times 30}{33\times 30}=\dfrac{450}{990}\].
Thus, we have the fractions \[\dfrac{4}{11},\dfrac{10}{15},\dfrac{6}{18},\dfrac{12}{22},\dfrac{15}{33}\] rewritten as \[\dfrac{360}{990},\dfrac{660}{990},\dfrac{330}{990},\dfrac{540}{990},\dfrac{450}{990}\].
Arranging these fractions in ascending order, we have \[\dfrac{330}{990}<\dfrac{360}{990}<\dfrac{450}{990}<\dfrac{540}{990}<\dfrac{660}{990}\].
Hence, the fractions arranged in ascending order are \[\dfrac{6}{18}<\dfrac{4}{11}<\dfrac{15}{33}<\dfrac{12}{22}<\dfrac{10}{15}\].
We can also arrange these fractions in descending order as \[\dfrac{10}{15}>\dfrac{12}{22}>\dfrac{15}{33}>\dfrac{4}{11}>\dfrac{6}{18}\].
Note: A fraction represents a part of a whole. Arranging the fractions in ascending order means arranging them in the increasing order of their value. While, arranging the fractions in descending order means arranging them in decreasing order of their values. Be careful while evaluating the LCM of the denominators as the LCM of any two numbers might not be the same as LCM of five numbers
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
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