Question

Give four numbers equivalent to \[\dfrac{5}{-3}\]

Answer 1

Hint: The given number is a rational number. For the given number multiplying with any number with both numerator and denominator gives equivalent rational numbers. Thus, multiplying the numerator and denominator by 4 different numbers will give four equivalent numbers.
Complete step-by-step answer:
Rational number: A rational number is a number that can be expressed as fraction p/q of two integers, a numerator p and a non zero denominator q.
The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
A real number that is not rational is called an irrational number.
Equivalent rational numbers: To obtain an equivalent rational number of the given rational number we have to multiply the numerator and denominator of a given rational number by the same nonzero number.
If \[\dfrac{a}{b}\] is a rational number and m is a non-zero integer then \[\dfrac{a\times m}{b\times m}\] is a rational number equivalent to \[\dfrac{a}{b}\].
Given number is \[\dfrac{5}{-3}\].
Multiplying with 2 in both numerator and denominator gives the following equivalent rational number as,
\[\Rightarrow \]\[\dfrac{5\times 2}{-3\times 2}=\dfrac{10}{-6}\]
Multiplying with 3 in both numerator and denominator gives the following equivalent rational number as
\[\Rightarrow \] \[\dfrac{5\times 3}{-3\times 3}=\dfrac{15}{-9}\]
Multiplying with 4 in both numerator and denominator gives the following equivalent rational number as
\[\Rightarrow \] \[\dfrac{5\times 4}{-3\times 4}=\dfrac{20}{-12}\]
Multiplying with 0.5 in both numerator and denominator gives the following equivalent rational number as
\[\Rightarrow \] \[\dfrac{5\times 0.5}{-3\times 0.5}=\dfrac{2.5}{-1.5}\]
Therefore the four numbers are \[\dfrac{10}{-6},\dfrac{15}{-9},\dfrac{20}{-12},\dfrac{2.5}{-1.5}\].
Note: The value in the denominator should be non zero. We can also multiply with negative numbers and can get equivalent rational numbers. This is a direct question which can be solved by multiplying numerator and denominator with the same number gives equivalent rational numbers.