Question

What is half of $1\dfrac{1}{3}$ cups?

Answer 1

Hint: Now first we will convert the mixed fraction $1\dfrac{1}{3}$ into normal fraction with the help of property $a\dfrac{p}{q}=\dfrac{aq+p}{q}$ . Now we will multiply $\dfrac{1}{2}$ to the obtained fraction. Hence we will get the solution to the given problem.

Complete step-by-step solution:
First let us understand the meaning of fractions.
Fractions are numbers which represent parts of the whole. A fraction is generally represented as $\dfrac{p}{q}$ . Where p is called the numerator and q is called the denominator of the fraction. Now consider the fraction $\dfrac{3}{4}$ this fraction means 3 parts of 4.
Now first let us calculate the value of $1\dfrac{1}{3}$ .
Now the given number is a mixed fraction of the form $a\dfrac{b}{c}$ . Now we first want to convert the given mixed fraction into normal fraction.
Now the mixed fraction can be converted into normal fraction by $a\dfrac{p}{q}=\dfrac{aq+p}{q}$ .
Hence we have \[1\dfrac{1}{3}=\dfrac{1\times 3+1}{3}\]
Now on simplifying the above equation we get$1\dfrac{1}{3}=\dfrac{4}{3}$ .
Now we want to find the value of half of $1\dfrac{1}{3}$ . To do so we will multiply half on both sides of the above equation.
$\Rightarrow 1\dfrac{1}{3}\times \dfrac{1}{2}=\dfrac{4}{3}\times \dfrac{1}{2}$
Now dividing the 4 in numerator with 2 from denominator we get,
$\Rightarrow 1\dfrac{1}{3}\times \dfrac{1}{3}=\dfrac{2}{3}$
Hence we get the half of $1\dfrac{1}{3}$ cups $\dfrac{2}{3}$ cups.

Note: Now note that mixed fraction contains integer and a fraction. Here the integer is not in multiplication with the fraction. The value of mixed fraction $a\dfrac{p}{q}$ is nothing but $a+\dfrac{p}{q}$ . Also note that for any fraction $\dfrac{p}{q}$ p and q can be any integers where q is not equal to 0.