Question

What is half of \[1\dfrac{1}{2}\] cups?

Answer 1

Hint: We can not directly perform any operation on improper fractions, to perform any algebraic operation like addition, multiplication, subtraction or division, we have to first convert the mixed fraction in proper fraction form. The improper fractions of the form \[a\dfrac{b}{c}\] can be written in proper form as \[\dfrac{ac+b}{c}\]. After converting to a proper fraction, we will multiply it by half.

Complete step by step solution:
We are asked to find the half of \[1\dfrac{1}{2}\]. As this is an improper fraction, we first have to convert into a proper fraction. We can convert it in proper form as \[1\dfrac{1}{2}=\dfrac{2\times 1+2}{2}=\dfrac{3}{2}\].
Now as we need to find the half of this value, we will multiply it by \[\dfrac{1}{2}\]. By doing this, we get \[\dfrac{3}{2}\times \dfrac{1}{2}\]. Multiplying the numerators and denominators separately, we get \[\dfrac{3\times 1}{2\times 2}=\dfrac{3}{4}\].

Thus, the half of \[1\dfrac{1}{2}\] equals \[\dfrac{3}{4}\].

Note: These types of questions can be simply converting all terms to proper fractions and writing them in their factored form. After writing the factored form, we cancel out the common factors that terms have in common in their numerator and denominator. Calculation mistakes while solving this should be avoided.
We could also use a different method to solve this question. After converting the proper fraction form, we will convert it to decimal form. Multiplying this decimal form by half or 0.5 we will get the final answer.
Converting \[\dfrac{3}{2}\] to decimal form, we get 1.5, multiplying this decimal number by 0.5 we get the required answer as follows: \[1.5\times 0.5=0.75\]. Thus, the required answer is 0.75