Question

What is \[10.5\] divided by \[1.5\] ?

Answer 1

Hint: The division is one of the four basic arithmetic operations, which involves combining numbers to create new ones. Addition, subtraction, and multiplication are the other operations. The division sign \[\left( \div \right)\] , which consists of a short horizontal line with a dot above and another dot below, is often used to represent mathematical division.

Complete step-by-step solution:
First, we have to write both numbers as proper fractions.
We are going to convert the decimal numbers to fractions through a simple method.
We know that \[0.5\] can be written as \[\dfrac{1}{2}\] in fraction.
So, we can write \[10.5\] as \[10\dfrac{1}{2}\] .
That is, \[10.5 = 10\dfrac{1}{2} = 10 + \dfrac{1}{2}\] .
To add \[10\] and \[\dfrac{1}{2}\] we have to multiply the denominator and numerator of \[10\] with \[2\] . We can only add two fractions after making the numerators of fractions the same. That is,
\[\dfrac{{10}}{1} + \dfrac{1}{2} = \dfrac{{20}}{2} + \dfrac{1}{2} = \dfrac{{21}}{2}\]
Now we are converting the other number into a fraction using the same method.
\[1.5 = 1\dfrac{1}{2} = 1 + \dfrac{1}{2}\]
\[\dfrac{1}{1} + \dfrac{1}{2} = \dfrac{2}{2} + \dfrac{1}{2} = \dfrac{3}{2}\]
Now, \[10.5 \div 1.5 = \dfrac{{21}}{2} \div \dfrac{3}{2}\]
Since dividing a fraction is equal to multiplying by its inverse, we get:
\[\dfrac{{21}}{2} \times \dfrac{2}{3} = \dfrac{{21}}{\require{cancel}{\cancel{2}}} \times \dfrac{\require{cancel}{\cancel{2}}}{3} = \dfrac{{21}}{3}\]
Solve the fraction completely to get the answer.
That is, \[\dfrac{{21}}{3} = 7\]
So, the answer is \[7\] .
Additional Information:
In most mathematical systems, division by zero is undefined since zero multiplied by some finite number always yields a product of zero. Most calculators will send you an error message if you enter such a phrase.

Note: There's a more efficient way to answer the problem. To get rid of the halves, we can double both numbers, and the answer will be the same:
\[\dfrac{{10.5}}{{1.5}} \times \dfrac{2}{2} = \dfrac{{21}}{3}\]
We have to solve the fraction to get the answer. That is,
\[\dfrac{{21}}{3} = 7\]