Answer
Verified
351k+ views
Hint: To convert given fractions into like fractions we will use LCM method. Firstly we will find out the LCM of all the denominators of the given fractions. Then we will multiply and divide each fraction with a number such that the denominator becomes equal to the LCM. Finally we will simplify each fraction and get the desired answer.
Complete step by step answer:
We have to convert the fractions given below into like fractions.
$\dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15},\dfrac{11}{30}$……..$\left( 1 \right)$
Firstly we know that denominator of all the fractions are:
$5,10,15,30$
So we will find the factors of each number and take out the each factor with highest power among them as follows:
$5=1\times 5$
$10=2\times 5$
$15=3\times 5$
$30=2\times 3\times 5$
We got the LCM of the denominator as follows:
$\begin{align}
& LCM\left( 5,10,15,30 \right)=2\times 3\times 5 \\
& LCM\left( 5,10,15,30 \right)=30 \\
\end{align}$
Next we will make denominator of the fractions from equation (1) 30 by multiplying dividing them by 6, 3, 2 and 1 respectively as below:
$\begin{align}
& \dfrac{3}{5}\times \dfrac{6}{6}=\dfrac{18}{30} \\
& \dfrac{7}{10}\times \dfrac{3}{3}=\dfrac{21}{30} \\
\end{align}$
$\begin{align}
& \dfrac{8}{15}\times \dfrac{2}{2}=\dfrac{16}{30} \\
& \dfrac{11}{30}\times \dfrac{1}{1}=\dfrac{11}{30} \\
\end{align}$
So we got the fractions as $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$
Hence the like fractions are $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$
Note: Like fractions are the group of two or more fractions which have exactly the same denominator. We simply have to find the LCM of the denominator of the fractions and then according to the LCM obtain multiply and divide a number with each fractions to make the denominator same. LCM is the least common multiple of numbers which is the smallest positive integer divided by all the numbers completely. LCM is used before a fraction can be added or subtracted so that we can make the denominator the same. Also, we can use LCM for comparing simple fractions.
Complete step by step answer:
We have to convert the fractions given below into like fractions.
$\dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15},\dfrac{11}{30}$……..$\left( 1 \right)$
Firstly we know that denominator of all the fractions are:
$5,10,15,30$
So we will find the factors of each number and take out the each factor with highest power among them as follows:
$5=1\times 5$
$10=2\times 5$
$15=3\times 5$
$30=2\times 3\times 5$
We got the LCM of the denominator as follows:
$\begin{align}
& LCM\left( 5,10,15,30 \right)=2\times 3\times 5 \\
& LCM\left( 5,10,15,30 \right)=30 \\
\end{align}$
Next we will make denominator of the fractions from equation (1) 30 by multiplying dividing them by 6, 3, 2 and 1 respectively as below:
$\begin{align}
& \dfrac{3}{5}\times \dfrac{6}{6}=\dfrac{18}{30} \\
& \dfrac{7}{10}\times \dfrac{3}{3}=\dfrac{21}{30} \\
\end{align}$
$\begin{align}
& \dfrac{8}{15}\times \dfrac{2}{2}=\dfrac{16}{30} \\
& \dfrac{11}{30}\times \dfrac{1}{1}=\dfrac{11}{30} \\
\end{align}$
So we got the fractions as $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$
Hence the like fractions are $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$
Note: Like fractions are the group of two or more fractions which have exactly the same denominator. We simply have to find the LCM of the denominator of the fractions and then according to the LCM obtain multiply and divide a number with each fractions to make the denominator same. LCM is the least common multiple of numbers which is the smallest positive integer divided by all the numbers completely. LCM is used before a fraction can be added or subtracted so that we can make the denominator the same. Also, we can use LCM for comparing simple fractions.
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE