Rational Number in Different Forms

We will learn how to find the rational number in different forms using the properties in expressing a given rational number.


1. Express \(\frac{-3}{10}\) as a rational number with denominator 20.

Solution:  

In order to express \(\frac{-3}{10}\) as a rational number with denominator 20, we first find the number which when multiplied by 10 gives 20. 
Clearly, such a number = 20 ÷ 10 = 2

Multiplying the numerator and denominator of \(\frac{-3}{10}\) by 2, we have 

\(\frac{-3}{10}\) = \(\frac{(-3)  ×  2}{10  ×  2}\) = \(\frac{-6}{20}\)

Therefore, expressing \(\frac{-3}{10}\) as a rational number with denominator 20 is \(\frac{-6}{20}\).

2. Express \(\frac{-3}{10}\) as a rational number with denominator -30.

Solution:  

In order to express \(\frac{-3}{10}\) as a rational number with denominator -30, we first
find a number which when multiplied by 10 gives -30.
Clearly, such a number is = (-30) ÷ 10 = -3.

Multiplying the numerator and denominator of \(\frac{-3}{10}\) by -3, we have

\(\frac{-3}{10}\) = \(\frac{(-3)  ×  (-3)}{10  ×  (-3)}\) = \(\frac{9}{-30}\)

Therefore, expressing \(\frac{-3}{10}\) as a rational number with denominator -30 is \(\frac{9}{-30}\).


3. Express \(\frac{42}{-63}\) as a rational number with denominator 3.

Solution:

In order to express \(\frac{42}{-63}\) as a rational number with denominator 3, we first find a number which gives 3 when -63 is divided by it.

Clearly, such a number = (-63) ÷ 3 = -21

Dividing the numerator and denominator of \(\frac{42}{-63}\) by -21, we get

\(\frac{42}{-63}\) = \(\frac{42  ÷  (-21)}{(-63)  ÷  (-21)}\) = \(\frac{-2}{3}\)

Therefore, expressing \(\frac{42}{-63}\) as a rational number in different form with denominator 3 is \(\frac{-2}{3}\).


4. Fill in the blanks with the appropriate number in the denominator:
\(\frac{7}{13}\) = \(\frac{35}{.....}\)  = \(\frac{-63}{.....}\)

Solution:

We have, 35 ÷ 7 = 5

Therefore, \(\frac{7}{13}\) = \(\frac{7  ×  5}{13  ×  5}\) = \(\frac{35}{65}\)

Similarly, we have (-63) ÷ 7 = -9

Therefore, \(\frac{7}{13}\) = \(\frac{7  ×  (-9)}{13  ×  (9)}\) = \(\frac{-63}{-117}\)

Hence, \(\frac{7}{13}\) = \(\frac{35}{65}\) = \(\frac{-63}{-117}\)

Rational Numbers

Introduction of 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

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers






8th Grade Math Practice 

From Rational Number in Different Forms 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.



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. Estimating Sum and Difference | Reasonable Estimate | Procedure | Math

    May 22, 24 06:21 PM

    The procedure of estimating sum and difference are in the following examples. Example 1: Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

    Read More

  2. Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

    May 22, 24 06:14 PM

    Round off to Nearest 1000
    While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5…

    Read More

  3. Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

    May 22, 24 05:17 PM

    Round off to Nearest 100
    While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

    Read More

  4. Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

    May 22, 24 03:49 PM

    Rounding to the Nearest 10
    Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…

    Read More

  5. Rounding Numbers | How do you Round Numbers?|Nearest Hundred, Thousand

    May 22, 24 02:33 PM

    rounding off numbers
    Rounding numbers is required when we deal with large numbers, for example, suppose the population of a district is 5834237, it is difficult to remember the seven digits and their order

    Read More

Rational Numbers - Worksheets

Worksheet on Rational Numbers

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

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers