Question

State whether the following statement is true or false.
\[3750\] grams is \[3\dfrac{1}{4}\] kilograms.
A. TRUE
B. FALSE

Answer 1

Hint: We solve this question using the conversion of grams into kilograms and using the unitary method which helps us to find the value of multiple units if we are given the value of a single unit by just multiplying the value of single unit to number of units. We solve the mixed fraction in kilograms and convert it into grams to see if both values are equal.

Complete step-by-step answer:
We know that \[1\] Kg \[ = 1000\] grams
Here we will convert the given value of weight from grams to kilograms.
We have to convert \[3750\] grams into kilograms.
We know \[1000\] grams \[ = 1\] kg
Therefore, to find the value of one gram we divide the values on both sides by \[1000\]
So, the value of one grams \[\dfrac{1}{{1000}}\] kg
Now using the unitary method we have to find the value of \[3750\]grams in kg, so we multiply both sides by \[3750\].
So, the value of \[3750\] grams \[ = \dfrac{1}{{1000}} \times 3750 = \dfrac{{3750}}{{1000}} kg\]
Since we can write \[\dfrac{{3750}}{{1000}} = \dfrac{{375 \times 10}}{{100 \times 10}}\]
Now we can cancel out the factor 10 from both numerator and denominator.
\[ \Rightarrow 3750g = \dfrac{{375}}{{100}} kg\]
Now using the method of converting fraction into decimal form we can write any number having the denominator of the type \[{10^m}\] as a number having decimal after m digits.
So here m is two, therefore we can write \[\dfrac{{375}}{{100}} = 3.75\]
\[ \Rightarrow 3750g = 3.75 kg\] … (i)
Now we solve the mixed fraction \[3\dfrac{1}{4}\] kilograms.
We know to solve a mixed fraction we always multiply the whole number to the denominator and add the numerator which forms our new numerator and then write the old denominator at its place.
In this case new numerator becomes \[3 \times 4 + 1 = 12 + 1 = 13\]
So, the mixed fraction is solved to a simple fraction and is written as \[\dfrac{{13}}{4} kg\]
Now using normal division we can write \[\dfrac{{13}}{4}kg = 3.25 kg\] … (ii)
Since both the values from equations (i) and (ii) are different so the statement in the question is false.

So, the correct answer is “Option B”.

Note: Students are likely to make mistakes in transforming a mixed fraction to a normal fraction as they tend to multiply the whole number to the numerator and then add the denominator which is wrong.