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# Are improper fractions rational numbers?

Rational numbers have the form p/q, where p and q are integers and q ≠ 0. Most people have difficulty distinguishing between fractions and rational numbers because of the underlying structure of numbers, the p/q form. When you divide a rational number, the result is in decimal form, which might be either ending or recurring. Examples of rational numbers are 2, -2, 4, -4, 7, and so on, which may be represented in fraction form as 2/1, 4/1, and 7/1.

A rational number is a kind of real number with the formula p/q, where q ≠ 0. When a rational number is divided, the outcome is a decimal number, which can be either ended or repeated.

### Improper Fractions

An improper fraction is one in which the numerator is higher than or greater than the denominator, such as 7/3 and 12/5. When compared to other types of fractions such as mixed fractions, improper fractions are easier to answer using addition and subtraction.

### Are improper fractions rational numbers?

If a numerator is greater than denominator in fraction then the improper fraction will be rational number.

• Example 1: We have fraction 5/4 its a improper fraction as here numerator is greater than denominator. After dividing 5 by 4 , the result will be 1.25 which is a terminating after decimal , therefore its an rational number.
• Example 2: Now fraction 6/5 its a improper fraction as numerator is greater than denominator. Therefore after dividing 6 by 5 , the result will be 1.2 its a rational number.

### Similar Questions

Question 1:  Identify improper fractions out of the below numbers,

13/5, 3, 2/9, 4/2, 4/5.

An improper fraction is one in which the numerator is higher than or greater than the denominator.

Here improper functions are: 13/5, 4/2, 3

Question 2: Is 16/4 rational or not?

Here Given 16/4, we can simplify it by dividing 16/4 is 4, therefore 4 can be written as 4/1 hence its an improper fraction and rational number.

Question 3: Identify whether the 17/5 improper fraction is rational or not?

An improper fraction is one in which the numerator is higher than or greater than the denominator, such as 7/3 and 12/5. When compared to other types of fractions such as mixed fractions, improper fractions are easier to answer using addition and subtraction.

Given: 17/5 which is an improper fraction, after dividing 17/5 we will get 3.4 which is terminating after decimal. Therefore 17/5 is a rational number

Question 4: Simplify improper fractions 6/5 + 8/5 and find out the result is rational or not?

Solution:

Given: 6/5 + 8/5

Here with the same denominator is 5.

= 6/5 + 8/5

= (6 + 8)/5

= 14/5

Here 14/5 is improper fraction.

After dividing 14/5 we will get 2.8 which is terminating digit after decimal,

Therefore its a rational number.

Question 5: Simplify improper fractions 4/5 – 12/5 and find out the result is rational or not?

Solution:

Given: 4/5 – 12/5

Here with the same denominator is 5.

= 4/5 – 12/5

= (4 – 12)/5

= – 8/5

Here – 8/5 is improper fraction.

After dividing 8/5 we will get -1.6 which is terminating digit after decimal, hence it is negative and rational number include all the integers.

Therefore its a rational number.

Question 6: Determine whether 11/5 is a rational number or an irrational number.