Ncert exemplar solutions mathematics class 8 Solutions for Chapter 1 rational numbers

Rational numbers follows x + y = y + x by taking x = ½, y = ½

There are ________ rational numbers between any two rational numbers.

The reciprocal of -\frac{3}{8}\times-\frac{7}{13} is _____________.

To get the product 1, we should multiply \frac{8}{21} by __________.

Rational numbers can be added or multiplied in any _______.

The reciprocal of -\frac{5}{7} is ________ .

The multiplicative inverse of 4/3 is ________ .

The rational number 10.11 in the from p/q is ________ .

The rational numbers \frac{1}{3} and -\frac{1}{3} are on the ___\__(same/opposite) sides of zero on the number line.

The negative of a negative rational number is always a ________ (positive/negative) rational number.

\frac{5}{10} lies between \frac{1}{2} and 1.

\frac{1}{5}\times\left[\frac{2}{7}+\frac{3}{8}\right]=\left[\frac{1}{5}\times\frac{2}{7}\right] + _________ .

\frac{5}{6} lies between \frac{2}{3} and 1.

If r/s is a rational number, then s cannot be equal to zero.

If p/q is a rational number, then p cannot be equal to zero.

-\frac{7}{2} lies between -3 and -4.

If a ≠ 0, the multiplicative inverse of \frac{a}{b} is \frac{b}{a} .

The additive inverse of ½ is -2.

\frac{9}{6} lies between 1 and 2.

The multiplicative inverse of -\frac{3}{5} is \frac{5}{3}.

For every rational number x, x + 1 = x.

If \frac{x}{y} is the additive inverse of \frac{c}{d}, then\frac{x}{y} + \frac{c}{d} = 0

If x/y is a rational number, then y is always a whole number.

If \frac{x}{y} is the additive inverse of \frac{c}{d} , then, \frac{x}{y} – \frac{c}{d} = 0

The two rational numbers lying between –2 and –5 with denominator as 1 are _________ and _________.

The reciprocal of a non-zero rational number q/p is the rational number q/p.

If x + y = 0, then –y is known as the negative of x, where x and y are rational numbers.

The negative of the negative of any rational number is the number itself.

The negative of 0 does not exist.

The negative of 1 is 1 itself.

For all rational numbers x and y, x – y = y – x.

For all rational numbers x and y, (x) × (y) = (y) × (x)

For every rational number x, x × 0 = x.

For every rational numbers x, y and z, x + (y × z) = (x + y) × (x + z).

For all rational numbers a, b and c, a (b + c) = ab + bc.

1 is the only number which is its own reciprocal.

–1 is not the reciprocal of any rational number.

For any rational number x, x + (–1) = –x.

Rational numbers are closed under addition and multiplication but not under subtraction.

The population of India in 2004 – 05 is a rational number.

There are countless rational numbers between 5/6 and 8/9.

The rational number 57/23 lies to the left of zero on the number line.

-¾ is smaller than -2.

Subtraction of rational number is commutative.

If x and y are negative rational numbers, then so is x + y.

Between any two rational numbers there are exactly ten rational numbers.

0 is a rational number.

All positive rational numbers lie between 0 and 1000.

The reciprocal of x^-1 is 1/x.

The rational number 7/-4 is lies to the right side zero on the number line.

Every integer is a rational number.

The rational number -8/-3 lies neither to the right nor to the left of zero on the number line.

Simplify \frac{-3}{5} \times\left\{\frac{3}{7}+\left(\frac{-5}{6}\right)\right\} using suitable property .

The rational numbers ½ and –1 are on the opposite sides of zero on the number line.

Every fraction is a rational number.

The negative of a negative rational number is a positive rational number.

The rational numbers can be represented on the number line.

If x and y are two rational numbers such that x > y, then x – y is always a positive rational number.

0 is the smallest rational number

Every whole number is an integer.

0 is whole number but it is not a rational number.

Every whole number is a rational number.

Rational numbers can be added (or multiplied) in any order \frac{-4}{5}\times\frac{-6}{5}=\frac{-6}{5}\times\frac{-4}{5}

The rational numbers ½ and -5/2 are on the opposite sides of 0 on the number line.

Rational numbers follow x × y = y × z substituting x = \frac{2}{3} and y = \frac{9}{4}

Which of the following rational numbers from the list, are also the integers?

Which of the following can be written as a rational number with denominator 4 in their lowest form?

Add:

-5+\frac{7}{10}+\frac{3}{7}+(-3)+\frac{5}{14}+\frac{-4}{5}

Rational numbers follows x + y = y + x by taking x=-\frac{2}{5},\ y=-\frac{9}{10}

Add:

\frac{4}{7}+\left(\frac{-4}{9}\right)+\frac{3}{7}+\left(\frac{-13}{9}\right)

Rational numbers follows x + y = y + x by taking x=-\frac{3}{7},\ y=\frac{20}{21}

The rational numbers \frac{1}{2} , \frac{2}{3} are closed under addition, subtraction, and multiplication.

Rational numbers follows x + y = y + x by taking x=-\frac{2}{3},\ y=-\frac{5}{6}

Which property allows you to compute the following?

\frac{1}{5}\times\left[\frac{5}{6}\times\frac{7}{9}\right]as\left[\frac{1}{5}\times\frac{5}{6}\right]\times\frac{7}{9}

Rational numbers follows x × y = y × z by substituting x = 7 and y = ½

Rational numbers follows x × y = y × z substituting x=-\frac{3}{8}\ and\ y=-\frac{4}{9}.

Rational numbers follows x × y = y × z substituting x=-\frac{5}{7}\ and\ y=\frac{14}{15}

The property x ×y = y× x is followed by rational numbers in case of x = 0, y = 1/2

The property x × (y × z) = (x × y) × z is followed by rational numbers in case of x=-\frac{2}{7},\ y=-\frac{5}{6}\ and\ z=\frac{1}{4}.

The property x × (y × z) = (x × y) × z is followed by rational numbers in case of x=\frac{2}{3},\ y=-\frac{3}{7}\ and\ z=\frac{1}{2}.

The property x × (y × z) = (x × y) × z is followed by rational numbers in case of x = 1, y = -½ and z = ¼.

The property x × (y+ z) = x × y + x × z is followed by rational numbers in case of x=-\frac{1}{5},\ y=\frac{2}{15},\ z=-\frac{3}{10}

The property x × (y+ z) = x × y + x × z is followed by rational numbers in case of x = -2/3, y = -4/6, z = -7/9

The property x × (y+ z) = x × y + x × z is followed by rational numbers in case of x = -½, y = ¾, z = ¼

The property x × (y + z) = x × y + x × z is followed by rational numbers in case of x = -½, y = 2/3, z = ¾

Use the distributivity of multiplication of rational numbers over subtraction to simplify \frac{3}{4} \times\left[\frac{8}{9}-40\right]

Use the distributivity of multiplication of rational numbers over addition to simplify

\frac{-5}{4} \times\left[\frac{8}{5}+\frac{16}{15}\right]

Use the distributivity of multiplication of rational numbers over addition to simplify

\frac{3}{5}\times\left[\frac{35}{24}+\frac{10}{1}\right]

Simplify \frac{7}{8}+\frac{1}{16}-\frac{1}{12}

Simplify \frac{3}{7}+\frac{-2}{21} \times \frac{-5}{6}

Simplify \frac{32}{5}+\frac{23}{15}+\frac{23}{15}

Use the distributivity of multiplication of rational numbers over subtraction to simplify

\frac{2}{7} \times\left[\frac{7}{16}-\frac{21}{4}\right]

A 117\frac{1}{3} m long rope is cut into equal pieces measuring 7\frac{1}{3}m each. How many such small pieces are these?

Which property allows you to compare the following?

\frac{-2}{3}\times\left[\frac{3}{4}+\frac{-1}{4}\right]=\left[\frac{-2}{3}\times\frac{3}{4}\right]+\left[\frac{-2}{3}\times\frac{-1}{4}\right]

A train travels \frac{1445}{2} km in \frac{17}{2} hours. What is the speed of the train in km/h?

\frac{2}{5} of total number of students of a school come by car while \frac{1}{4} of students come by bus to school. All the other students walk to school of which \frac{1}{3} walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in that school?

The product of two rational numbers is –7. If one of the number is –5, which is the other?

\frac{1}{6} of the class students are above average, \frac{1}{4} are average and the rest are below average. If there are 48 students in all, how many students are below average in the class?

A mother and her two daughters got a room constructed for ₹ 62,000. The elder daughter contributes \frac{3}{8} of her mother’s contribution while the younger daughter contributes ½ of her mother’s share. How much is contribution of mother?

The product of two rational numbers is -\frac{14}{27} . If one of the numbers is \frac{7}{9} , which is the other rational number?

By which number should we multiply -\frac{8}{13} so that the product will be 24?

Which is the multiplicative inverse of -1\frac{1}{8}?

Which property allows you to compare the following?

\frac{3}{8}\times1=1\times\frac{3}{8}=\frac{3}{8}

Which property allows you to compare the following?

\frac{-2}{7}+0=0+\frac{-2}{7}=\frac{-2}{7}

Arrange the numbers \frac{1}{4},\frac{13}{16},\frac{5}{8} in the descending order.

Which rational number that does not belong with the other three?

The cost of \frac{19}{4} metres of wire is ₹ \frac{171}{2}. What is the cost of one metre of the wire?

By which number should we multiply -\frac{15}{20} so that the product will be -\frac{5}{7}?

Which is the rational number whose multiplicative inverse is –1?

From a rope 40 metres long, pieces of equal size are cut. If the length of one piece is \frac{10}{3} metre,what is the number of such pieces?

5½ metres long rope is cut into 12 equal pieces. What is the length of each piece?

Which is the rational number whose absolute value is \frac{1}{5}?

Arrange the following rational numbers in descending order.

\frac{8}{7},-\frac{9}{8},-\frac{3}{2},0,\frac{2}{5}

Select the correct option.

Which is a rational number between 0 and 1?

What is the value of 0 ÷ \frac{2}{3}?

What is the value of:

\frac{1}{3}\times\frac{-5}{7}\times\frac{-21}{10}=?

What is the product of additive inverse and multiplicative inverse of \frac{1}{3}?

The diagram shows the wingspans of different species of birds.

How much longer is the wingspan of a Golden eagle than the wingspan of a Blue jay?

What is the sum of additive inverse and multiplicative inverse of 7?

The table given below shows the distances, in kilometers, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect.

What is the difference in distance between them?

Shalini has to cut out circles of diameter 1¼ cm from an aluminum strip of dimensions 8¾ cm by 1¼ cm. What is the area of Aluminium strip?

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

How farther did Soni hop than Nancy?

One fruit salad recipe requires ½ cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to \frac{1}{16} cup, how much more sugar does the first recipe require?

The table shows the portion of some common materials that are recycled.

Is the rational number expressing the amount of paper recycled more than ½ or less than ½?

The diagram shows the wingspans of different species of birds.

How much longer is the wingspan of an Albatross than the wingspan of a Sea gull?

On a winter day the temperature at a place in Himachal Pradesh was –16°C. Convert it in degree Fahrenheit (°F) by using the formula and select the correct option:

\frac{C}{5}=\frac{F-32}{9}

The table given below shows the distances, in kilometers, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect.

If you drove from Himgaon to Sonapur and then from Sonapur to Rawalpur, how far would you drive?

The table shows the portion of some common materials that are recycled.

Arrange the rate of recycling the materials from the greatest to the smallest.

The table shows the portion of some common materials that are recycled.

Which items have a recycled amount less than ½?

The overall width in cm of several wide-screen televisions are 97.28\mathrm{\ cm},98\frac{4}{9}\mathrm{\ cm},\ 98\frac{1}{25}\mathrm{\ cm}\ and\ 97.94\ cm. **Express these numbers as rational numbers in the form p/q and arrange the widths in ascending order.**

Here is a table which gives the information about the total rainfall for June compared to the average monthly rains of a town. Write decimal form to rational form p/q and select the correct option.

Here is a table which gives the information about the total rainfall for July compared to the average monthly rains of a town. Write decimal form to rational form p/q and select the correct option.

Roller Coaster at an amusement park is \frac{2}{3} m high. If a new roller coaster is built that is \frac{3}{5} times the height of the existing coaster, what will be the height of the new roller coaster?

Express it in decimal in the form p/q.

Here is a table which gives the information about the total rainfall for May compared to the average monthly rains of a town. Write decimal form to rational form p/q and select correct option.

Express it in decimal in the form p/q.

Express it in decimal in the form p/q.

The average life expectancies of males for several states are shown in the table. Express each decimal in the form p/q and arrange the states from the least to the greatest male life expectancy.

Here is a table which gives the information about the total rainfall for August compared to the average monthly rains of a town. Write decimal form to rational form p/q and select the correct option.

Manavi receives an allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If the allowance of each is ₹ 1260, what is the amount left with each?

Simplify \frac{3}{7} \times \frac{28}{15} \div \frac{14}{5}

If 16 shirts of equal size can be made out of 24 m of cloth, how much cloth is needed for making one shirt?

\frac{7}{11} of all the money in Hamid’s bank account is ₹ 77,000. How much money does Hamid have in his bank account?

If 16 shirts of equal size can be made out of 24 m of cloth, how much cloth is needed for making three shirts?

The cost of \frac{19}{4} metres of wire is ₹ \frac{171}{2}. What is the cost of three metre of the wire?

Manavi receives an allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If allowance of each is ₹ 1260, what is the amount left with each?

Shalini has to cut out circles of diameter 1¼ cm from an aluminum strip of dimensions 8¾ cm by 1¼ cm. Calculate the wastage of the aluminum strip and select the correct option.

– (-x) = x for x =\frac{3}{5}

The equivalent of \frac{5}{7} , whose numerator is 45 is _______ .

For rational numbers x and y, if x < y then x – y is a positive rational number.

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

What is the total distance covered by Seema and Megha?

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

Who hopped farthest?

A skirt that is 35\frac{7}{8} cm long has a hem of 3\frac{1}{8}cm. How long will the skirt be if the hem is let down?

A number of the form \frac{p}{q} is said to be a rational number if _____

Which of the following is not true?

\left(-\frac{3}{8}\right)+\left(\frac{1}{7}\right)=\left(\frac{1}{7}\right)+\left(-\frac{3}{8}\right) is an example to show that _______

One is _________.

The additive inverse of -\frac{7}{19} is _____

The reciprocal of 0 is _______.

Which of the following is an example of distributive property of multiplication over addition for rational numbers?

– (-x) = x for x = –\frac{7}{9}

Simplify \left[\frac{1}{2}\times\frac{2}{5}\right]-\left[\frac{1}{2}\times\frac{2}{15}\right] using suitable property .

Simplify \left[\frac{1}{2}\times\frac{1}{4}\right]+\left[\frac{1}{2}\times6\right] using suitable property .

– (-x) = x for x =\frac{13}{-15}

Which property allows you to compare the following?

\frac{2}{3}\times\left[\frac{3}{4}\times\frac{5}{7}\right]\text{ and }\left[\frac{2}{3}\times\frac{5}{7}\right]\times\frac{3}{4}

Which property allows you to compare the following?

-\frac{7}{11}\times\frac{-3}{5}=\frac{-3}{5}\times\frac{-7}{11}

Which property allows you to compare the following?

\frac{1}{3}+\left[\frac{4}{9}+\left(\frac{-4}{3}\right)\right]=\left[\frac{1}{3}+\frac{4}{9}\right]+\left[\frac{-4}{3}\right]

Which is the multiplicative inverse of 3\frac{1}{3}?

If x + 0 = 0 + x = x, which is rational number, then 0 is called ________.

Which of the following expressions shows that rational numbers are associative under multiplication?

The numerical expression \frac{3}{8}+(-\frac{5}{7})=(-\frac{19}{56}) shows that _____.

A number which can be expressed as \frac{p}{q}, where p and q are integers and q≠0 is __________.

The equivalent rational number of \frac{7}{9} , whose denominator is 45 is ______.

The reciprocal of any rational number \frac{p}{q} , where p and q are integers and q ≠ 0, is ________

-\frac{5}{7} is _______ than -3.

– (-x) is same as _________.

If x be any rational number then x + 0 is equal to ___________.

The multiplicative inverse of -1\ \frac{1}{7} is ______

Multiplicative inverse of a negative rational number is _______

The reciprocal of 1 is _______.

The reciprocal of -1 is ______.

If y be the reciprocal of rational number x, then the reciprocal of y will be ______.

Between two given rational numbers, we can find ______.

(213\times657)^{-1}=213^{-1}\times___

\frac{(x+y)}{2} is a rational number ____.

If y be the reciprocal of x, then the reciprocal of y² in terms of x will be _____________ .

Between the numbers \frac{15}{20} and \frac{35}{40}, the greater number is _________.

Which of the following statements is always true?

The reciprocal of** \frac{2\times\left(-4\right)}{5\times9} is ___________ .

The numbers ________ and ________ are their own reciprocal.

The reciprocal of a positive rational number is _________ .

The reciprocal of a negative rational number is _________ .

Zero has ________ reciprocal.

The negative of 1 is _______ .

Zero (0) is ______

For rational numbers \frac{a}{b} , \frac{c}{d} and \frac{e}{f} we have \frac{a}{b} × (\frac{c}{d} + \frac{e}{f} )

= _______ + _______

A number which can be expressed as p/q where p and q are integers and q≠0 is

(a) natural number.

(b) whole number.

(c) integer.

(d) rational number.

A number of the form p/q is said to be a rational number if

(a) p and q are integers.

(b) p and q are integers and q ≠ 0

(c) p and q are integers and p ≠ 0

(d) p and q are integers and p ≠ 0 also q ≠ 0

The numerical expression (3/8) + (-5/7) = (-19/56) shows that

(a) rational numbers are closed under addition.

(b) rational numbers are not closed under addition.

(c) rational numbers are closed under multiplication.

(d) addition of rational numbers is not commutative.

Which of the following is not true?

(a) rational numbers are closed under addition.

(b) rational numbers are closed under subtraction.

(c) rational numbers are closed under multiplication.

(d) rational numbers are closed under division.

(-3/8) + (1/7) = (1/7) + (-3/8) is an example to show that

(a) addition of rational numbers is commutative.

(b) rational numbers are closed under addition.

(c) addition of rational number is associative.

(d) rational numbers are distributive under addition.

Which of the following expressions shows that rational numbers are associative under multiplication.

(a) [(2/3) × ((-6/7) × (3/5))] = [((2/3) × (-6/7)) × (3/5)]

(b) [(2/3) × ((-6/7) × (3/5))] = [(2/3) × ((3/5) × (-6/7))]

(c) [(2/3) × ((-6/7) × (3/5))] = [((3/5) × (2/3)) × (-6/7)]

Zero (0) is

(a) the identity for the addition of rational numbers.

(b) the identity for the subtraction of rational numbers.

(c) the identity for the multiplication of rational numbers.

(d) the identity for the division of rational numbers.

One (1) is

(a) the identity for the addition of rational numbers.

(b) the identity for the subtraction of rational numbers.

(c) the identity for the multiplication of rational numbers.

(d) the identity for the division of rational numbers.

The additive inverse of -7/19 is

(a) -7/19

(b) 7/19

(c) 19/7

(d) -19/7

Multiplicative inverse of a negative rational number is

(a) a positive rational number.

(b) a negative rational number.

(c) 0

(d) 1

If x + 0 = 0 + x = x, which is rational number, then 0 is called

(a) identity for the addition of rational numbers.

(b) additive inverse of x.

(c) multiplicative inverse of x.

(d) reciprocal of x.

To get the product 1, we should multiply (8/21) by

(a) 8/21

(b) -8/21

(c) 21/8

(d) -21/8

– (-x) is same as

(a) –x

(b) x

(c) 1/x

(d) -1/x

The multiplicative inverse of is

(a) 8/7 (b) -8/7 (c) 7/8 (d) 7/-8

If x be any rational number then x + 0 is equal to

(a) x

(b) 0

(c) –x

(d) Not defined

The reciprocal of 1 is

(a) 1 (b) -1 (c) 0 (d) Not defined

The reciprocal of -1 is

(a) 1 (b) -1 (c) 0 (d) Not defined

The reciprocal of 0 is

(a) 1 (b) -1 (c) 0 (d) Not defined

The reciprocal of any rational number p/q, where p and q are integers and q ≠ 0, is

(a) p/q (b) 1 (c) 0 (d) q/p

If y be the reciprocal of rational number x, then the reciprocal of y will be

(a) x (b) y (c) x/y (d) y/x

The reciprocal of (-3/8) × (-7/13) is

(a) 104/21 (b) -104/21 (c) 21/104 (d) -21/104

Which of the following is an example of distributive property of multiplication over addition for rational numbers.

(a) – (1/4) × {(2/3) + (-4/7)} = [-(1/4) × (2/3)] + [(-1/4) × (-4/7)]

(b) – (1/4) × {(2/3) + (-4/7)} = [(1/4) × (2/3)] – (-4/7)

(c) – (1/4) × {(2/3) + (-4/7)} = (2/3) + (-1/4) × (-4/7)

(d) – (1/4) × {(2/3) + (-4/7)} = {(2/3) + (-4/7)} – (1/4)

Between two given rational numbers, we can find

(a) one and only one rational number.

(b) only two rational numbers.

(c) only ten rational numbers.

(d) infinitely many rational numbers.

(x + y)/2 is a rational number

(a) Between x and y

(b) Less than x and y both.

(c) Greater than x and y both.

(d) Less than x but greater than y

Which of the following statements is always true?

(a) (x – y)/2 is a rational number between x and y.

(b) (x + y)/2 is a rational number between x and y.

(c) (x × y)/2 is a rational number between x and y.

(d) (x ÷ y)/2 is a rational number between x and y.

The equivalent of 5/7, whose numerator is 45 is___ .

The equivalent rational number of 7/9, whose denominator is 45 is_ .

Between the numbers (15/20) and (35/40), the greater number is__ .

The reciprocal of a positive rational number is___ .

The reciprocal of a negative rational number is__ .

Zero has____ reciprocal.

The numbers____ and__ are their own reciprocal.

If y be the reciprocal of x, then the reciprocal of y^2 in terms of x will be___ .

The reciprocal of (2/5) × (-4/9) is____ .

\left(213\times657\right)^{-1}=213^{-1}\times—

The negative of 1 is _____.

For rational numbers (a/b), (c/d) and (e/f) we have (a/b) × ((c/d) + (e/f)) =__ +___

-5/7 is___ than -3.

There are _________ rational numbers between any two rational numbers.

The rational numbers 1/3 and -1/3 are on the ________ sides of zero on the number line.

The negative of a negative rational number is always a ________ rational number.

Rational numbers can be added or multiplied in any _________ .

The reciprocal of -5/7 is ________ .

The multiplicative inverse of 4/3 is ________ .

The rational number 10.11 in the from p/q is ______ .

(1/5) × [(2/7) + (3/8)] = [(1/5) × (2/7)] + _____________ .

The two rational numbers lying between –2 and –5 with denominator as 1 are _________ and _________.

If x/y is a rational number, then y is always a whole number.

If p/q is a rational number, then p cannot be equal to zero.

If r/s is a rational number, then s cannot be equal to zero.

5/6 lies between 2/3 and 1.

5/10 lies between ½ and 1.

-7/2 lies between -3 and -4.

9/6 lies between 1 and 2.

If a ≠ 0, the multiplicative inverse of a/b is b/a.

The multiplicative inverse of -3/5 is 5/3

The additive inverse of ½ is -2.

If x/y is the additive inverse of c/d, then (x/y) + (c/d) = 0

For every rational number x, x + 1 = x.

If x/y is the additive inverse of c/d, then, (x/y) – (c/d) = 0

The reciprocal of a non-zero rational number q/p is the rational number q/p.

If x + y = 0, then –y is known as the negative of x, where x and y are rational.

The negative of the negative of any rational number is the number itself.

The negative of 0 does not exist.

The negative of 1 is 1 itself.

For all rational numbers x and y, x – y = y – x.

For all rational numbers x and y, (x) × (y) = (y) × (x)

For every rational number x, x × 0 = x.

For every rational numbers x, y and z, x + (y × z) = (x + y) × (x + z).

For all rational numbers a, b and c, a (b + c) = ab + bc.

1 is the only number which is its own reciprocal.

–1 is not the reciprocal of any rational number.

For any rational number x, x + (–1) = –x.

For rational numbers x and y, if x < y then x – y is a positive rational number.

If x and y are negative rational numbers, then so is x + y.

Between any two rational numbers there are exactly ten rational numbers.

Rational numbers are closed under addition and multiplication but not under subtraction.

Subtraction of rational number is commutative.

-¾ is smaller than -2.

0 is a rational number.

All positive rational numbers lie between 0 and 1000.

The population of India in 2004 – 05 is a rational number.

There are countless rational numbers between 5/6 and 8/9.

The reciprocal of x^-1 is 1/x.

The rational number 57/23 lies to the left of zero on the number line.

The rational number 7/-4 is lies to the right side zero on the number line.

The rational number -8/-3 lies neither to the right nor to the left of zero on the number line.

The rational numbers ½ and –1 are on the opposite sides of zero on the number line.

Every fraction is a rational number.

Every integer is a rational number.

The rational numbers can be represented on the number line.

The negative of a negative rational number is a positive rational number.

If x and y are two rational numbers such that x > y, then x – y is always a positive rational number.

0 is the smallest rational number

Every whole number is an integer.

Every whole number is a rational number.

0 is whole number but it is not a rational number.

The rational numbers ½ and -5/2 are on the opposite sides of 0 on the number line.

Rational numbers can be added (or multiplied) in any order

(-4/5) × (-6/5) = (-6/5) × (-4/5)

Solve the following: Select the rational numbers from the list which are also the integers.

9/4, 8/4, 7/4, 6/4, 9/3, 8/3, 7/3, 6/3, 5/2, 4/2, 3/1, 3/2, 1/1, 0/1, -1/1, -2/1, -3/2, -4/2, -5/2, -6/2

Select those which can be written as a rational number with denominator 4 in their lowest form:

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

Using suitable rearrangement, find the sum:

(a) (4/7) + (-4/9) + (3/7) + (-13/9)

(b) -5 + (7/10) + (3/7) + (-3) + (5/45) + (-4/5)

Verify – (-x) = x for

(i) x = 3/5

(ii) x = -7/9

(iii) x = 13/-15

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Verify the property x + y = y + x of rational numbers by taking

(a) x = ½, y = ½

(b) x = -2/3, y = -5/6

(c) x = -3/7, y = 20/21

(d) x = -2/5, y = – 9/10

Simplify each of the following by using suitable property. Also name the

property.

(a) [(½) × (¼)] + [(½) × 6]

(b) [(1/5) × (2/15)] – [(1/5) × (2/5)]

(c) (-3/5) × {(3/7) + (-5/6)}

Tell which property allows you to compute

(1/5) × [(5/6) × (7/9)] as [(1/5) × (5/6)] × (7/9)

Verify the property x × y = y × z of rational numbers by using

(a) x = 7 and y = ½

(b) x = 2/3 and y = 9/4

(c) x = -5/7 and y = 14/15

(d) x = -3/8 and y = -4/9

Verify the property x × (y × z) = (x × y) × z of rational numbers by using

(a) x = 1, y = -½ and z = ¼

(b) x = 2/3, y = -3/7 and z = ½

(c) x = -2/7, y = -5/6 and z = ¼

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.

(a) x = -½, y = ¾, z = ¼

(b) x = -½, y = 2/3, z = ¾

(c) x = -2/3, y = -4/6, z = -7/9

(d) x = -1/5, y = 2/15, z = -3/10

Use the distributivity of multiplication of rational numbers over addition to simplify.

(a) (3/5) × [(35/24) + (10/1)]

(b) (-5/4) × [(8/5) + (16/15)]

(c) (2/7) × [(7/16) – (21/4)]

Simplify

(a) (32/5) + (23/11) × (22/15)

(b) (3/7) × (28/15) ÷ (14/5)

(c) (3/7) + (-2/21) × (-5/6)

(d) (7/8) + (1/6) – (1/12)

Identify the rational number that does not belong with the other three. Explain your reasoning (-5/11), (-1/2), (-4/9), (-7/3)

The cost of 19/4 metres of wire is ₹ 171/2. Find the cost of one metre of the wire.

A train travels 1445/2 km in 17/2 hours. Find the speed of the train in km/h.

If 16 shirts of equal size can be made out of 24m of cloth, how much cloth is needed for making one shirt?

7/11th of all the money in Hamid’s bank account is ₹ 77,000. How much money does Hamid have in his bank account?

A 1171/3m long rope is cut into equal pieces measuring 71/3m each. How many such small pieces are these?

1/6 of the class students are above average, ¼ are average and rest are below average. If there are 48 students in all, how many students are below average in the class?

2/5 of total number of students of a school come by car while ¼ of students come by bus to school. All the other students walk to school of which 1/3 walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in that school?

Huma, Hubna and Seema received a total of ₹ 2,016 as monthly allowance from their mother such that Seema gets ½ of what Huma gets and Hubna gets times Seema’s share. How much money do the three sisters get individually?

A mother and her two daughters got a room constructed for ₹ 62,000. The elder daughter contributes 3/8 of her mother’s contribution while the younger daughter contributes ½ of her mother’s share. How much do the three contribute individually?

Tell which property allows you to compare

(2/3) × [¾ × (5/7)] and [(2/3) × (5/7)] × ¾

Name the property used in each of the following.

(i) (-7/4) × (-3/4) = (-3/5) × (-7/11)

(ii) (-2/3) × [(3/4) + (-½)] = [(-2/3) × (3/4)] + [(-2/3) × (½)]

(iii) (1/3) + [(4/9) + (-4/3)] = [(1/3) + (4/9)] + [-4/3]

(iv) (-2/7) + 0 = 0 + (-2/7) = (-2/7)

(v) (3/8) × 1 = 1 × (3/8) = (3/8)

Find the multiplicative inverse of

(i)-1*1/8

(ii)3*1/3

Arrange the numbers ¼, 13/16, 5/8 in the descending order.

The product of two rational numbers is -14/27. If one of the numbers be 7/9, find the other.

By what numbers should we multiply -15/20 so that the product may be -5/7?

By what number should we multiply -8/13 so that the product may be 24?

The product of two rational numbers is –7. If one of the number is –5, find the other?

Can you find a rational number whose multiplicative inverse is –1?

Find five rational numbers between 0 and 1.

Find two rational numbers whose absolute value is 1/5.

From a rope 40 metres long, pieces of equal size are cut. If the length of one piece is 10/3 metre, find the number of such pieces.

5½ metres long rope is cut into 12 equal pieces. What is the length of each piece?

Write the following rational numbers in the descending order.

(8/7), (-9/8), (-3/2), 0, (2/5)

Find (i) 0 ÷ (2/3)

On a winter day the temperature at a place in Himachal Pradesh was –16°C.

Convert it in degree Fahrenheit (oF) by using the formula.

(C/5) = (F – 32)/9

Find the sum of additive inverse and multiplicative inverse of 7.

Find the product of additive inverse and multiplicative inverse of 1/3.

The diagram shows the wingspans of different species of birds. Use the diagram to answer the question given below:

(a) How much longer is the wingspan of an Albatross than the wingspan of a Sea gull?

Shalini has to cut out circles of diameter 1¼ cm from an aluminum strip of dimensions 8¾ cm by 1¼ cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminum strip.

One fruit salad recipe requires ½ cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to 1/16 cup, how much more sugar does the first recipe require?

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

(a) How further did Soni hop than Nancy?

(b) What is the total distance covered by Seema and Megha?

(c) Who walked further, Nancy or Megha?

The table given below shows the distances, in kilometres, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect.

(a) Compare the distance between Himgaon and Rawalpur to Sonapur and Ramgarh?

(b) If you drove from Himgaon to Sonapur and then from Sonapur to Rawalpur, how far would you drive?

The table shows the portion of some common materials that are recycled.

(a) Is the rational number expressing the amount of paper recycled more than ½ or less than ½?

(b) Which items have a recycled amount less than ½?

(c) Is the quantity of aluminium cans recycled more (or less) than half of the number of aluminium cans?

(d) Arrange the rate of recycling the materials from the greatest to the smallest.

The overall width in cm of several wide-screen televisions are 97.28 cm, 98*4/9 cm,

98*1/25cm and 97.94 cm. Express these numbers as rational numbers in the form p/q

and arrange the widths in ascending order.

Roller Coaster at an amusement park is 2/3m high. If a new roller coaster is built that is 3/5 times the height of the existing coaster, what will be the height of the new roller coaster?

Here is a table which gives information about the total rainfall for several months compared to the average monthly rains of a town. Write each decimal in the form of rational number p/q.

The average life expectancies of males for several states are shown in the table. Express each decimal in the form p/q and arrange the states from the least to the greatest male life expectancy. State-wise data are included below; more indicators can be found in the “FACTFILE” section on the homepage for each state.

A skirt that is 357/8 cm long has a hem of 31/8 cm. How long will the skirt be if the hem is let down?

Manavi and Kuber each receives an equal allowance. The table shows the fraction of their allowance each deposit into his/her saving account and the fraction each spends at the mall. If the allowance of each is ₹ 1260 find the amount left with each.