Answer
Verified
376.2k+ views
Hint: A fraction is just a numerical value which denotes the equal parts of a whole (or collection). We may apply the fraction in our daily life. For example, when we slice a guava, it will split into two or four and so on.
Example:$\dfrac{1}{2},\dfrac{1}{4},\dfrac{2}{3}$
Here, the number above the line is usually called the numerator and the number below the line is called the denominator.
Fractions having same denominators are called like fractions and fractions having different denominators are called unlike fractions.
Complete step by step answer:
Let us consider a group of $5$unlike fractions which are listed below.
$1,\dfrac{4}{5},\dfrac{7}{{10}},\dfrac{1}{2}$
$\dfrac{3}{4},\dfrac{5}{6},\dfrac{1}{3}$
$\dfrac{2}{9},\dfrac{5}{6}$
$\dfrac{3}{4},\dfrac{1}{2},\dfrac{2}{6},\dfrac{3}{9}$
$\dfrac{1}{2},\dfrac{3}{6},\dfrac{5}{9}$
When we are asked to convert unlike fractions into like fractions, we need to find the LCM for the denominators of unlike fractions and then we have to adjust the fractions to the LCM.
i) LCM of $1,5,10,2$ is $10$
Now, we need to adjust the numerator of the fractions to the LCM$10$.
Consider the fraction$\dfrac{1}{1}$ .
When we multiply the numerator by$10$, we get the required fraction (i.e.)$\dfrac{{10}}{{10}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{10}}{{10}},\dfrac{8}{{10}},\dfrac{7}{{10}},\dfrac{5}{{10}}$
ii) LCM of $4,6,3$ is $12$
Now, we need to adjust the numerator of the fractions to the LCM$12$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$3$, we get the required fraction (i.e.)$\dfrac{9}{{12}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{12}},\dfrac{{10}}{{12}},\dfrac{4}{{12}}$
iii) LCM of $9,6$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{2}{9}$ .
When we multiply the numerator by$2$, we get the required fraction (i.e.)$\dfrac{4}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{4}{{18}},\dfrac{{15}}{{18}}$
iv) LCM of $4,2,9,6$ is $36$
Now, we need to adjust the numerator of the fractions to the LCM$36$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{{27}}{{36}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{27}}{{36}},\dfrac{{13}}{{36}},\dfrac{{12}}{{36}},\dfrac{{12}}{{36}}$
v) LCM of $2,6,9$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{1}{2}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{9}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{18}},\dfrac{6}{{18}},\dfrac{{10}}{{18}}$
Note: Fractions are classified into many types. Among them, the important types of fraction are as follows.
Proper fraction: It is a fraction in which the numerator is less than the denominator.
Example:$\dfrac{4}{5}$
Improper fraction: It is a fraction in which the numerator is more than or equal to the denominator.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
Mixed fraction: It is a fraction containing both the integral part and a proper fraction.
Example:$5\dfrac{1}{4}$
Like fractions: Fractions contain the same denominators.
Example:$\dfrac{7}{4},\dfrac{3}{4}$
Unlike fractions: Fractions contain different denominators.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
Example:$\dfrac{1}{2},\dfrac{1}{4},\dfrac{2}{3}$
Here, the number above the line is usually called the numerator and the number below the line is called the denominator.
Fractions having same denominators are called like fractions and fractions having different denominators are called unlike fractions.
Complete step by step answer:
Let us consider a group of $5$unlike fractions which are listed below.
$1,\dfrac{4}{5},\dfrac{7}{{10}},\dfrac{1}{2}$
$\dfrac{3}{4},\dfrac{5}{6},\dfrac{1}{3}$
$\dfrac{2}{9},\dfrac{5}{6}$
$\dfrac{3}{4},\dfrac{1}{2},\dfrac{2}{6},\dfrac{3}{9}$
$\dfrac{1}{2},\dfrac{3}{6},\dfrac{5}{9}$
When we are asked to convert unlike fractions into like fractions, we need to find the LCM for the denominators of unlike fractions and then we have to adjust the fractions to the LCM.
i) LCM of $1,5,10,2$ is $10$
Now, we need to adjust the numerator of the fractions to the LCM$10$.
Consider the fraction$\dfrac{1}{1}$ .
When we multiply the numerator by$10$, we get the required fraction (i.e.)$\dfrac{{10}}{{10}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{10}}{{10}},\dfrac{8}{{10}},\dfrac{7}{{10}},\dfrac{5}{{10}}$
ii) LCM of $4,6,3$ is $12$
Now, we need to adjust the numerator of the fractions to the LCM$12$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$3$, we get the required fraction (i.e.)$\dfrac{9}{{12}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{12}},\dfrac{{10}}{{12}},\dfrac{4}{{12}}$
iii) LCM of $9,6$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{2}{9}$ .
When we multiply the numerator by$2$, we get the required fraction (i.e.)$\dfrac{4}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{4}{{18}},\dfrac{{15}}{{18}}$
iv) LCM of $4,2,9,6$ is $36$
Now, we need to adjust the numerator of the fractions to the LCM$36$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{{27}}{{36}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{27}}{{36}},\dfrac{{13}}{{36}},\dfrac{{12}}{{36}},\dfrac{{12}}{{36}}$
v) LCM of $2,6,9$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{1}{2}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{9}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{18}},\dfrac{6}{{18}},\dfrac{{10}}{{18}}$
Note: Fractions are classified into many types. Among them, the important types of fraction are as follows.
Proper fraction: It is a fraction in which the numerator is less than the denominator.
Example:$\dfrac{4}{5}$
Improper fraction: It is a fraction in which the numerator is more than or equal to the denominator.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
Mixed fraction: It is a fraction containing both the integral part and a proper fraction.
Example:$5\dfrac{1}{4}$
Like fractions: Fractions contain the same denominators.
Example:$\dfrac{7}{4},\dfrac{3}{4}$
Unlike fractions: Fractions contain different denominators.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
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
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
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
Why is there a time difference of about 5 hours between class 10 social science CBSE