  # Worksheet on Lowest Form of a Rational Number | Reducing Rational Numbers to Simplest Form Worksheet

Feeling difficult on how to reduce rational numbers to their lowest form? Don’t Fret as we have got a Worksheet on Lowest Form of a Rational Number for your practice. Try solving the Questions in the Reducing Rational Numbers to Lowest Form Worksheet and understand your preparation standards. A Rational Number is said to be in its lowest form if its numerator and denominator have no other common factors other than 1.
Use the Reducing Rational Numbers to Simplest Form Worksheet as a part of your study and estimate the kind of questions to be asked in exams regarding the topic. Have a look at the Rational Numbers Worksheets if you want to get a grip on the entire chapter and not just this concept.
1. Convert the Rational Number -15/30 to its lowest form?

Solution:

-15/30 is not in its Lowest Form Since it has common factors other than 1
Find the GCF(15, 30) = 15 and then divide the numerator and denominator of the Rational Number with GCF to obtain the lowest form
-15/30 = (-15·15)/(30·15)
= -1/2

2. Determine whether the following Rational Numbers are in its Lowest Form or Not?
a) 1/3 b) -7/2 c) 14/16 d) 17/5

Solution:

Rational Numbers 1/3, -7/2, 17/5 are in their Lowest Form as all of them have no other common factors other than 1. Whereas, Rational Number 14/16 is not in its Lowest Form as it has common factors other than 1 and can be simplified.

3. Reduce Rational Number 35/40 to its Lowest Form?

Solution:

Given Rational Number is 35/40
In Order to find the Lowest Form of the Rational Number find the GCF of numerator and denominator
GCF(35, 40) = 5
Divide the Numerator and Denominator of Rational Number with the GCF Obtained.
35/40 = (35·5)/(40·5) = 7/8
Therefore, 35/40 Reduced to its Simplest or Lowest Form is 7/8.

4. A Rational Number a/b is said to be in its lowest form if a and b has no …….

Solution:

Rational Number a/b is in its lowest form if a, b has no other common factors other than 1.

5. Express each of the following Rational Numbers to their Simplest Form
(i)5/45 (ii) -30/18

Solution:

Given Rational Number is 5/45
GCF(5, 45) = 5
Divide the Rational Number with the GCF
5/45 = (5·5)/(45·5)
= 1/9
Therefore, 5/45 in its Lowest Form is 1/9
Given Rational Number is -30/18
GCF(30, 18) = 6
Divide the Rational Number with the GCF
-30/18 = (-30·6)/(18·6)
= -5/3
Therefore, -30/18 in its Lowest Form is -5/3.

6. Which of the following Rational Numbers are in its Lowest Form?
a) -32/-56 b) 6/-13 c) -17/37 d) 24/-64

Solution:

b) & c)
Options B and C are in the Lowest Form as they can’t be simplified further and they have no other common factors other than 1.

7. Convert Rational Number -14/49 to its Lowest Form?

Solution:

Given Rational Number is -14/49
GCF(14, 49) = 7
Divide the Rational Number with the GCF obtained
-14/49 = (-14·7)/(49·7) = -2/7
Therefore, -14/49 reduced to its lowest form is -2/7.

8. Fill in the Blanks
-4/6 = €¦./30

Solution:

Consider the number to be found as x
Cross multiplying we have
6x= -4*30
6x = -120
x = -20