Tag: maths

Questions Related to maths

State the following statement is True or False
Multiplication and Division of two negative numbers is always a negative number

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. True

  2. False

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Correct Option: B
Explanation:

Multiplication and Division of two negative numbers is always a positive number.

$-32\times x= 160$, $-23\times y= -115$
What is the value of $x\div y$?

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $-1$

  2. $1$

  3. $-5$

  4. $5$

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Correct Option: A
Explanation:
Given, $-32\times x=160, -23\times y=-115$
We have $x=\dfrac{160}{-32}$

and $ y=\dfrac{-115}{-23}=\dfrac{115}{23}$

Thus $\dfrac{x}{y}=\dfrac{160\times 23}{-32\times 115}=-\dfrac{32\times23}{32\times 23}=-1$

State the following statement is True or False
Multiplication of one negative number and one positive number results into negative number

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. True

  2. False

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Correct Option: A
Explanation:

$(-)\times (+)=(-)\Rightarrow $   Multiplication of one negative number and one positive number results into negative number

State the following statement is True or False
The value of $-32\times -13= -416$

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. True

  2. False

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Correct Option: B
Explanation:

The value of $-32\times -13$ is $416$.

Multiplication of two negative numbers results into a positive number.

Which of the following statements is true?

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. The product of a positive and a negative integer is negative

  2. The product of a negative and a positive integer may be zero

  3. For all non-zero integers a and b, $a\times b$ is always greater than either a or b

  4. None of these

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Correct Option: A
Explanation:

a) The product of a positive and a negative integer is negative = True

b) The product of a negative and a positive integer may be zero = False
c) For all non-zero integers $a$ and $b$, $a\times b$ is always greater than either $a$ or $b$ = False
Hence option A is correct answer.

The sign of the product of two unlike integers is __________.

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. Positive

  2. Negative

  3. Positive or negative

  4. Cannot be determined

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Correct Option: B
Explanation:

The sign of the product of two unlike integers i.e.positive integer and negative integer is always negative.
Hence the correct answer is option B.

What will be the sign of the product if we together multiply $199$ negative integers and $10$ positive integers?

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. Negative

  2. Positive

  3. Can't say

  4. Data is insufficient

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Correct Option: A
Explanation:

Multiplication of $2$ negative integer result into positive integer.

 
If we multiply $199$ negative integer, then the result will be negative integer

Now if we multiply $10$ positive numbers with $199$ negative integers 

we will get a negative integer because multiplication of negative and positive 
integer will always result in negative integer.

Hence option A is correct.

Which of the following statement is CORRECT?

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. The product of a positive and a negative integer is always negative.

  2. The addition of a negative and a positive integer is always zero.

  3. For all non-zero integers a and b, a X b is always greater than either a or b.

  4. None of these

Show answer
Correct Option: A
Explanation:

In option (A)       $-x\times x=-x^{2}$ which is always negative. option is correct.

In option (B)        $ -x+y$ not equals to $0$ it zero only when $x=y$  option is incorrect.
In option (C)         let $a=-3$ and $b=4$ then $a\times b=-3\times 4=-12$  which is less than both a and b. hence this option is also incorrect.
hence only option $A$ is correct.

The product of each negative integer with $-1$ is always ______.

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. Positive

  2. Negative

  3. $0$

  4. Not defined

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Correct Option: A
Explanation:

When we multiply negative integer with $-1$ because we get a positive quantity when we multiply two negative quantities we get a positive quantity. 

A teacher assigns $5$ points for a correct answer, and $-2$ points for an incorrect answer, and $0$ points for leaving the questioned unanswered. What is the score for a student who had $22$ correct
answers, $15$ incorrect answers, and $7$ unanswered questions? 

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $60$

  2. $75$

  3. $80$

  4. $93$

Show answer
Correct Option: C
Explanation:

Since, the teacher assigns 5 points for a correct answer, and −2 points for an correct answer, and 0 points for leaving the questioned unanswered.

So,the student gets $(22\times 5) +(15\times -2)+ (7\times 0)  = 80$