Identities of Mathematical Operations

Q.

Rational numbers are not closed under which operation?

1. multiplication

2. division

3. subtraction

4. addition

Q. Why is rational number not closed under division

Q.

Which number is its own reciprocal?

Q.

The reciprocal of a negative rational number is ___________.

Q. What is additive inverse and multiplicative inverse of 5/7 & -5/7

Q.

Question 7
Zero (0) is:
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.

Q.

Question 11
If x + 0 = 0 + x = x, which is rational number, then 0 is called:
(a) identity for addition of rational numbers.
(b) additive inverse of x.
(c) multiplicative inverse of x.
(d) reciprocal of x.

Q.

What is the opposite and reciprocal of $\frac{1}{3}$?

Q.

Sequence of reciprocals of natural numbers.

Q.

Question 8
One(1) is:
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.

Q.

Multiplicative and additive identities for rational numbers are respectively

1. $0and1$

2. $1and0$

3. $0and-1$

4. $-1and0$

Q.

When an integer is divided by itself then the quotient _________

Q.

^{_{Name the property involved in the following example: 8/5+0=8/5=0+8/5}}

Q.

How do you find the additive and multiplicative inverse of $\left(-\frac{8}{3}\right)$?

Q.

Right additive inverse of-1/2and3/4 and also write multiplicative inverse of the sum

Q.

$\left(a\right)$ What is the additive inverse of $0$?

$\left(b\right)$ What is the multiplicative inverse of $1$?

$\left(c\right)$ Which integers have their own multiplicative inverses?

Q.

Multiply $\frac{7}{18}$ to the reciprocal of $\left(\frac{-5}{13}\right)$. [2 MARKS]

Q.

The reciprocal of a negative rational number is

1. a positive rational number

2. a negative rational number

3. cannot be determined

4. can be either a positive or a negative rational number

Q.

What is additive and multiplicative inverse l

Q. Question 124(iv)
Name the property used here:

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

Q.

Question 7
Zero (0) is:
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.

Q.

If a, b, c are rational numbers such that a² + b² + c² − ab − bc − ca = 0, prove that a = b = c.

Q.

Which of the following property(s) for division of Rational numbers do not exist?

1. Identity

2. Closure

3. Inverse

4. none of these

Q.

a^-m is the ______ inverse of a^m.

1. distributive

2. additive

3. commutative

4. multiplicative

Q.

For positive integers, multiplicative identity is $1$ and for negative integers, multiplicative identity is $-1$

1. True
2. False

Q. Question 124(iv)
Name the property used here:

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

Q. a. Write additive inverse of $\frac{2}{8}and\frac{-6}{-5}$
b. Write multiplicative inverse of $-13and\frac{-13}{19}$

Q. Question 77
Rational numbers are closed under addition and multiplication but not under subtraction.

Q.

Which of the following rational number does not have a reciprocal.

1. $1$

2. $-1$

3. $0$

4. none of the above

Q.

Which of the following is the multiplicative identity for an integer $a$?

1. $a$

2. $1$

3. $0$

4. $-1$