What should be subtracted from \[8\dfrac{3}{10}\] to get \[2\dfrac{2}{3}\]?

Hint: Take the quantity to be subtracted as x and form an equation, \[8\dfrac{3}{10}-x = 2\dfrac{2}{3}\] and hence find x.

Complete step-by-step answer:

In the question we are asked to find a fraction that should be subtracted from \[8\dfrac{3}{10}\] to get \[2\dfrac{2}{3}\].

Before proceeding we will first learn briefly about fractions.

A fraction represents a part of a whole or more generally any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one – half, eight – fifths, three – quarters. A common, vulgar or simple fraction for example: \[\dfrac{1}{2}\], \[\dfrac{17}{2}\] consists of a numerator displayed above a line (or before a slash) and a non – zero denominator, displayed be low or after the line. Numerators and denominators are also used in fractions that are not in common, including compound fractions and mixed numerals.

Generally, fractions in the form \[a\dfrac{b}{c}\] are called mixed fractions; they are changed to fractions by multiplying a by c and then adding b. The resulting fraction would be, \[\dfrac{ac+b}{c}\].

So, \[8\dfrac{3}{10}\] will be \[\dfrac{8\times 10+3}{10}\] or \[\dfrac{83}{10}\].

And \[2\dfrac{2}{3}\] will be as \[\dfrac{2\times 3+2}{3}\] or \[\dfrac{8}{3}\] .

So, we have to find a fraction which when subtracted from \[\dfrac{83}{10}\] the fraction becomes \[\dfrac{8}{3}\].

Let that be x. So, we can write it as,

\[\dfrac{83}{3}-x=\dfrac{8}{3}\]

Hence, x is equal to \[\dfrac{83}{3}-\dfrac{8}{3}\].

We will first take L.C.M and do accordingly,

\[\dfrac{249-80}{30}\]

So, on simplifying we get,

\[\dfrac{169}{30}\]

So, the fraction is \[\dfrac{169}{30}\].

Note: The mixed fractions in form of \[a\dfrac{b}{c}\] can also be written as \[a+\dfrac{b}{c}\]. So, we can write \[\dfrac{83}{3}-\dfrac{8}{3}\] as \[8+\dfrac{3}{10}-2-\dfrac{2}{3}\], by this calculation becomes easier.