Tag: multiplication of a fraction

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Questions Related to multiplication of a fraction

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Which pair of numbers does not have a product equal to $36$?

  1. $\{ -4, -9\}$
  2. $\{ -3, -12\}$
  3. $\left\{ \displaystyle\frac{1}{2} , -72\right\}$
  4. $\{1, 36\}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option A= Product of $-4$ and $-9$=$-4\times -9=36$

Option B=Product of $-3$ and $-12$= $-3\times -12=36$
Option C= Product of $\dfrac{1}{2}$ and $-72$=$\dfrac{1}{2}\times{-72}=-36$
Option D= Product of $1$ and $36$ = $1\times 36=36$
Option C is the correct answer.

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Which of the following statements is INCORRECT?

  1. Zero has a reciprocal

  2. The product of two negative rational numbers is always positive

  3. The reciprocal of a positive rational number is always positive

  4. The product of two positive rational numbers is always positive
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Zero can't have a reciprocal because
$1/0$ is not defined.
The rest statements are
$(-a)\times (-b)=ab$
Reciprocal of $a$ is $1/a$
$a\times b=ab$
where $a$ and $b$ are positive.

Rest all statements are true except for option A.

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

The value of $\left (-\dfrac {7}{2}\right )^{-1}$ is _________.

  1. $-1$
  2. $\dfrac {7}{2}$
  3. $-\dfrac {2}{7}$
  4. $\dfrac {-7}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find $\left(-\dfrac{7}{2}\right)^{-1}$


Any fraction raised to negative power yields same result as of its reciprocal with modulus of the power.

$\therefore \left(-\dfrac{7}{2}\right)^{-1} = -\dfrac{2}{7}$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Which of the following statements is true?

  1. Every point on the number line represents a rational number
  2. The product of a rational number and its reciprocal to $0$
  3. $(17\times 12)^{-1}=17^{-1}\times 12$
  4. Reciprocal of $\displaystyle\frac{1}{a}$, $a$ $\neq 0$ is $a$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(1) Every point on the line doesn't represent a ration number, it represents the real number,  which includes both rational and irrational numbers.


(2) Let's say $a$ is a rational number,
Its reciprocal will be $\dfrac{1}{a}$
The product will be $ a \times  \dfrac{1}{a} =1$.

(3) $(17 \times  12)^{-1}$
$=$ $ \dfrac{1}{17\times 12}$
$=$ $ \dfrac{1}{17} \times  \dfrac{1}{12}$
$=$ ${17}^{-1} \times  {12}^{-1}$

(4) Reciprocal of $\dfrac{1}{a}$
$= \dfrac{1}{\dfrac{1}{a}}$
$=$ $a$
But $\dfrac{1}{a}$ is defined only if $ a \neq0$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

The algebraic expression for the statement "Product of $x$ and reciprocal of $a$, subtracted from the product of $y$ and reciprocal of $b"$ is ___________.

  1. $\dfrac {y}{b} - \dfrac {x}{a}$
  2. $\dfrac {y - x}{a - b}$
  3. $xa - yb$
  4. $\dfrac {1}{yb - xa}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Product of $x$ and reciprocal of $a$ $=$ $x\times \dfrac{1}{a}= \dfrac{x}{a}$
Product of $y$ and reciprocal of $b$ $=$ $y\times \dfrac{1}{b}= \dfrac{y}{b}$
Therefore, the algebraic expression is $\dfrac{y}{b}-\dfrac{x}{a}$.

Hence, option A is correct.