Question

The value of a for which the two rational numbers a/5,

31/5 are equivalent is _____​

Answer 1

The value of a is 31 as calculated using the properties of rational numbers.

To determine the value of 'a' for which the rational numbers $\frac{a}{5} \text{ and }\frac{31}{5}$ are equivalent, we need to set up an equation and solve for 'a'.

Since two rational numbers are equivalent if their fractions are equal, we can write:

$\frac{a}{5} =\frac{31}{5}$

To solve for 'a', we can cross-multiply:

$5 \times a = 5 \times 31$

This simplifies to:

$a = 31$

A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. In other words, a rational number is any number that can be written in the form of "p/q", where 'p' and 'q' are integers and 'q' is not equal to zero.

Rational numbers can be positive, negative, or zero. They can also be finite or have repeating or terminating decimal representations. For instance, $\frac{1}{2}$ is a rational number with a finite decimal representation of 0.5, while $\frac{1}{3}$ is a rational number with a repeating decimal representation of 0.333...

Therefore, the value of 'a' for which the two rational numbers  $\frac{a}{5} \text{ and }\frac{31}{5}$ are equivalent is 31.

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