Question

What fraction of 1 kg is 650 g ?

Answer 1

Hint: To solve this question, we need to know that the quantity 1 kg is equal to 1000 grams and also that the fraction can also be expressed as $\dfrac{a}{b}$. Now we have to find the fraction of 1 kg to 650 grams so, we will first convert 1 kgs to grams using the formula 1 kg = 1000 grams then after we will express it in the fraction form and we can apply all that operations on $\dfrac{a}{b}$.

Complete step-by-step answer:
We have to find the value of a fraction of 1kg is 650 g.
We will write one kilogram in terms of grams and then calculate the value of fraction.
We are already aware that 1 kg = 1000 grams.
To find the value of fraction, we will write 650 grams as numerator and one kilogram as denominator.
Thus, the value of fraction is $\dfrac{{650}}{{1000}}$.
We will now reduce this fraction into simplest form or lowest terms.
For reducing the fraction into its lowest term, we will find the HCF of numerator and denominator.
We will find HCF for both numbers by writing the prime factorization of each of the numbers. We will choose the common prime factors of all the two numbers. The number obtained by choosing the common prime factors of all the numbers will be the HCF of two numbers.
The prime factorization of 650 is $650 = 2 \times {5^2} \times 13$.
The prime factorization of 1000 is $1000 = {2^3} \times {5^3}$.
The terms which are common to prime factorization of both the numbers is $2 \times {5^2} = 50$.
Thus, the HCF of 650 and 1000 is 50.
We will now reduce the fraction by dividing both numerator and denominator by their HCF, which is 50.
Thus, we have $\dfrac{{650}}{{1000}} = \dfrac{{\dfrac{{650}}{{50}}}}{{\dfrac{{1000}}{{50}}}} = \dfrac{{13}}{{20}}$.
So, the fraction of 1 kg is 650 gram is $\dfrac{{13}}{{20}}$.

Note: If this type of question is asked in subjective exams then you have to show each and every step that you used in order to solve the question. Fraction represents a part of a whole. We should be careful while writing the fractions as the units of numerator and denominator should always be the same. Otherwise, we will get an incorrect answer. Reduce the fraction into lowest terms by taking out common terms of numerator and denominator.