How to solve a proper fraction
Introduction about fraction: Fractions are none other than a certain part in a whole thing. Fractions are denoted by a numerator and denominator. Fractions are classified as,
Classification of fraction
Proper Fractions
Proper fractions are the fraction where the numerator is lesser than the denominator.
Ex: `3/4`
Improper fractions
Improper fractions are the fraction where the numerator is greater than the denominator value Ex: `7/5`
Mixed fractions
Mixed fractions are a whole number with a proper fraction in it.
Ex: 2`2/3`
Examples on how to solve a proper fraction
Addition and subtraction of proper fractions
1. Addition and subtraction on proper fraction with same denominator
2. Addition and subtraction on proper fraction with different denominator
1.Examples On Solving Subtraction with same denominator
Ex 1: Subtract `7/17` - `6/17`
Solution
Here the denominators are equal. So we just subtract the numerator alone
`(7-6)/17`
`1/17` is the answer
The result of the proper fractions may or may not be the proper fractions. The answer may be in improper fractions also.
2. Examples on Solving Addition with different denominator
Ex 2:
Add `4/5` + `2/3`
Sol:
Here the denominators are different
So we have to find the LCM to make the denominator equal
The LCM of 5, 3 = 15
So `(4*3)/ (5*3)` = `12/15`
`(2*5) / (3*5)` = `10 /15`
Now we add
`12/15` + `10/15`
`(12+10)/15`
` 22 / 15` is the solution
Here the solution is in practice improper fraction
Ex 3:
Multiply `2/5` * ` 3/4`
Sol:
Multiplication is just simple. Multiply the numerators of both the proper fraction and denominator of proper fraction.
`(2*3) / (5*4)`
`6/20` by simplifying this to least term we get `3/10`
Ex 4: Divide `3/5` `-:` ` 3/4`
Solution
Keep the first fraction as it is and change the sign to multiplication and take inverse of the second proper fraction
`3/5` * `4/3`
`(3*4)/ (5*3)`
`12/15` this can be simplified by 3
`4/5`
Practice problem on how to solve a proper fraction
1. Add `1/21` + `2/21`
2. Subtract `4/5` - `5/7`
3. Multiply `2/5` * `1/5`
4. Divide `3/7` `-:` `2/3`
Answer
- Proper fraction
- Improper fraction
- Mixed fraction
Classification of fraction
Proper Fractions
Proper fractions are the fraction where the numerator is lesser than the denominator.
Ex: `3/4`
Improper fractions
Improper fractions are the fraction where the numerator is greater than the denominator value Ex: `7/5`
Mixed fractions
Mixed fractions are a whole number with a proper fraction in it.
Ex: 2`2/3`
Examples on how to solve a proper fraction
Addition and subtraction of proper fractions
1. Addition and subtraction on proper fraction with same denominator
2. Addition and subtraction on proper fraction with different denominator
1.Examples On Solving Subtraction with same denominator
Ex 1: Subtract `7/17` - `6/17`
Solution
Here the denominators are equal. So we just subtract the numerator alone
`(7-6)/17`
`1/17` is the answer
The result of the proper fractions may or may not be the proper fractions. The answer may be in improper fractions also.
2. Examples on Solving Addition with different denominator
Ex 2:
Add `4/5` + `2/3`
Sol:
Here the denominators are different
So we have to find the LCM to make the denominator equal
The LCM of 5, 3 = 15
So `(4*3)/ (5*3)` = `12/15`
`(2*5) / (3*5)` = `10 /15`
Now we add
`12/15` + `10/15`
`(12+10)/15`
` 22 / 15` is the solution
Here the solution is in practice improper fraction
Ex 3:
Multiply `2/5` * ` 3/4`
Sol:
Multiplication is just simple. Multiply the numerators of both the proper fraction and denominator of proper fraction.
`(2*3) / (5*4)`
`6/20` by simplifying this to least term we get `3/10`
Ex 4: Divide `3/5` `-:` ` 3/4`
Solution
Keep the first fraction as it is and change the sign to multiplication and take inverse of the second proper fraction
`3/5` * `4/3`
`(3*4)/ (5*3)`
`12/15` this can be simplified by 3
`4/5`
Practice problem on how to solve a proper fraction
1. Add `1/21` + `2/21`
2. Subtract `4/5` - `5/7`
3. Multiply `2/5` * `1/5`
4. Divide `3/7` `-:` `2/3`
Answer
- `1/7`
- `3/35`
- `1/5`
- `9/14`