Properties of Multiplication of Integers

Q.

Question 4(d)

Find the product using suitable properties:

$1005\times 168$

Q.

Natural numbers are not closed under multiplication.

1. True
2. False

Q.

Find the products using suitable rearrangements.

$625\times 20\times 50\times 8$.

Q.

If$a\ne 0,$the multiplicative inverse of $\frac{a}{b}$is $\frac{b}{a}$. State whether the statement is true (T) or false (F).

1. True
2. False

Q. Name the property under multiplication used in $\frac{-4}{5}\times 1=1\times \frac{-4}{5}=\frac{-4}{5}$

Q.

$\begin{array}{cc}\text{Properties of multiplication}& \text{Representation}\\ 1.\text{Distributive Property}& a.a\times b=b\times a\\ 2.\text{Commutative Property}& b.a\times (b\times c)=(a\times b)\times c\\ 3.\text{Associative Property}& c.a\times (b+c)=a\times b+a\times c\end{array}$

Pick the option which shows the correct match.

1. $1-a;2-b;3-c$

2. $1-b;2-a;3-c$

3. $1-c;2-b;3-a$

4. $1-c;2-a;3-b$

Q.

Question 133

Fill in the blank to make the statement true.

32 $\times$ (27 $\times$ 19) = (32 $\times$ ...........) $\times$ 19

Q.

Answer in one word

What is the product of any integer with $0$

Q. (i) Find three consecutive numbers whose sum is 108
(ii) Find three consecutive odd numbers whose sum is 93

Q. When we multiply any given integer with 1, the result is always ___________.

1. half the integer
2. the same integer
3. double the integer
4. 1

Q. Find the value of $20(13+4)$. Then, using the variables $a,b,$ and $c$, show the distributive property of multiplication over addition.

Q. Find the product using suitable property:
(a) 205 × 1989
(b) 1991 × 1005
(3 marks)

Q.

If $a$ and $b$ are whole numbers then verify $a+b=b+a$ taking $a=12$and $b=13$.

Q.

Which number is the multiplicative identity for integers?
_____

Q. Write four negative integers less than $-10$

Q.

Simplify: $36÷\left[\right(5–11)\times 2]+12–7$

1. $2$

2. $-2$

3. $1$

4. $0$

Q. Assertion :If the sequence $\left\{t_n\right\}$ is monotonically increasing ihen the sequence $\{\sum t_n\},$ Where $\sum t_n=\frac{t_1+t_2+...+t_n}{n}$ is also monotonically increasing Reason: If $\left\{t_n\right\}$ is monotonically increasing then the expression $\sum t_{n+1}-\sum t_n$ is positive

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Using distributive property find the answer of:
a) 3 + 6 + 9 + 12 + 15
(Remember to use distributive property)

Q. $4\times (5+6)=4\times 5-4\times 6$

1. False
2. True

Q.

What is the successor of the predecessor of –50?​

(a) -48
(b) -49
(c) -50
(d) -51

Q. $200+(300+100)=(200+300)+100$
$\text{This is an example of}$.

1. identity
2. distributivity
3. commutativity
4. associativity

Q. The value of $|-5-6|\times |-4+3|$ on simplification is

1. 13
2. 12
3. 11
4. 10

Q. $200+(300+100)=(200+300)+100$
$\text{This is an example of}$.

1. distributivity
2. associativity
3. commutativity
4. identity

Q. $-6\times 6=36$

1. True
2. False

Q. Write the integers between the pairs of integers given below. Also, choose the biggest and smallest integers from them.
$3,-2$

Q. Multiplication is NOT commutative.

1. False
2. True

Q. Which of these operations are commutative for integers?

1. Addition
2. Subtraction
3. Multiplication
4. Division

Q.

Find the values of each of the following using properties of multiplication.

$756x52-756x2$

Q. Integers are closed under addition, subtraction and multiplication.

1. False
2. True

Q. Associative property can be expressed as:
$a\times (b\times c)=(a\times b)\times c$

1. True
2. False