Properties of Multiplication of Integers

Q.

If $p$ and $q$ are simple propositions, then $p\iff ~q$ is true when

1. $p$is true and $q$is true

2. Both $p$ and $q$ are false

3. $p$is false and $q$is true

4. None of these

Q.

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

1. identity for addition of rational numbers

2. additive inverse of $x$

3. multiplicative inverse of $x$

4. reciprocal of $x$

Q.

How do you combine real and imaginary numbers?

Q.

For every integer $a$, $a\times 1=1\times a=a$.
This shows

1. associative property

2. distributive property

3. existence of multiplicative inverse

4. existence of multiplicative identity

Q.

Using distributive property of multiplication over addition, simplify:
$397\times 27+397\times 13$

Q.

Question 88

State whether the statement is True or False.

Product of two negative integers is a negative integer.

Q.

From these two statements, what logic can be drawn for the multiplicative identity of integers?

Statement $1$: $0$ is the additive identity for integers.

Statement $2$: Any integer added to zero results in the integer itself.

1. Any integer multiplied to it will give $0$ as the result

2. Any integer multiplied to it will give $1$ as the result

3. No logic can be drawn

4. Any integer multiplied to it will give the same integer as the result

Q.

Question 90

State whether the statement is True or False.

Product of a negative integer and a positive integer is a positive integer.

Q. Find the values of following determinants.

(1) $\left|\begin{array}{cc}-1& 7\\ 2& 4\end{array}\right|$


(2) $\left|\begin{array}{cc}5& 3\\ -7& 0\end{array}\right|$

(3) $\left|\begin{array}{cc}\frac{7}{3}& \frac{5}{3}\\ \frac{3}{2}& \frac{1}{2}\end{array}\right|$

Q.

$(-3)\times (-2)\times \left(5\right)\times (-6)\times (-1)\times 1=$

1. $180$

2. $-180$

3. $120$

4. $-120$

Q. 7 If the sum of all positive rational numbers n such that n +84n+1941 is an integer is 189/k, then find k.

Q.

The sum of the reciprocal of Rehman's age (in years) $3$ years ago and $5$ years from now is $\frac{1}{3}$. Find his present age.

Q. 26.If (3a-8)x2 +ax + 10 and x belongs to real numbers then a belongs to

Q. Find value of a and b such that: 5+√3/7+2√3=a-b√3

Q.

Using distributive property of multiplication over addition, simplify: $74\times 231+74\times 269$

Q.

Name the property represented by

$72\times (48+2)=72\times 48+72\times 2$