Explore topic-wise InterviewSolutions in .

Rational number between – 1 and 2

= (-1+2)/2 = 1/2

∵ Middle rational number = (a + b)/2

∴ -1 < 1/2< 2.

(i) False 

(ii) True 

(iii) True 

(iv) False 

(v) False

True.

Let x = 4, y = 2

Then,

= x – y

= 4 – 2

= 2

\(\frac{8}{-15}=\frac{8\times-1}{-15\times-1}=\frac{-8}{15}\)

And,

\(\frac{4}{-3}=\frac{4\times-1}{-3\times-1}=\frac{-4}{3}\)

\(\Rightarrow\) \(\frac{8}{-15}+\frac{4}{-3}=\frac{-8}{15}+\frac{-4}{3}\)

\(\Rightarrow\) \(\frac{-8\times3+(-4)\times15}{45}\)

\(\Rightarrow\) \(\frac{-24-60}{45}\)

\(=\frac{-84}{45}=\frac{-84\div3}{45\div3}=\frac{-28}{15}\)

\(3=\frac{3}{1}\)

\(\frac{5}{-7}=\frac{5\times-1}{-7\times-1}=\frac{-5}{7}\)

\(\Rightarrow\) \(3+\frac{5}{-7}=\frac{3}{1}+\frac{-5}{7}\)

\(=\frac{3\times7+(-5)\times1}{7}\)

\(=\frac{21-5}{7}\)

\(=\frac{16}{7}\)

Multiplicative inverse of given number are 1/3, 5, 7/-3, 3/2, 6/-5.

False.

Negative rational number below 0 is infinite. So, the smallest rational number does not exist.

\(\frac{7}{-26}=\frac{7\times-1}{-26\times-1}=\frac{-7}{26}\)

\(\Rightarrow\) \(\frac{7}{-26}+\frac{16}{39}=\frac{-7}{26}+\frac{16}{39}\)

\(=\frac{-7\times3+16\times2}{78}\)

\(=\frac{-21+32}{78}\)

\(=\frac{11}{78}\)

True

Additive Inverse of -7/19 is 7/19.

Additive inverse of a/b is -a/b.

False

e.g. -7/8 is a rational number, but it is not a whole number, because whole numbers are  0,1,2….

True.

Every whole number is an integer but, every integer is not whole number.

Let the required number be x. Then,

= x × (-8/15) = 24

= (x) = 24 ÷ (-8/15)

= x = (24/1) × (15/-8)

= x = (24 ×15)/ (1 ×-8)

= x = (3 × 15) / (1 × -1)

= x = -45

Then,

x = -45

(i) Additive inverse of -1/3 is 1/3

(ii) Additive inverse of 7/2 is -7/2

(iii) Additive inverse of is 7/2 is -7/2

(iv) Additive inverse of is -3/5 is 3/5

(v) Additive inverse of is 9/2 is -9/2

3/8 x 1 = 1 x 3/8 = 3/8

order

Rational numbers can be added or multiplied in any order and this concept is known as commutative property.

Let x be multiplied by \(\frac{-8}{39}\) to get \(\frac{1}{26}\)

It can be written as,

\(\frac{-8}{39}\times\) \(\text{x}=\frac{1}{26}\)

\(\Rightarrow\) \(\text{x}=\frac{1}{26}\div\frac{1}{26}\) 

\(\Rightarrow\) \(\text{x}=\frac{1}{26}\times\frac{39}{-8}\)

\(\Rightarrow\) \(\text{x}= \frac{1\times39}{26\times-8}\)

\(\Rightarrow\) \(\text{x}=\frac{39}{-208}=\frac{39\times-1}{-208\times-1}=\frac{-39}{208}\)

\(\Rightarrow\) \(\text{x}=\frac{-39}{208}=\frac{-39\div13}{208\div13}=\frac{-3}{16}\)

Hence, 

it should be multiplied by is \(\frac{-3}{16}\)

True

Every whole number can be written in the form of -p/q, where p, q are integers and q ≠ 0 .

Hence, every whole number is a rational number.

Rational numbers are closed under subtraction.

True.

The arrangements of given rational number is as per the commutative law under multiplication. i.e. a × b = b × c

The rational number zero is the additive identity for rational numbers.

(i) reciprocal 

(ii) left 

(iii) right 

(iv) zero 

(v) one.

False

0 is a whole number and also a rational number.

(-5/2)× (-2/5) = 1

Let u assume the missing rational number be y.

Then,

y × (-2/5) = 1

y = -5/2

True.

½ is positive rational number so it is lies to the right side of 0 on the number line.

-5/2 is negative rational number so it is lies to the left side of 0 on the number line.

Between any two rational numbers there are infinite rational numbers.

The standard form of rational number –1 is -1.

A rational number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

If p and q are positive integers, then p/q is a positive rational number and – p/q is a negative rational number.

As we know that, When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number.

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

True.

½ is positive rational number so it is lies to the right side of 0 on the number line.

-1 is negative rational number so it is lies to the left side of 0 on the number line.

False.

We know that, a fraction is not changed whether the both numerator and denominator are multiplied by the same number or divided by the same number.

True.

A fraction is not changed whether the both numerator and denominator are multiplied by the same number or divided by the same number.

True.

A fraction is not changed whether the both numerator and denominator are multiplied by the same number or divided by the same number.

False

Because all the integers are rational numbers, whether it is negative/positive but vice-versa is not true.

True.

In integer denominator remain 1. So, every integer is a rational number.

True.

6/3 is an integer. Since if we simplify 6/3 to its lowest term we get 2/1 = 2, which is an integer.

True

e.g. 1/2 is a rational number, but not a natural number.

I would not agree with Hamid’s argument. Since 5/3  is a rational number. But ‘5’ is not only a natural number, it is also a rational number. Since every natural number is a rational number, 

According to Shikha’s opinion 5/3 , 5 are rational numbers. 

∴ I agree with Shikha’s opinion.

From the question it is given that,

7/11 of all the money in Hamid’s bank account = ₹ 77,000

Now, let us assume money in Hamid’s bank account be ₹ y.

Then,

= (7/11) × (x) = 77,000

x = 77,000/ (7/11)

x = 77000 × (11/7)

x = 11000 × (11/1)

x = 121000

∴The total money in Hamid’s bank account is ₹ 121000.

From the question it is given that,

The length of the rope =  117 1/3 m

= (117 × 3 + 1)/3

= 352/3 m

Then length of each piece measures = 7 1/3 m

= 22/3 m

So, the number of pieces of the rope = total length of the rope/ length of each piece

= (352/3)/ (22/3)

= (352/3) × (3/22)

= (16/1) × (1/1)

= 16

Hence, number of small pieces cut from the 117 1/3 m long rope is 16.

Sum of two rational numbers = \(\frac{-1}{2}\)

One number = \(\frac{5}{6}\)

Let the other rational number = x

Now,

According to question,

\(\frac{5}{6}\)+ x = \(\frac{-1}{2}\)

\(\Rightarrow\) x = \(\frac{-1}{2}-\frac{5}{6}\) 

\(\Rightarrow\) x \(=\frac{-3-5}{6}\)

\(\Rightarrow\) x = \(\frac{-8}{6}\)

In lowest terms,

x \(=\frac{-8÷2}{6÷2}= \frac{-4}{3}\)

Therefore, the other rational number is \(\frac{-4}{3}\)

Sum of two rational numbers = -2

One number = \(\frac{-14}{5}\)

Let the other rational number = x

Now,

\(\frac{-14}{5}+ \) x = \(-2\)

\(\Rightarrow\) x = \(-2-\frac{-14}{5}\)

\(\Rightarrow\) x \(=\frac{-10-(-14)}{5}\) 

\(\Rightarrow\) x \(=\frac{-10+14}{5}\) 

\(\Rightarrow\) x \(=\frac{4}{5}\)

Therefore, the other rational number is \(\frac{4}{5}\)

Sum of two rational numbers = \(\frac{-1}{2}\)

One number = \(\frac{5}{6}\)

Let the other rational number = x

Now,

According to question,

\(\frac{5}{6}+\) x \(=\frac{-1}{2}\) 

\(\Rightarrow\) x \(=\frac{-1}{2}-\frac{5}{6}\)

\(\Rightarrow\) x \(= \frac{-3-5}{6}\)

\(\Rightarrow\) x \(=\frac{-8}{6}\)

In lowest terms,

x \(= \frac{-8÷2}{6÷2}= \frac{-4}{3}\)

Therefore, the other rational number is \(\frac{-4}{3}\)

Length of rope = 11 m 

Length of first piece cut = \(2\frac{3}{5}\) m

Length of second piece cut = \(3\frac{3}{10}\) m

Total length cut = Length of first piece cut + Length of second piece cut

= \(2\frac{3}{5}\)m + \(3\frac{3}{10}\)m

= \(\frac{13}{5}\)m + \(\frac{33}{10}\)m

= \(\frac{26+33}{10}\)m

= \(\frac{59}{10}\)m

Length of remaining rope = Length of rope - Total length cut

= 11m - \(\frac{59}{10}\)m

= \(\frac{110-59}{10}\)m

= \(\frac{51}{10}\)m

= \(5\frac{1}{10}\)m

Hence, 

Length of remaining rope \(5\frac{1}{10}\)m

Weight of drum full of rice = \(40 \frac{1}{6}\) kg

Weight of empty drum \(=13\frac{3}{4}\)kg

Weight of rice Weight of drum full of rice - Weight of empty drum

 \(=40\frac{1}{6}\)kg - \(13\frac{3}{4}\)kg

\(=\frac{241}{6}\)kg - \(\frac{55}{4}\)kg

\(=\frac{482-165}{12}\)kg

\(=\frac{317}{12}\)kg

\(=26\frac{5}{12}\)kg

Hence, 

Weight of rice \(=26\frac{5}{12}\)kg

(i) 0 

(ii) 1 and -1 

(iii) 0 

\(\frac{10}{1}\), \(\frac{9}{2}\), \(\frac{8}{3}\), \(\frac{7}{4}\), \(\frac{6}{5}\), \(\frac{5}{6}\), \(\frac{4}{7}\), \(\frac{3}{8}\), \(\frac{2}{9}\), \(\frac{1}{10}\)

(i) m + 6 = 8

m = 8 – 6

(ii) m + 25 = 15

m =15 – 25 

m = -10

(iii) m – 40 = -26

m = – 26 + 40 

m = 14

(iv) m + 28 = – 49

m = – 49 – 28 

m = – 77

\(\frac{3}{-2}\) is a rational number because the denominator is negative. 

It can be written as \(\frac{3}{-2}\) since \(\frac{3}{-2}\) is same as \(\frac{3}{-2}\)