Free fraction lessons
Introduction :
Fraction is breaking the whole thing in to the small pieces. Each piece represents the fraction. Fraction has two parts. They are numerator and denominator. Fraction is denoted as a/b where a is called as numerator and the b is called as denominator. Numerator denotes the number of equal part. Denominator denotes how many equal parts is made from whole thing.
Examples and explanations for free fraction lessons:
Addition operation for free fraction lessons:
Example 1:
Solve: `2/8` + `4/8`
Solution:
`2/8` + `4/8`
In this example, denominators are same. So the numerators are added like below
`(2+4)/8`
So we get,
`6/8` now we have to divide both numerator and denominator by the common number 2
`(6-:2)/(8-:2)`
`3/4`
Example 2:
Solve `2/7` + `4/9`
Solution:
`2/7` + `4/9`
In this example denominators are not same. So we need how to find the least common denominator. The least common denominator for the denominator 7 and 8 is 63.
The denominator 7 from the fraction 2/7 is 9 times in least common denominator 63. So we have to multiply numerator 2 by 9. 2 `xx` 9 = 18.
The denominator 5 from the fraction 4/9 is 7 times in least common denominator 63. So we have to multiply numerator 4 by 7. 4 `xx` 7 = 28.
Therefore,
= `(18+28)/63`
= `46/63`
Subtraction operation for free fraction lessons:
Example 1:
Solve: `2/8` - `4/8`
Solution:
`2/8` - `4/8`
In this example, denominators are same. So the numerators are added like below
(2-4)/8
So we get,
`-2/8` now we have to divide both numerator and denominators by the common number 2
`(-2-:2)/(8-:2)`
`-1/4`
Example 2:
Solve `2/7` - `4/9`
Solution:
`2/7` - `4/9`
In this example denominators are not same. So we need to find out the least common denominator. The least common denominator for the denominator 7 and 8 is 63.
The denominator 7 from the fraction 2/7 is 9 times in least common denominator 63. So we have to multiply numerator 2 by 9. 2 `xx` 9 = 18.
The denominator 5 from the fraction 4/9 is 7 times in least common denominator 63. So we have to multiply numerator 4 by 7. 4 `xx` 7 = 28.
Therefore,
= `(18-28)/63`
= `-10/63`
Multiplication operation for free fraction lessons:
Example:
Solve` 2/7` ` xx` `4/9`
Solution:
`2/7` `xx` `4/9` (multiply numerators by numerators and denominators by denominators)
= `(2 xx 4)/(7 xx 9)`
= `8/63`
Division operation for free fraction lessons:
Example:
Solve `2/7`` -:` `4/9`
Solution:
`2/7` ` -:` `4/9`
Division operation of fraction is multiplying dividend fraction by reciprocal for divisor fraction. Fraction reciprocal is interchanging the numerator to denominator and the denominator to numerator. Therefore, the reciprocal of the divisor fraction 4/9 is 9/4.
So we get,
`2/7` `xx` `9/4` (multiply numerators by numerators and denominators by denominators. So we get)
= `(2 xx 9) / (7xx 4)`
= `18/28` (both numerators and denominators are divided by the common number 2. So we get)
= `(18-:2)/(28-:2)`
= `9/14`
Fraction is breaking the whole thing in to the small pieces. Each piece represents the fraction. Fraction has two parts. They are numerator and denominator. Fraction is denoted as a/b where a is called as numerator and the b is called as denominator. Numerator denotes the number of equal part. Denominator denotes how many equal parts is made from whole thing.
Examples and explanations for free fraction lessons:
Addition operation for free fraction lessons:
Example 1:
Solve: `2/8` + `4/8`
Solution:
`2/8` + `4/8`
In this example, denominators are same. So the numerators are added like below
`(2+4)/8`
So we get,
`6/8` now we have to divide both numerator and denominator by the common number 2
`(6-:2)/(8-:2)`
`3/4`
Example 2:
Solve `2/7` + `4/9`
Solution:
`2/7` + `4/9`
In this example denominators are not same. So we need how to find the least common denominator. The least common denominator for the denominator 7 and 8 is 63.
The denominator 7 from the fraction 2/7 is 9 times in least common denominator 63. So we have to multiply numerator 2 by 9. 2 `xx` 9 = 18.
The denominator 5 from the fraction 4/9 is 7 times in least common denominator 63. So we have to multiply numerator 4 by 7. 4 `xx` 7 = 28.
Therefore,
= `(18+28)/63`
= `46/63`
Subtraction operation for free fraction lessons:
Example 1:
Solve: `2/8` - `4/8`
Solution:
`2/8` - `4/8`
In this example, denominators are same. So the numerators are added like below
(2-4)/8
So we get,
`-2/8` now we have to divide both numerator and denominators by the common number 2
`(-2-:2)/(8-:2)`
`-1/4`
Example 2:
Solve `2/7` - `4/9`
Solution:
`2/7` - `4/9`
In this example denominators are not same. So we need to find out the least common denominator. The least common denominator for the denominator 7 and 8 is 63.
The denominator 7 from the fraction 2/7 is 9 times in least common denominator 63. So we have to multiply numerator 2 by 9. 2 `xx` 9 = 18.
The denominator 5 from the fraction 4/9 is 7 times in least common denominator 63. So we have to multiply numerator 4 by 7. 4 `xx` 7 = 28.
Therefore,
= `(18-28)/63`
= `-10/63`
Multiplication operation for free fraction lessons:
Example:
Solve` 2/7` ` xx` `4/9`
Solution:
`2/7` `xx` `4/9` (multiply numerators by numerators and denominators by denominators)
= `(2 xx 4)/(7 xx 9)`
= `8/63`
Division operation for free fraction lessons:
Example:
Solve `2/7`` -:` `4/9`
Solution:
`2/7` ` -:` `4/9`
Division operation of fraction is multiplying dividend fraction by reciprocal for divisor fraction. Fraction reciprocal is interchanging the numerator to denominator and the denominator to numerator. Therefore, the reciprocal of the divisor fraction 4/9 is 9/4.
So we get,
`2/7` `xx` `9/4` (multiply numerators by numerators and denominators by denominators. So we get)
= `(2 xx 9) / (7xx 4)`
= `18/28` (both numerators and denominators are divided by the common number 2. So we get)
= `(18-:2)/(28-:2)`
= `9/14`