Properties of Multiplication of Integers

Q. Solve:(7/5*-3/12)+(7/5*5/12) using distributive property.

Q.

The product of three negative integers is a __ integer.

Q. Tell what property allows you to compute $\frac{1}{3}\times \left(\begin{array}{c}6\times \frac{4}{3}\end{array}\right)$ as $\left(\begin{array}{c}\frac{1}{3}\times 6\end{array}\right)\times \frac{4}{3}$.

Q.

The product of two negative integers is

Q. The maximum number of identity relations = 1 .How ?Also describe about identity relations .

Q. Using the rearrangement property find the sum:
(i) $\frac{4}{3}+\frac{3}{5}+\frac{-2}{3}+\frac{-11}{5}$
(ii) $\frac{-8}{3}+\frac{-1}{4}+\frac{-11}{6}+\frac{3}{8}$
(iii) $\frac{-13}{20}+\frac{11}{14}+\frac{-5}{7}+\frac{7}{10}$
(iv) $\frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7}$

Q.

Simplify the following using distributive property;
(i). $\frac{2}{5}(\frac{1}{9}+\frac{2}{5})$ (ii). $\frac{5}{12}(\frac{25}{9}+\frac{32}{5})$ (iii). $\frac{8}{9}(\frac{11}{2}+\frac{2}{9})$

Q.

Use the distributive property and calculate :$\frac{11}{37}(\frac{5}{11}+\frac{2}{3})$

Q.

If 'a' and 'b' are any two integers and a × (b + c) = (a × b) + (a × c). The property used here is __.

Q.

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

1. 
   −14 × {23 + (−47)} = [−14 × 23] + [−14 × (−47)]
2. 
   −14 × {23 + (−47)} = [14 × 23] − (−47)
3. 
   −14 × {23 + (−47)} = 23 + (−14) × −47
   
4. 
   −14 × {23 + (−47)} = {23 + (−47)} − 14

Q. In a class test containing 20 questions, 4 marks are awarded for every correct answer and -2 marks are awarded for every incorrect answer and 0 for not attempted questions. Pranav gets 9 correct and 3 incorrect answers. What is his score?

Q.

Which of the following correctly explains distributive law?

1. $a\times (b+c)=b\times a+a\times c$

2. $b\times (a+c)=b\times a+b\times c$

3. $(a+c)\times b=a\times b+c\times b$

4. All of these

Q.

Verify the associative property of addition.

$(-137)+0+37$

Q.

Verify the associative property of addition.

$(-45)+(-67)+82$

Q.

Which property is illustrated by the following statement?

150 × (-30 + 63) = 150 × -30 + 150 × 63

1. Associative property of integers

2. Distributive property of addition over multiplication

3. Distributive property of multiplication over addition

4. Commutative property of integers

Q.

Multiplicative identity of whole number is given by

1. $1$

2. $0$

3. Both $0\text{\hspace{0.17em}and\hspace{0.17em}}1$

4. None

Q.

Find the value of the following expression ​_​​​​​​​​ ( with the steps )​​​​_​​​ :

_​​​​( 8 × (4²)⁴ × 3³ × 27²) + (9 × 6³ × 4⁷ × (3²)³)

____________________________________________

(24 × (6^​​​​​​​²)⁴ × (2⁴)²) + (144 × (2³)⁴ × (9²)² × 4²

^{​​​​​}

Q.

Verify the associative property of addition.

$(-91)+(-112)+(-150)$

Q.

Verify the associative property of addition.

$15+(-23)+(-9)$

Q. Evaluate:
(i) 69 × 71
(ii) 94 × 106

Q. The multiplicative inverse of $-3\frac{4}{7}$ is:

Q. Multiply 17 x 105 by using the distributive property a x (b+c)=a x b +a x c. What are the most suitable choices of a, b and c?

Q.

Using distributive property of multiplication then simplify 3/5(10/11-40).

Q. Which of the following is an example of multiplicative identity?
[1 mark]

A. $\frac{2}{3}\times \frac{3}{2}=1$

B. $\frac{2}{3}+0=\frac{2}{3}$

C. $\frac{2}{3}\times 1=\frac{2}{3}$

D. $\frac{2}{3}\times 0=0$

Q. Find the value of using the short-cut method:
(25)³

Q. Multiply (2a2 + 9a + 10) by 4a.
$\left[2Marks\right]$

Q.

The multiplicative identity for integers is

___.

1. 1
2. First whole number
3. First natural number
4. -1

Q.

Can’t you do these in your head?

(i) (13 × 8) + (7 × 8)

(ii) (15 × 9) + (5 × 9)

(iii)

(iv)

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

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

Q.

128² - 127² =

1. 260

2. 250

3. 255

4. 245