Introduction to fractions
A fraction is a number that can represent part of a whole. A fraction consists two parts, a numerator and a denominator, the numerator represents the number of equal parts and the denominator represents number of equal parts make up a whole.
For example, `2/3` is a fraction. Here, the number above the fraction bar is called as the numerator (2) and number below the fraction bar is called as the denominator (3) of the fraction.
Here we are going to study about fractions
Sample Problems on Fractions
Here we are going to study about adding and subtracting fractions with same denominators and different numerators.
Example 1
`2/11` + `5/11`
Solution
Here the given problem is to add the fractions `2/11` and `5/11`
Notice that the denominators of both fractions are same, so we can just add the numerators.
So,
`2/11 + 5/11` = `(2 + 5)/11`
= `7/11`
So, the sum of `2/11` and `5/11` is `7/11`
Example 2
`6/14 - 3/14`
Solution
Here the given problem is to subtract `3/14` from `6/14`
Here the denominators are same, so we can just subtract the numerators.
`6/14 - 3/14` = `(6 - 3)/14`
= `3/14`
Few more Sample Problems on Fractions
Here we are going to study about adding and subtracting fractions with different numerators and denominators.
Example 1
`2/5 + 1/4`
Solution
Here the given problem is to add `2/5` and `1/4`
Notice that the denominators are different in the given fractions and we cannot add the fractions directly. The given fractions can be added with the help of least common denominator.
The least common denominator of `2/5` and `1/4` is 20. Because, 20 is the least common multiple of the denominators 5 and 4.
So, the fractions can be re-written as,
`2/5` = `2/5` * `4/4` = `8/20`
`1/4` = `1/4` * `5/5` = `5/20`
Now the problem becomes,
`8/20 + 5/20` = `(8 + 5)/20`
= `13/20`
Example 2
`3/7 - 1/3`
Solution
Here the given problem is to subtract `1/3` from `3/7`
Notice that the denominators are different in the given fractions and we cannot subtract the fractions directly. The given fractions can be subtracted with the help of least common denominator.
The least common denominator of `1/3` and `3/7` is 21. Because, 21 is the least common multiple of the denominators 3 and 7.
So, the fractions can be re-written as,
`3/7` = `3/7` * `3/3` = `9/21`
`1/3` = `1/3` * `7/7` = `7/21`
Now the problem becomes,
`9/21 - 7/21` = `(9 - 7)/21`
= `2/21`
A fraction is a number that can represent part of a whole. A fraction consists two parts, a numerator and a denominator, the numerator represents the number of equal parts and the denominator represents number of equal parts make up a whole.
For example, `2/3` is a fraction. Here, the number above the fraction bar is called as the numerator (2) and number below the fraction bar is called as the denominator (3) of the fraction.
Here we are going to study about fractions
Sample Problems on Fractions
Here we are going to study about adding and subtracting fractions with same denominators and different numerators.
Example 1
`2/11` + `5/11`
Solution
Here the given problem is to add the fractions `2/11` and `5/11`
Notice that the denominators of both fractions are same, so we can just add the numerators.
So,
`2/11 + 5/11` = `(2 + 5)/11`
= `7/11`
So, the sum of `2/11` and `5/11` is `7/11`
Example 2
`6/14 - 3/14`
Solution
Here the given problem is to subtract `3/14` from `6/14`
Here the denominators are same, so we can just subtract the numerators.
`6/14 - 3/14` = `(6 - 3)/14`
= `3/14`
Few more Sample Problems on Fractions
Here we are going to study about adding and subtracting fractions with different numerators and denominators.
Example 1
`2/5 + 1/4`
Solution
Here the given problem is to add `2/5` and `1/4`
Notice that the denominators are different in the given fractions and we cannot add the fractions directly. The given fractions can be added with the help of least common denominator.
The least common denominator of `2/5` and `1/4` is 20. Because, 20 is the least common multiple of the denominators 5 and 4.
So, the fractions can be re-written as,
`2/5` = `2/5` * `4/4` = `8/20`
`1/4` = `1/4` * `5/5` = `5/20`
Now the problem becomes,
`8/20 + 5/20` = `(8 + 5)/20`
= `13/20`
Example 2
`3/7 - 1/3`
Solution
Here the given problem is to subtract `1/3` from `3/7`
Notice that the denominators are different in the given fractions and we cannot subtract the fractions directly. The given fractions can be subtracted with the help of least common denominator.
The least common denominator of `1/3` and `3/7` is 21. Because, 21 is the least common multiple of the denominators 3 and 7.
So, the fractions can be re-written as,
`3/7` = `3/7` * `3/3` = `9/21`
`1/3` = `1/3` * `7/7` = `7/21`
Now the problem becomes,
`9/21 - 7/21` = `(9 - 7)/21`
= `2/21`
