Graph the rational numbers on a number line. 2 , 2 1 3 , - 2 2 3 , 0 , - 2 1 3

The graph, showing the rational numbers 2 , 2 1 3 , - 2 2 3 , 0 , - 2 1 3 on a number line is shown below. Here, note that the positive rational numbers are on the right side of the ' 0 ' mark on the number line and the negative numbers are on the left side of ' 0 ' mark.

A rational number - 2 3 is

Lies to the left side of 0 on the number line.

Lies to the right side of 0 on the number line.

Is not possible to represent on the number line.

Write three rational numbers equivalent to - 6 5 .

Given, - 6 5 Equivalent rational numbers are rational numbers that have the same value but which are represented in a different form. In order to find equivalent rational numbers, we need to multiply the numerator and denominator of the given number with the same number. Therefore, - 6 5 × 2 2 = - 12 10 , - 6 5 × 3 3 = - 18 15 and - 6 5 × 4 4 = - 24 20 Hence, three rational numbers equivalent to - 6 5 are - 12 10 , - 18 15 , - 24 20 .

Express - 3 5 as a rational number with denominator 20 .

We have to express - 3 5 as a rational number with denominator 20 . We know that equivalent rational numbers are rational numbers which have the same value when expressed in the simplest form. Here, we need to find the equivalent rational number of - 3 5 with denominator 20 . So, we need to multiply the numerator and denominator with 4 . ⇒ - 3 5 = - 3 × 4 5 × 4 = - 12 20 Hence, the required rational number is - 12 20 .

Find the simplest form of 368 496

Prime factorization of 368 and 496 is: 368 = 2 4 × 23 496 = 2 4 × 31 HCF = 2 4 = 16 Divide the numerator and denominator by their HCF Therefore, 368 496 = 368 ÷ 16 496 ÷ 16 = 23 31 Thus, simplest form of 368 496 = 23 31

Represent the following number on a number line. 7 4

Given, Fraction 7 4 The given rational number is an improper fraction, so we can convert it as a mixed fraction. We get, 7 4 = 1 3 4 The result is a mixed number containing 1 integer part and 3 4 fractional part. Thus, this rational number will lie between 1 and 2 . Now divide the space between the numbers into 4 equal parts. Mark the required divisions as fractions with denominator 4. Thus the rational number 7 4 can be represented on the number line.

Express - 12 30 as a rational number in standard form.

We need to express - 12 30 as a rational number in standard form. If a rational number is in standard form, then the HCF of numerator and denominator should be 1 . The HCF of 12 and 30 is 6 . So, dividing the numerator and denominator by 6 , ⇒ - 12 30 = - 12 ÷ 6 30 ÷ 6 = - 2 5 Hence, the required answer is - 2 5 .

Express - 48 60 as a rational number with denominator 5 .

We have to express - 48 60 as a rational number with denominator 5 . We know that equivalent rational numbers are rational numbers which have the same value when expressed in the simplest form. Here, we need to find the equivalent rational number of - 48 60 with denominator 5 . So, we need to divide the numerator and denominator with 12 . ⇒ - 48 60 = - 48 ÷ 12 60 ÷ 12 = - 4 5 Hence, the required rational number is - 4 5 .

Express - 42 98 as a rational number with denominator 7 .

We have to express - 42 98 as a rational number with denominator 7 . We know that equivalent rational numbers are rational numbers which have the same value when expressed in the simplest form. Here, we need to find the equivalent rational number of - 42 98 with denominator 7 . So, we need to divide the numerator and denominator with 14 . ⇒ - 42 98 = - 42 ÷ 14 98 ÷ 14 = - 3 7 Hence, the required rational number is - 3 7 .

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A rational number equivalent to $\frac{- 7}{- 4}$ is

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Important Questions on Rational Numbers

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Find between which two integers the given rational numbers lie. Also, find their actual position on a number line.

\frac{12}{5}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

\frac{5}{8}

is the rational number between

\frac{3}{4}

and

\frac{1}{2}

. Which of the following is not a rational number between

\frac{3}{4}

and

\frac{1}{2}

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Draw the number line and represent the rational number

\frac{3}{4}

on it.

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Graph the rational numbers on a number line.

2, 2 \frac{1}{3}, - 2 \frac{2}{3}, 0, - 2 \frac{1}{3}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Write four rational numbers equivalent to the rational number

\frac{6}{7}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

A rational number

- \frac{2}{3}

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Write three rational numbers equivalent to

\frac{- 6}{5}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Express $\frac{- 3}{5}$ as a rational number with denominator $20$ .

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

p :

every fraction is a rational number and

q :

every rational number is a fraction, then which of the following options hold?

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Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

The points $P, Q, R, S, T, U, A$ and $B$ on the number line are such that, $T R = R S = S U$ and $A P = P Q = Q B$ . Name the rational numbers represented by $P, Q, R$ and $S$ .

Question Image .

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Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Write four rational numbers equivalent to the following rational number.

\frac{11}{18}

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Write four rational numbers equivalent to the following rational number.

\frac{5}{- 11}

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Find the simplest form of

\frac{368}{496}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Represent the following number on a number line.

\frac{7}{4}

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Express $\frac{- 12}{30}$ as a rational number in standard form.

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Which of the following options are equivalent rational numbers?

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Express $\frac{- 48}{60}$ as a rational number with denominator $5$ .

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Express $\frac{- 42}{98}$ as a rational number with denominator $7$ .

EASY

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Rational Number and Its Representation on Number Line

Write four rational numbers equivalent to the following rational number.

\frac{- 8}{9}

A rational number equivalent to -7-4 is

Important Questions on Rational Numbers

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A rational number equivalent to $\frac{- 7}{- 4}$ is