Question

How do you translate “two-thirds of a number” into a mathematical expression?

Answer 1

Hint: Here we are asked to depict a fraction of a number. Represent that fraction in mathematical form and try to relate it to that number as given in the question. Focus on words because some words have special meaning in mathematics. Think of it as representing some fraction of a thing mathematically.

Complete step by step answer:
In mathematics, sometimes English phrases can be used to represent a mathematical expression. But they do not vary vastly. Sometimes they can be arranged in a way to trick minds but if read carefully they rather come out to be simple mathematics operations.
You may have come across many terms such as ‘sum of’, ‘difference of’, ‘divided in’, ‘gained by’, ‘loss of’ and many more. Similarly, the word ‘of’ has a special meaning in mathematics. The word ‘of’ is used to depict multiplication.
Like in this question, we are asked to translate two-thirds of a number into a mathematical expression. Let's say the number we are discussing is $x$ . Now we are asked to depict some fraction of that number. The fraction is two-third or $\dfrac{2}{3}$ . Now from the whole portion of $x$ we are supposed to show $\dfrac{2}{3}$ part of $x$ . If we write it down mathematically the fraction would be,
$\dfrac{2}{3}$ of $x$ which translates to,
 $ \Rightarrow \dfrac{2}{3} \times x$ , or this can be written as
 $ \Rightarrow \dfrac{2}{3}x$
The expression above represents two-third part of the number $x$ which is nothing but $66.67\% $ of $x$ .
So $\dfrac{2}{3}x$ is the required mathematical expression.

Note: Expressions like these should be kept in mind. Like ‘loss by’ represents difference, ‘gain by’ represents addition, ‘of’ represents multiplication. Sometimes this representation can be tricky also for example, “one-sixth of eight out of tenth part of seventy” would be represented as $\dfrac{1}{6} \times \dfrac{8}{{10}} \times 70$ .