R d sharma solutions mathematics class 7 Solutions for Chapter 4 rational numbers

Write down the numerator of each of the following rationalnumbers:

(i) (-7/5)

(ii) (14/-4)

(iii) (-17/-21)

(iv) (8/9)

(v) 5

Write down the numerator of each of the following rational numbers:

(i) (-7/5)

(ii) (14/-4)

(iii) (-17/-21)

(iv) (8/9)

(v) 5

Write down the denominator of each of the following rationalnumbers:

(i) (-4/5)

(ii) (11/-34)

(iii) (-15/-82)

(iv) 15

(v) 0

Write down the denominator of each of the following rational numbers:

(i) (-4/5)

(ii) (11/-34)

(iii) (-15/-82)

(iv) 15

(v) 0

Write down the rational number whose numerator is (-3) × 4, andwhose denominator is (34 – 23) × (7 – 4).

Write down the rational number whose numerator is (-3) × 4, and whose denominator is (34 – 23) × (7 – 4).

Write down the rational numbers as integers: (7/1), (-12/1), (34/1), (-73/1),(95/1)

Write the following integers as rational numbers: -15, 17, 85,-100

Write the following integers as rational numbers: -15, 17, 85, -100

Write down the rational number whose numerator is the smallest threedigit number and denominator is the largest four digit number.

Write down the rational number whose numerator is the smallestthreedigit number and denominator is the largest four digit number

Separate positive and negative rational numbers from thefollowingrational numbers:

(-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)

Separate positive and negative rational numbers from the following rational numbers:

(-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)

Which of the following rational numbers are positive:

(i) (-8/7)

(ii) (9/8)

(iii) (-19/-13)

(iv) (-21/13)

Which of the following rational numbers are positive:

(i) (-8/7)

(ii) (9/8)

(iii) (-19/-13)

(iv) (-21/13)

Which of the following rational numbers are negative:

(i) (-3/7)

(ii) (-5/-8)

(iii) (9/-83)

(iv) (-115/-197)

Which of the following rational numbers are negative:

(i) (-3/7)

(ii) (-5/-8)

(iii) (9/-83)

(iv) (-115/-197)

Express each of the following as a rational number with positivedenominator.

(i) (-15/-28)

(ii)(6/-9)

(iii) (-28/-11)

(iv) (19/-7)

Express each of the following as a rational number with positive denominator.

(i) (-15/-28)

(ii) (6/-9)

(iii) (-28/-11)

(iv) (19/-7)

Express (3/5) as a rational number with numerator:

(i) 6

(ii) -15

(iii) 21

(iv) -27

Express (3/5) as a rational number with numerator:

(i) 6

(ii) -15

(iii) 21

(iv) -27

Express (5/7) as a rational number with denominator:

(i) -14

(ii) 70

(iii) -28

(iv) -84

Express (5/7) as a rational number with denominator:

(i) -14

(ii) 70

(iii) -28

(iv) -84

Express (3/4) as a rational number with denominator:

(i) 20

(ii) 36

(iii) 44

(iv) -80

Express (3/4) as a rational number with denominator:

(i) 20

(ii) 36

(iii) 44

(iv) -80

Express (2/5) as a rational number with numerator:

(i) -56

(ii) 154

(iii) -750

(iv) 500

Express (2/5) as a rational number with numerator:

(i) -56

(ii) 154

(iii) -750

(iv) 500

Express (-192/108) as a rational number with numerator:

(i) 64

(ii) -16

(iii) 32

(iv) -48

Express (-192/108) as a rational number with numerator:

(i) 64

(ii) -16

(iii) 32

(iv) -48

Express (169/-294) as a rational number with denominator:

(i) 14

(ii) -7

(iii) -49

(iv) 1470

Express (169/-294) as a rational number with denominator:

(i) 14

(ii) -7

(iii) -49

(iv) 1470

Write (-14/42) in a form so that the numerator is equal to:

(i) -2

(ii) 7

(iii) 42

(iv) -70

Write (-14/42) in a form so that the numerator is equal to:

(i) -2

(ii) 7

(iii) 42

(iv) -70

Select those rational numbers which can be written as a rational numberwith numerator 6:

(1/22), (2/3), (3/4), (4/-5), (5/6), (-6/7), (-7/8)

Select those rational numbers which can be written as a rational number with numerator 6:

(1/22), (2/3), (3/4), (4/-5), (5/6), (-6/7), (-7/8)

Select those rational numbers which can be written as rational number with denominator 4:

(7/8), (64/16), (36/-12), (-16/17), (5/-4), (140/28)

Select those rational numbers which can be written as rational numberwith denominator 4:

(7/8), (64/16), (36/-12), (-16/17), (5/-4), (140/28)

In each of the following, find an equivalent form of the rational number havinga common denominator:

(i) (3/4) and (5/12)

(ii) (2/3), (7/6) and (11/12)

(iii) (5/7), (3/8), (9/14) and (20/21)

In each of the following, find an equivalent form of the rational numberhavinga common denominator:

(i) (3/4) and (5/12)

(ii) (2/3), (7/6) and (11/12)

(iii) (5/7), (3/8), (9/14) and (20/21)

Determine whether the following rational numbers are in the lowest form or not:

(i) (65/84)

(ii) (-15/32)

(iii) (24/128)

(iv) (-56/-32)

Determine whether the following rational numbers are in the lowest form or not:

(i) (65/84)

(ii) (-15/32)

(iii) (24/128)

(iv) (-56/-32)

Express each of the following rational numbers to the lowestform:

(i) (4/22)

(ii) (-36/180)

(iii) (132/-428)

(iv) (-32/-56)

Express each of the following rational numbers to the lowest form:

(i) (4/22)

(ii) (-36/180)

(iii) (132/-428)

(iv) (-32/-56)

Fill in the blanks:

(i) (-5/7) = (…/35) = (…/49)

(ii) (-4/-9) = (…/18) = (12/…)

(iii) (6/-13) = (-12/…) = (24/…)

(iv) (-6/…) = (3/11) = (…/-55)

Fill in the blanks:

(i) (-5/7) = (…/35) = (…/49)

(ii) (-4/-9) = (…/18) = (12/…)

(iii) (6/-13) = (-12/…) = (24/…)

(iv) (-6/…) = (3/11) = (…/-55)

Write each of the following rational numbers in the standard form:

(i) (2/10)

(ii) (-8/36)

(iii) (4/-16)

(iv) (-15/-35)

(v) (299/-161)

(vi)(-63/-210)

(vii) (68/-119)

(viii) (-195/275)

Write each of the following rational numbers in the standard form:

(i) (2/10)

(ii) (-8/36)

(iii) (4/-16)

(iv) (-15/-35)

(v) (299/-161)

(vi) (-63/-210)

(vii) (68/-119)

(viii) (-195/275)

Which of the following rational numbers areequal?

(i) (-9/12) and (8/-12)

(ii) (-16/20) and (20/-25)

(iii) (-7/21) and (3/-9)

(iv) (-8/-14) and (13/21)

Which of the following rational numbers are equal?

(i) (-9/12) and (8/-12)

(ii) (-16/20) and (20/-25)

(iii) (-7/21) and (3/-9)

(iv) (-8/-14) and (13/21)

In each of the following pairs represent a pair of equivalent rational numbers, find the values of x.

(i) (2/3) and (5/x)

(ii) (-3/7) and (x/4)

(iii) (3/5) and (x/-25)

(iv) (13/6) and (-65/x)

In each of the following pairs represent a pair of equivalent rational numbers,find the values of x.

(i) (2/3) and (5/x)

(ii) (-3/7) and (x/4)

(iii) (3/5) and (x/-25)

(iv) (13/6) and (-65/x)

In each of the following, fill in the blanks so as to make the statementtrue:

(i) A number which can be expressed in the form p/q, where p and q are integersand q is not equal to zero, is called a ………..

(ii) If the integers p and q have no common divisor other than 1 and q is positive,then the rational number (p/q) is said to be in the ….

(iii) Two rational numbers are said to be equal, if they have the same ….form

(iv) If m is a common divisor of a and b, then (a/b) = (a ÷ m)/…..

(v) If p and q are positive Integers, then p/q is a…… rational number and (p/-q) is a …… rational number.

(vi) The standard form of -1 is …

(vii) If (p/q) is a rational number, then q cannot be ….

(viii) Two rational numbers with different numerators are equal, if their numerators are in the same …. as their denominators.

In each of the following, fill in the blanks so as to make the statement true:

(i) A number which can be expressed in the form p/q, where p and q are integers and q is not equal to zero, is called a ………..

(ii) If the integers p and q have no common divisor other than 1 and q is positive, then the rational number (p/q) is said to be in the ….

(iii) Two rational numbers are said to be equal, if they have the same …. form

(iv) If m is a common divisor of a and b, then (a/b) = (a ÷ m)/…..

(v) If p and q are positive Integers, then p/q is a …… rational number and (p/-q) is a

…… rational number.

(vi) The standard form of -1 is …

(vii) If (p/q) is a rational number, then q cannot be ….

(viii) Two rational numbers with different numerators are equal, if their numerators are in the same …. as their denominators

In each of the following state if the statement is true (T) or false (F):

(i) The quotient of two integers is always an integer.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every traction is a rationalnumber.

(v) Every rational number is afraction.

(vi) If a/b is a rational number and m any integer, then (a/b) = (a x m)/ (b xm)

(vii) Two rational numbers with different numerators cannot be equal.

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

(ix) 8 can be written as a rational number with any integer as numerator.

(x) (2/3) is equal to (4/6).

In each of the following state if the statement is true (T) or false (F):

(i) The quotient of two integers is always an integer.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every traction is a rational number.

(v) Every rational number is a fraction.

(vi) If a/b is a rational number and m any integer, then (a/b) = (a x m)/ (b x m)

(vii) Two rational numbers with different numerators cannot be equal.

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

(ix) 8 can be written as a rational number with any integer as numerator.

(x) (2/3) is equal to (4/6).

Draw the number line and represent following rational number onit:

(i) (2/3)

(ii) (3/4)

(iii) (3/8)

(iv) (-5/8)

(v) (-3/16)

(vi) (-7/3)

(vii) (22/-7)

(viii) (-31/3)

Which of the two rational numbers in each of the following pairs of rationalnumber is greater?

(i) (-3/8), 0

(ii) (5/2), 0

(iii) (– 4/11), (3/11)

(iv) (– 7/12), (5/- 8)

(v) (4/-9), (– 3/- 7)

(vi) (– 5/8), (3/- 4)

(vii) (5/9), (-3/- 8)

(viii) (5/- 8), (-7/12)

Which of the two rational numbers in each of the following pairs of rationalnumber is greater?

(i) (-3/8), 0

(ii) (5/2), 0

(iii) (– 4/11),(3/11)

(iv) (– 7/12), (5/- 8)

(v) (4/-9), (– 3/- 7)

(vi) (– 5/8), (3/- 4)

(vii) (5/9), (-3/- 8)

(viii) (5/- 8), (-7/12)

Which of the two rational numbers in each of the following pairs ofrational numbers is smaller?

(i) (-6/-13), (7/13)

(ii) (16/-5), 3

(iii) (-4/3), (8/-7)

(iv) (-12/5), (-3)

Which of the two rational numbers in each of the following pairs ofrational numbers is smaller?

(i) (-6/-13), (7/13)

(ii) (16/-5), 3

(iii) (-4/3), (8/-7)

(iv) (-12/5), (-3)

Fill in the blanks by the correct symbol out of >, =, or <:

(i) (-6/7) …. (7/13)

(ii) (-3/5) …. (-5/6)

(iii) (-2/3) …. (5/-8)

(iv) 0 …. (-2/5)

Fill in the blanks by the correct symbol out of >, =, or <:

(i) (-6/7) …. (7/13)

(ii) (-3/5) …. (-5/6)

(iii) (-2/3) …. (5/-8)

(iv) 0 …. (-2/5)

Arrange the following rational numbers in ascendingorder:

(i) (3/5), (-17/-30), (8/-15), (-7/10)

(ii) (-4/9), (5/-12), (7/-18), (2/-3)

Arrange the following rational numbers in ascending order:

(i) (3/5), (-17/-30), (8/-15), (-7/10)

(ii) (-4/9), (5/-12), (7/-18), (2/-3)

Arrange the following rational numbers in descendingorder:

(i) (7/8), (64/16), (39/-12), (5/-4), (140/28)

(ii) (-3/10), (17/-30), (7/-15), (-11/20)

Arrange the following rational numbers in descending order:

(i) (7/8), (64/16), (39/-12), (5/-4), (140/28)

(ii) (-3/10), (17/-30), (7/-15), (-11/20)

Which of the following statements are true:

(i) The rational number (29/23) lies to the left of zero on the number line.

(ii) The rational number (-12/-17) lies to the left of zero on the number line.

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

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

(v) The rational number (-2/15) and (7/-31) are on the opposite side of zero onthe number line.

(vi) The rational number (- 3/-5) is on the right of (- 4/7) on the number line.

Which of the following statements are true:

(i) The rational number (29/23) lies to the left of zero on the number line.

(ii) The rational number (-12/-17) lies to the left of zero on the numberline.

(iii) The rational number (3/4) lies to the right of zero on the numberline.

(iv) The rational number (-12/-5) and (- 7/17) are on the opposite side of zero onthe number line.

(v) The rational number (-2/15) and (7/-31) are on the opposite side of zeroonthe number line.

(vi) The rational number (- 3/-5) is on the right of (- 4/7) on the numberline.