Question

It is asked, If \[\dfrac{2}{3}\] of a number is 10, then what is 1.75 of that number?

Answer 1

Hint: We know that \[\dfrac{2}{3}\] of a number is \[10\] so we assume the number as x then we are given that if \[\dfrac{2}{3}\] of a number is \[10\] then we write as \[\dfrac{2}{3}\times x=10\] from where we find the value of the number x which is the needed number thereafter we find the multiplication of \[1.75\] and the number which is the answer as asked in the question.

Complete step-by-step solution:
The term “\[\dfrac{2}{3}\] of a number means that if we multiply \[\dfrac{2}{3}\] with the number we get the number \[10\]”, so we write the equation
\[\dfrac{2}{3}\times x=10\]
\[\dfrac{2x}{3}=10\]
We now use cross multiplication method to separate the values to either side,
\[2x=10\times 3\]
\[x=15\]
By solving the above equation, we can obtain the value of the unknown number x, which can be done by cross multiplication method,
The line “\[1.75\] times the number” means that we have to find the number obtained by multiplying \[1.75\] and x.
For example m times the number n implies that we have to add the value of n to itself n times and so \[m\times n\]
\[1.75\times 15\]
\[26.25\]
Hence we have obtained the answer to the above question which is \[26.25\].

Note: The student must be aware of the concept of fractions as well as the concept of decimal and concept of variable. The mistakes committed by students include calculation mistakes, writing the fractions wrong, Inability to visualize the unknown number n. we must also learn how we should multiply decimal numbers which are very important.