Fraction worksheets with answers
Introduction:
A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. A fraction, consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole.(Source: From Wikipedia).
For example, `5/7` is a fraction, (proper fraction, numerator < denominator) and 5 is the numerator and 7 is the denominator. Here we will see some example problems and work sheets with answers in fractions.
Example problems and work sheet with answers in fractions
Types of fractions
Proper fraction
A fraction is said to be a proper fraction, where the numerator is less than the denominator
Example: `3/5`; (3 < 5)
Improper fraction
A fraction is said to be an improper fraction, where the numerator is greater than the denominator.
Example: `5/3` ; (5 > 3)
Mixed fraction
The combination of a whole number and a proper fraction is called as a mixed number or mixed fraction.
Example: `2 3/5` ; (2- whole number, `3/5` - proper fraction)
Example problems
Example 1
`2/5` + `3/7`
Solution
Here the denominators of both fraction are different, so we cannot add the fractions. However, by changing the denominators into a common denominator we can add them. To find the common denominator, we have to find the least common multiple of the denominators or least common denominator.
Least common multiple of 5 and 7 is 35, so the fractions can be re-written as follows,
`2/5` = `2/5` * `7/7` = `14/35`
and,
`3/7` = `3/7` * `5/5` = `15/35`
Now the problem becomes,
`14/35` + `15/35` = `(14+15)/35`
= `29/35`
Answer = `29/35`
Example 2
Convert the improper fraction `7/2` into a mixed number
Solution
To convert the improper fraction `7/2` into a mixed fraction, divide the numerator (7) by the denominator (2).
We get, quotient = 3 and reminder = 1
Now the equivalent mixed fraction of the fraction `7/2` can be written as follows,
The quotient becomes (3) and reminder (1) becomes the whole number and numerator for the mixed number respectively. The denominator is same for both fractions.
Answer: `7/2` = `3 1/2`
Fraction worksheets with answers
Worksheet for adding fractions with answers
1. `2/5` + `3/8`
Answer: `31/40`
2. `3/5` + `2/3`
Answer: `19/15`
3. `1/5` + `3/5`
Answer: `4/5`
4. `11/19` + `2/17`
Answer: `225/323`
5. `23/25` + `3/7`
Answer: `236/175`
Worksheet for converting fractions
1. Convert `21/5` into a mixed fraction
Answer: `4 1/5`
2. Convert `33/21` into a mixed fraction
Answer: `1 4/7`
3. Convert `2 1/6` into an improper fraction
Answer: `13/6`
4. Convert `1 5/8` into an improper fraction
Answer: `13/8`
A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. A fraction, consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole.(Source: From Wikipedia).
For example, `5/7` is a fraction, (proper fraction, numerator < denominator) and 5 is the numerator and 7 is the denominator. Here we will see some example problems and work sheets with answers in fractions.
Example problems and work sheet with answers in fractions
Types of fractions
Proper fraction
A fraction is said to be a proper fraction, where the numerator is less than the denominator
Example: `3/5`; (3 < 5)
Improper fraction
A fraction is said to be an improper fraction, where the numerator is greater than the denominator.
Example: `5/3` ; (5 > 3)
Mixed fraction
The combination of a whole number and a proper fraction is called as a mixed number or mixed fraction.
Example: `2 3/5` ; (2- whole number, `3/5` - proper fraction)
Example problems
Example 1
`2/5` + `3/7`
Solution
Here the denominators of both fraction are different, so we cannot add the fractions. However, by changing the denominators into a common denominator we can add them. To find the common denominator, we have to find the least common multiple of the denominators or least common denominator.
Least common multiple of 5 and 7 is 35, so the fractions can be re-written as follows,
`2/5` = `2/5` * `7/7` = `14/35`
and,
`3/7` = `3/7` * `5/5` = `15/35`
Now the problem becomes,
`14/35` + `15/35` = `(14+15)/35`
= `29/35`
Answer = `29/35`
Example 2
Convert the improper fraction `7/2` into a mixed number
Solution
To convert the improper fraction `7/2` into a mixed fraction, divide the numerator (7) by the denominator (2).
We get, quotient = 3 and reminder = 1
Now the equivalent mixed fraction of the fraction `7/2` can be written as follows,
The quotient becomes (3) and reminder (1) becomes the whole number and numerator for the mixed number respectively. The denominator is same for both fractions.
Answer: `7/2` = `3 1/2`
Fraction worksheets with answers
Worksheet for adding fractions with answers
1. `2/5` + `3/8`
Answer: `31/40`
2. `3/5` + `2/3`
Answer: `19/15`
3. `1/5` + `3/5`
Answer: `4/5`
4. `11/19` + `2/17`
Answer: `225/323`
5. `23/25` + `3/7`
Answer: `236/175`
Worksheet for converting fractions
1. Convert `21/5` into a mixed fraction
Answer: `4 1/5`
2. Convert `33/21` into a mixed fraction
Answer: `1 4/7`
3. Convert `2 1/6` into an improper fraction
Answer: `13/6`
4. Convert `1 5/8` into an improper fraction
Answer: `13/8`