Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
Simplify Rational Expressions Involving the Sum or Difference
In order to simplify rational expressions involving the sum or difference of three or more rational numbers, we may use the following steps:
Step I: Find the LCM of the denominator of all the numbers involved.
Step II: Write a rational number whose denominator is the LCM obtained in Step I and numerator is computed as follows:
Divide the LCM obtained in step I by the denominator of first rational number and get a quotient. Multiply the numerator of first rational number by this quotient. Repeat this procedure for all rational numbers. Retain the given signs of addition and subtraction between the given rational numbers and get an expression involving integers. Simplify this expression to get an integer as the numerator.
Step III: Reduce the rational number obtained in step II to the lowest form if it is not already so. This rational number so obtained is the required rational number.
How to simplify rational expressions involving the sum or difference of two or more rational numbers?
The following examples will illustrate the above procedure to simplify the expressions.
1. Simplify: -3/4 + 9/8 - (-5)/6
Solution:
We have,
-3/4 + 9/8 - (-5)/6 = -3/4 + 9/8 + 5/6, [Since, -(-5)/6 = 5/6]
Clearly, denominators of the three rational numbers are positive. We now re-write them so that they have a common denominator equal to the LCM of the denominators.
In this case the denominators are 4, 8 and 6.
The LCM of 4, 8 and 6 is 24.
Now, -3/4 = (-3) × 6/4 × 6 = -28/24,
9/8 = 9 × 3/8 × 3 = 27/24 and
5/6 = 5 × 4/6 × 4 = 20/24
Therefore, -3/4 + 9/8 - (-5)/6
= -3/4 + 9/8 + 5/6
= -28/24 + 27/24 + 20/24
= (-28 + 27 + 20)/24
= 19/24
Thus, -3/4 + 9/8 - (-5)/6 = 19/24
2. Simplify: 7/10 - (-7)/14 + 9/-5
Solution:
First we write each of the given numbers with positive denominator.
Clearly, denominators of 7/10 and (-7)/14 are positive.
The denominator of 9/-5 is negative.
The rational number 9/-4 with positive denominator is -9/5.
Therefore, 7/10 - (-7)/14 + 9/-5 = 7/10 - (-7)/14 + (-9)/5
We now re-write them so that they have a common denominator equal to the LCM of the denominators.
In this case the denominators are 10, 14 and 5.
The LCM of 10, 14 and 5 is 70.
Now, 7/10 = 7 × 7/10 × 7 = 49/70,
(-7)/14 = (-7) × 5/14 × 5 = (-35)/70 and
(-9)/5 = (-9) × 14/5 × 14 = (-126)/70
Therefore, 7/10 - (-7)/14 + 9/-5
= 7/10 - (-7)/14 + (-9)/5
= 49/70 - (-35)/70 + (-126)/70
= 49/70 + 35/70 + (-126)/70, [Since, - (-35)/70 = 35/70]
= [49 + 35 + (-126)]/70
= -42/70
= -3/5
Thus, 7/10 - (-7)/14 + 9/-5 = -3/5
● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
From Simplify Rational Expressions Involving the Sum or Difference to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Successor and Predecessor | Successor of a Whole Number | Predecessor
Jul 29, 25 12:59 AM
The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number… -
Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo
Jul 28, 25 01:52 PM
In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar… -
Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox
Jul 25, 25 03:15 AM
We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks: -
Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume
Jul 24, 25 03:46 PM
Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur… -
Volume of a Cube | How to Calculate the Volume of a Cube? | Examples
Jul 23, 25 11:37 AM
A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…
● Rational Numbers - Worksheets
Worksheet on Equivalent Rational Numbers
Worksheet on Lowest form of a Rational Number
Worksheet on Standard form of a Rational Number
Worksheet on Equality of Rational Numbers
Worksheet on Comparison of Rational Numbers
Worksheet on Representation of Rational Number on a Number Line
Worksheet on Adding Rational Numbers
Worksheet on Properties of Addition of Rational Numbers
Worksheet on Subtracting Rational Numbers
Worksheet on Addition and
Subtraction of Rational Number
Worksheet on Rational Expressions Involving Sum and Difference
Worksheet on Multiplication of Rational Number
Worksheet on Properties of Multiplication of Rational Numbers
Worksheet on Division of Rational Numbers
Worksheet on Properties of Division of Rational Numbers
Worksheet on Finding Rational Numbers between Two Rational Numbers
Worksheet on Word Problems on Rational Numbers
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.