Multiplication of Integers

Q.

Give an example to show that the product of

(a) an even number of negative integers is positive .

(b) an odd number of negative integers is negative.

Q. What should be multiplied by (-12) in order to get 180?

1. 15
2. 16
3. -15
4. -16

Q. In a test, $4$ marks are given for every correct answer and $-2$ marks, for every incorrect answer. Asha answered all the questions and scored $26$ marks though she got nine correct answers. Varun also answered all the questions and scored $2$ marks though he got five correct answers. How many questions did each answer incorrectly?

1. $4,10$
2. $5,9$
3. $10,8$
4. $9,18$

Q. In a game, Ted has to earn coins. If he gets a gold coin, he gains 20 points, but if by mistake he gets a red coin, he loses 5 points. What is his total score if he gets 19 gold coins and 7 red coins?

Q.

Evaluate:- $(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

1. $\frac{-1}{27}$

2. $\frac{1}{27}$

3. $\frac{-1}{9}$

4. $\frac{1}{9}$

Q. Three consecutive integers are such that when they are taken in increasing order and multiplied by $2,3$ and $4$ respectively, they add upto $74$. Find these numbers.

Q. Three consecutive integers add up to $51$. What are these integers?

1. The three consecutive numbers are $10,14$ and $19$
2. The three consecutive numbers are $13,15$ and $19$.
3. The three consecutive numbers are $16$, $17$ and $18$.
4. The three consecutive numbers are $11,13$ and $15$.

Q. Find the value of:
-32 $\times$ 12 = ___
12 $\times$ (-32) = ___

1. 384, 384
2. -384, -384
3. 382, 382
4. 496, -496

Q. Find the value of $(-1)\times (-1)\times (-1)...$ so on till 47 times.

Q. Which of the following is obtained when we subtract 1/2 from its reciprocal?

1. 1
2. 3/2
3. 1/2
4. 2/3

Q.

Answer in one word

What is the result if $-1$ is multiplied twelve times

Q. 41. 2+3 / 32-23 = a-b6

Q. Using the law of exponents, find the exponential form of $2^5\times 2^3$

Q. Without adding, find the sum:
(i) (1 + 3 + 5 + 7 + 9 + 11 + 13)
(ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
(iii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)

Q.

Identify the property.

$13\times (12+15)=(13\times 12)+(13\times 15)$

Q.

The product of three negative integers is a $\underline{}$ integer. [negative/positive]

Q. Find the sum of odd integer from $1$ and $2001$.

Q. Product of two integers is

1. Always positive

2. Always negative

3. Always non-negative

4. Cannot say

Q. Find the sum of integers from $1$ to $100$ which are divisible by $2$ or $5$

Q. Three integers are multiplied to give 12. One of the numbers is the second smallest natural number. Other two numbers are not whole numbers and they differ by one unit. What are the three integers?

Q. A number when divided by $18$ gives $20$ as the quotient leaving a remainder of $16$. Find the number.

Q. Find using distributivity : $\left(\frac{7}{5}\times \left(\frac{-3}{12}\right)\right\}+\left(\frac{7}{5}\times \left(\frac{5}{12}\right)\right\}$

Q. For the fractions on the left, if the numerator is decreased by $1$ and the denominator is increased by $2$, match them with their resultant forms.

Q.

Question 63

In the following question, state whether the statement is True (T) or False (F):

The product of one negative and one positive term is a negative term.

Q.

Evaluate the expression $-5.3·(-2)$.

Q. In the following pairs, reduce second number from first.
(i) $72,60$
(ii) $52,78$

Q.

Evaluate:- $(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

1. $\frac{-1}{9}$

2. $\frac{-1}{27}$

3. $\frac{1}{9}$

4. $\frac{1}{27}$

Q. On dividing $15968$ by a certain number, the quotient is $89$ and the remainder is $37$. Find the divisor.

Q. If $a$ is an odd integer and $b$ is an even integer, which of the following is an odd integer?

1. $3b$
2. $a+3$
3. $2(a+b)$
4. $a+2b$
5. $2a+b$

Q.

A lift descends into an underground floor at the rate of 6 metres per minute. If the descend starts from 10 metres above the ground level, how much time will it take to descend 350 metres underground?

1. 30 minutes

2. 50 minutes

3. 1 hour

4. 1 hour 30 minutes