Subtraction of Rational Number with Different Denominator

We will learn the subtraction of rational number with different denominator. To find the difference of two rational numbers which do not have the same denominator, we follow the following steps:

Step I: Let us obtain the rational numbers and see whether their denominators are positive or not. If the denominator of one (or both) of the numerators is negative, re-arrange it so that the denominators become positive.

Step II: Obtain the denominators of the rational numbers in step I.

Step III: Find the lowest common multiple of the denominators of the two given rational numbers.

Step IV: Express both the rational numbers in step I so that the lowest common multiple of the denominators becomes their common denominator.

Step V: Write a rational number whose numerator is equal to the difference of the numerators of rational numbers obtained in step IV and denominators is the lowest common multiple obtained in step III.

Step VI: The rational number obtained in step V is the required difference (simplify if required).

Following examples will illustrate the above procedure.

1. Subtract 9 from 4/5

Solution:

We have, 9 = 9/1

Clearly, denominators of the two 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 1 and 5.

The LCM of 1 and 5 is 5.

We have, 9 = 9/1 = 9 × 5/1 × 5 = 45/5

Therefore, 4/5 - 9

= 4/5 - 9/1

= 4/5 - 45/5

= (4 - 45)/5

= -41/5

Therefore, 4/5 - 9 = -41/5

2. Find the difference of: -3/4 - 5/6

Solution:

The denominators of the given rational numbers are 4 and 6 respectively.

LCM of 4 and 6 = (2 × 2 × 3) = 12.

Now, -3/4 = (-3) × 3/4 × 3 = -9/12

and 5/6 = 5 × 2/6 × 2 = 10/12

Therefore, -3/4 - 5/6

= -9/12 - 10/12

= (-9 - 10)/12

= -19/12

Therefore, -3/4 - 5/6 = -19/12

3. Simplify: 3/-15 - 7/-12

Solution:

First we write each of the given numbers with positive denominator.

3/-15 = 3 × (-1)/(-15) × (-1) = -3/15, [Multiplying the numerator and denominator by -1]

⇒ 3/-15 = -3/15

7/-12 = 7 × (-1)/(-12) ×  (-1) = -7/12, [Multiplying the numerator and denominator by -1]

⇒ 7/-12 = -7/12

Therefore, 3/-15 - 7/-12 = -3/15 - (-7)/12

Now, we find the LCM of 15 and 12.

The LCM of 15 and 12 = 60

Rewriting -3/15 in the form in which it has denominator 60, we get

-3/15 = -3 × 4/15 × 4 = -12/60

Rewriting -7/12 in the form in which it has denominator 60, we get

-7/12 = -7 × 5/12 × 5 = -35/60

Therefore, 3/-15 - 7/-12

= -3/15 - (-7)/12

= -12/60 - (-35)/60

= (-12) - (-35)/60

= -12 + 35/60

= 23/60

Thus, 3/-15 - 7/-12 = 23/60.

4. Simplify: 11/-18 - 5/12

Solution:

First we write each one of the given rational numbers with positive denominator.

Clearly, denominator of 5/12 is positive.

The denominator of 11/-18 is negative.

The rational number 11/-18 with positive denominator is -11/18.

Therefore, 11/-18 - 5/12 = -11/18 - 5/12

The LCM of 18 and 12 is 36.

Rewriting -11/18 in forms having the same denominator 36, we get

-11/18 = (-11) × 2/18 × 2, [Multiplying the numerator and denominator by 2]

⇒ -11/18 = -22/36

Rewriting 5/12 in forms having the same denominator 66, we get

5/12 = 5 × 3/12 × 3, [Multiplying the numerator and denominator by 3]

⇒ 5/12 = 15/36

Therefore, 11/-18 - 5/12

= -11/18 - 5/12

= -22/36 - 15/36

= -22 - 15/36

= -37/36

Therefore, 11/-18 - 5/12 = -37/36

If a/b and c/d are two rational numbers such that b and d do not have a common factor other than 1, i.e., HCF of b and d is 1, then

a/b - c/d = a × d - c × b/b × d

For example, 5/18 - 3/13 = 5 × 13 - 3 × 18/18 × 13 = 65 - 54/234 = 11/234

and -2/11 - 3/14 = (-2) × 14 - (3 × 11)/11 × 14 = -28 - 33/154 = -61/154

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

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

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

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

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

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.

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.

Share this page: What’s this?

Recent Articles

1. 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

Read More

2. Three Digit Numbers | What is Spike Abacus? | Abacus for Kids|3 Digits

Sep 14, 24 03:39 PM

Three digit numbers are from 100 to 999. We know that there are nine one-digit numbers, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two digit numbers i.e., from 10 to 99. One digit numbers are ma

Read More

3. Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 14, 24 02:12 PM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

Read More

4. Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

Read More

5. Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers

Read More

Rational Numbers - Worksheets

Worksheet on 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 Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers