Question

Use mental math to find the product of 60 and \[\dfrac{1}{2}\] ?

Answer 1

Hint: Mental math refers to calculation without using calculators or any other device which is faster and one can do calculations in their mind. Example: twice of 30 will be 30 added two times i.e. 60.
Product of any two numbers means the multiplication of the two numbers. If one of the numbers is in fraction form then we can multiply the whole number with the numerator and make the fraction in simplest form by cancellation.

Complete step by step solution:
We have to use mental math to calculate product of 60 and \[\dfrac{1}{2}\]
When a person tries to calculate a product of any two numbers, he/she directly multiplies the numbers. Here one of the numbers is in fraction form so we can write the multiplication of the whole number with the fraction as the whole number multiplied to the numerator of the fraction and the denominator remains the same.
\[ \Rightarrow \] Product of 60 and \[\dfrac{1}{2} = 60 \times \dfrac{1}{2}\]
\[ \Rightarrow \] Product of 60 and \[\dfrac{1}{2} = \dfrac{{60}}{2}\]
Now we know half of any number is the number which when added to itself forms the twice of the number. Any number divided by 2 means the value will be halved.
So, the number that is added to itself to obtain 60 will be
\[30 + 30 = 60\]
Half of 60 is 30 as when we add 30 to 30 we get 60.
\[\therefore \] The product of 60 and \[\dfrac{1}{2}\] is 30.

Note: Alternative method:
We can simply see the product of 60 and \[\dfrac{1}{2}\] will be half the value of 60. As we know 30 added to 30 gives us 60, then the value of half of 60 is 30.
\[\therefore \] The product of 60 and \[\dfrac{1}{2}\] is 30.