NCERT Exemplar solutions for Mathematics [English] Class 7 chapter 8 - Rationals Numbers [Latest edition]

A rational number is defined as a number that can be expressed in the form `p/q`, where p and q are integers and ______.

Which of the following rational numbers is positive?

Which of the following rational numbers is negative?

In the standard form of a rational number, the common factor of numerator and denominator is always ______.

Which of the following rational numbers is equal to its reciprocal?

The reciprocal of `1/2` is ______.

The standard form of `(-48)/60` is ______.

Which of the following is equivalent to `4/5`?

How many rational numbers are there between two rational numbers?

In the standard form of a rational number, the denominator is always a ______.

To reduce a rational number to its standard form, we divide its numerator and denominator by their ______.

Which is greater number in the following?

`-3/8` is a ______ rational number.

1 is a ______ rational number.

The standard form of `(-8)/(-36)` is ______.

The standard form of `18/(-24)` is ______.

On a number line, `(-1)/2` is to the ______ of zero (0).

On a number line, `4/3` is to the ______ of zero (0).

`(-1)/2` is ______ than `1/5`.

`-3/5` is ______ than 0.

`(-16)/24` and `20/(-16)` represent ______ rational numbers.

`(-27)/45` and `(-3)/5` represent ______ rational numbers.

Additive inverse of `2/3` is ______.

`(-3)/5 + 2/5` = ______.

`(-5)/6 + (-1)/6` = ______.

`3/4 xx ((-2)/3)` = ______.

`(-5)/3 xx ((-3)/5)` = ______.

`(-6)/7 =  underline()/42`

`1/2 = 6/underline`

`(-2)/9 - 7/9` = ______.

Fill in the box with the correct symbol >, < or =.

`7/(-8) square 8/9`

Fill in the box with the correct symbol >, < or =.

`3/7 square (-5)/6`

Fill in the box with the correct symbol >, < or =.

`5/6 square 8/4`

Fill in the box with the correct symbol >, < or =.

`(-9)/7 square 4/(-7)`

Fill in the box with the correct symbol >, < or =.

`8/8 square 2/2`

The reciprocal of ______ does not exist.

The reciprocal of 1 is ______.

`(-3)/7 ÷ ((-7)/3)` = ______.

`0 ÷ ((-5)/6)` = ______.

`0 xx ((-5)/6)` = ______.

______ × `((-2)/5)` = 1.

The standard form of rational number –1 is ______.

If m is a common divisor of a and b, then `a/b = (a ÷ m)/underline`

If p and q are positive integers, then `p/q` is a ______ rational number and `p/(-q)` is a ______ rational number.

Two rational numbers are said to be equivalent or equal, if they have the same ______ form.

If `p/q` is a rational number, then q cannot be ______.

Every natural number is a rational number but every rational number need not be a natural number.

Zero is a rational number.

Every integer is a rational number but every rational number need not be an integer.

Every negative integer is not a negative rational number.

If `p/q` is a rational number and m is a non-zero integer, then `p/q = (p xx m)/(q xx m)`.

If `p/q` is a rational number and m is a non-zero common divisor of p and q, then `p/q = (p ÷ m)/(q ÷ m)`.

In a rational number, denominator always has to be a non-zero integer.

If `p/q` is a rational number and m is a non-zero integer, then `(p xx m)/(q xx m)` is a rational number not equivalent to `p/q`.

Sum of two rational numbers is always a rational number.

All decimal numbers are also rational numbers.

The quotient of two rationals is always a rational number.

Every fraction is a rational number.

Two rationals with different numerators can never be equal.

8 can be written as a rational number with any integer as denominator.

`4/6` is equivalent to `2/3`.

The rational number `(-3)/4` lies to the right of zero on the number line.

The rational numbers `(-12)/(-5)` and `(-7)/17` are on the opposite sides of zero on the number line.

Every rational number is a whole number.

Zero is the smallest rational number.

Match the following:

Write the following rational numbers with positive denominators:

`5/(-8)`

Write the following rational numbers with positive denominators:

`15/(-28)`

Write the following rational numbers with positive denominators:

`(-17)/(-13)`

Express `3/4` as a rational number with denominator:

36

Express `3/4` as a rational number with denominator:

–80

Reduce the following rational numbers in its lowest form:

`(-60)/72`

Reduce the following rational numbers in its lowest form:

`91/(-364)`

Express the following rational numbers in its standard form:

`(-12)/(-30)`

Express the following rational numbers in its standard form:

`14/(-49)`

Express the following rational numbers in its standard form:

`(-15)/35`

Express the following rational numbers in its standard form:

`299/(-161)`

Are the rational numbers `(-8)/28` and `32/(-112)` equivalent? Give reason.

Arrange the rational numbers `(-7)/10, 5/(-8), 2/(-3), (-1)/4, (-3)/5` in ascending order.

Represent the following rational numbers on a number line:

`3/8, (-7)/3, 22/(-6)`

If `(-5)/7 = x/28`, find the value of x.

Give three rational numbers equivalent to:

`(-3)/4`

Give three rational numbers equivalent to:

`7/11`

Write the next three rational numbers to complete the pattern:

`4/(-5), 8/(-10), 12/(-15), 16/(-20)`, ______, ______, ______.

Write the next three rational numbers to complete the pattern:

`(-8)/7, (-16)/14, (-24)/21, (-32)/28`, ______, ______, ______.

List four rational numbers between `5/7` and `7/8`.

Find the sum of `8/13` and `3/11`.

Find the sum of `7/3` and `(-4)/3`.

Solve:

`29/4 - 30/7`

Solve:

`5/13 - (-8)/26`

Find the product of:

 `(-4)/5` and `(-5)/12`

Find the product of:

 `(-22)/11` and `(-21)/11`

Simplify:

`13/11 xx (-14)/5 + 13/11 xx (-7)/5 + (-13)/11 xx 34/5`

Simplify:

`6/5 xx 3/7 - 1/5 xx 3/7`

Simplify:

`3/7 ÷ (21/-55)`

Simplify:

`1 ÷ (-1/2)`

Which is greater in the following?

`3/4, 7/8`

Which is greater in the following?

`-3 5/7, 3 1/9`

Write a rational number in which the numerator is less than ‘–7 × 11’ and the denominator is greater than ‘12 + 4’.

If x = `1/10` and y = `(-3)/8`, then evaluate x + y, x – y, x × y and x ÷ y.

Find the reciprocal of the following:

`(1/2 xx 1/4) + (1/2 xx 6)`

Find the reciprocal of the following:

`20/51 xx 4/91`

Find the reciprocal of the following:

`3/13 ÷ (-4)/65`

Find the reciprocal of the following:

`(-5 xx 12/15) - (-3 xx 2/9)`

Complete the following table by finding the sums:

Write the following numbers in the form `p/q` where p and q are integers:

Six-eighths

Write the following numbers in the form `p/q` where p and q are integers:

Three and half

Write the following numbers in the form `p/q` where p and q are integers:

Opposite of 1

Write the following numbers in the form `p/q`, where p and q are integers:

One-fourth

Write the following numbers in the form `p/q` where p and q are integers:

Zero

Write the following numbers in the form `p/q` where p and q are integers:

Opposite of three-fifths

If p = m × t and q = n × t, then `p=q = square/square`

Given that `p/q` and `r/s` are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers we say that:

`square/square` < `square/square`, if p × s < r × q

Given that `p/q` and `r/s` are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers we say that:

`p/q = r/s`, if ______ = ______

Given that `p/q` and `r/s` are two rational numbers with different denominators and both of them are in standard form. To compare these rational numbers we say that:

`square/square` > `square/square`, if p × s > r × q

Write the rational number whose numerator and denominator are respectively as under:

5 – 39 and 54 – 6

Write the rational number whose numerator and denominator are respectively as under:

(–4) × 6 and 8 ÷ 2

Write the rational number whose numerator and denominator are respectively as under:

35 ÷ (–7) and 35 – 18

Write the rational number whose numerator and denominator are respectively as under:

25 + 15 and 81 ÷ 40

Write the following as rational numbers in their standard form:

35%

Write the following as rational numbers in their standard form:

1.2

Write the following as rational numbers in their standard form:

`-6 3/7`

Write the following as rational numbers in their standard form:

240 ÷ (–840)

Write the following as rational numbers in their standard form:

115 ÷ 207

Find a rational number exactly halfway between:

`(-1)/3` and `1/3`

Find a rational number exactly halfway between:

`1/6` and `1/9`

Find a rational number exactly halfway between:

`5/(-13)` and `(-7)/9`

Find a rational number exactly halfway between:

`1/15` and `1/12`

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the rational number which when added to x gives y.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the rational number which subtracted from y gives z.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the rational number which when added to z gives us x.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the rational number which when multiplied by y to get x.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the reciprocal of x + y.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find the sum of reciprocals of x and y

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find (x ÷ y) × z.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find (x – y) + z.

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find x + (y + z).

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find x ÷ (y ÷ z).

Taking x = `(-4)/9`, y = `5/12` and z = `7/18`, find x – (y + z).

What should be added to `(-1)/2` to obtain the nearest natural number?

What should be subtracted from `(-2)/3` to obtain the nearest integer?

What should be multiplied with `(-5)/8` to obtain the nearest integer?

What should be divided by `1/2` to obtain the greatest negative integer?

From a rope 68 m long, pieces of equal size are cut. If length of one piece is `4 1/4`m, find the number of such pieces.

If 12 shirts of equal size can be prepared from 27m cloth, what is length of cloth required for each shirt?

Insert 3 equivalent rational numbers between `(-1)/2` and `1/5`

Insert 3 equivalent rational numbers between 0 and –10

Put the (√), wherever applicable

‘a’ and ‘b’ are two different numbers taken from the numbers 1 – 50. What is the largest value that `(a - b)/(a + b)` can have? What is the largest value that `(a + b)/(a - b)` can have?

150 students are studying English, Maths or both. 62 per cent of the students are studying English and 68 per cent are studying Maths. How many students are studying both?

A body floats `2/9` of its volume above the surface. What is the ratio of the body submerged volume to its exposed volume? Re-write it as a rational number.

Find the odd one out of the following and give reason.

Find the odd one out of the following and give reason.

Find the odd one out of the following and give reason.

Find the odd one out of the following and give reason.

Chhaya simplified a rational number in this manner `(-25)/(-30) = (-5)/6`. What error did the student make?