Question

What is 10.5 divided by 1.5?

Answer 1

Hint: Assume the required expression as E. Now, consider 10.5 as the numerator and 1.5 as the denominator in the assumed expression. Remove the decimal point of the numerator and the denominator by multiplying both with 10. Cancel the common factors to simplify the expression and to get the answer in simplest form.

Complete step-by-step answer:
Here we have been asked to divide 10.5 by 1.5. So the dividend (numerator) is 10.5 and the divisor (denominator) is 1.5. Let us assume this expression as E, so we have,
\[\Rightarrow E=10.5\div 1.5\]
Now, when we have to divide a number ‘a’ with another number ‘b’ then what we do is, we first take the reciprocal of the number ‘b’ and then multiply it with number ‘a’. To take the reciprocal of a number we divide 1 by that number. For example: - reciprocal of b will be \[\dfrac{1}{b}\].
So let us come to the question. Taking the reciprocal of 1.5 we get \[\dfrac{1}{1.5}\]. Now, we have to multiply \[\dfrac{1}{1.5}\] with 1.5. So we get,
\[\begin{align}
  & \Rightarrow E=10.5\times \left( \dfrac{1}{1.5} \right) \\
 & \Rightarrow E=\dfrac{10.5}{1.5} \\
\end{align}\]
Now, let us remove the decimal point from both the numerator and the denominator. As we can see that there is only one digit after the decimal point in 10.5 and 1.5 so we need to multiply them with 10. This will automatically get balances since we are multiplying both with the same factor. So we get,
\[\begin{align}
  & \Rightarrow E=\dfrac{10.5}{1.5}\times \dfrac{10}{10} \\
 & \Rightarrow E=\dfrac{105}{15} \\
\end{align}\]
Cancelling the common factors we get,
\[\therefore E=7\]
Hence, the value of the given expression is 7.

Note: Do not get confused considering the numerator and the denominator of the required expression otherwise you will get the reciprocal of the value we have got as the answer. Always remember that to remove the decimal point from a number we multiply it with ${{10}^{n}}$ where n denotes the number of digits after the decimal point present in the number.