# 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

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

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