Answer
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Hint: Here we are given two quantities and are asked to perform the mathematical operation, addition. In the question, we can see two types of quantities. One is tons and another one is a pound. To add these quantities easily, we convert both the terms into the same quantity. Converting it into a lower quantity would be easier. So, convert tons into pounds and then add.
Complete step by step solution:
The given quantities are $12\dfrac{1}{3}$ tons and $20\;$ tons $500\;$ pounds.
First let us consider the first term, $12\dfrac{1}{3}$ tons
The given fraction is known as a mixed fraction and we must convert it into an improper fraction.
For that, we must multiply the denominator of the mixed fraction to the whole number, which is placed in front, and then add the numerator part. Then we write the calculated part in the numerator and write the denominator the same as given in the question.
$\Rightarrow \dfrac{36+1}{3}$
$\Rightarrow \dfrac{37}{3}$ tons
Since we know that $1$ ton is equal to $2000\;$ pounds,
$\dfrac{37}{3}$ tones will be equal to $\dfrac{37}{3}\times 2000=\dfrac{74000}{3}$ pounds.
Now let us consider the second term, $20\;$ tons $500\;$ pounds.
$20\;$ tons $500\;$ pounds will be equal to $\left( 20\times 2000 \right)+500$ which is $40500\;$ pounds.
Now add these quantities since they have the same units.
$\Rightarrow \dfrac{74000}{3}+40500$
By taking the least common factor and multiplying it to the numerator to get a common denominator we get,
$\Rightarrow \dfrac{74000+3\left( 40500 \right)}{3}$
$\Rightarrow \dfrac{74000+121500}{3}$
On evaluating we get,
$\Rightarrow \dfrac{195500}{3}$ pounds
Now to represent our answer in a smaller way we convert it back into tons.
To convert back we divide the value by $2000\;$ .
$\Rightarrow \dfrac{195500}{3\times 2000}$
On evaluation,
$\Rightarrow \dfrac{391}{3\times 4}$
$\Rightarrow \dfrac{391}{12}$ tons
Now write it as a mixed fraction.
$\Rightarrow 32\dfrac{7}{12}$ tones
Hence, when we add $12\dfrac{1}{3}$ tons to $20\;$ tons $500\;$ pounds we get, $32\dfrac{7}{12}$ tons.
Note: Never forget to write the units of the given quantity after the whole evaluation. Units are what give the quantity the recognition and identity. Make sure the units are the same for the quantities while performing any mathematical operation. If they are not of the same units, convert them first and then write the expression.
Complete step by step solution:
The given quantities are $12\dfrac{1}{3}$ tons and $20\;$ tons $500\;$ pounds.
First let us consider the first term, $12\dfrac{1}{3}$ tons
The given fraction is known as a mixed fraction and we must convert it into an improper fraction.
For that, we must multiply the denominator of the mixed fraction to the whole number, which is placed in front, and then add the numerator part. Then we write the calculated part in the numerator and write the denominator the same as given in the question.
$\Rightarrow \dfrac{36+1}{3}$
$\Rightarrow \dfrac{37}{3}$ tons
Since we know that $1$ ton is equal to $2000\;$ pounds,
$\dfrac{37}{3}$ tones will be equal to $\dfrac{37}{3}\times 2000=\dfrac{74000}{3}$ pounds.
Now let us consider the second term, $20\;$ tons $500\;$ pounds.
$20\;$ tons $500\;$ pounds will be equal to $\left( 20\times 2000 \right)+500$ which is $40500\;$ pounds.
Now add these quantities since they have the same units.
$\Rightarrow \dfrac{74000}{3}+40500$
By taking the least common factor and multiplying it to the numerator to get a common denominator we get,
$\Rightarrow \dfrac{74000+3\left( 40500 \right)}{3}$
$\Rightarrow \dfrac{74000+121500}{3}$
On evaluating we get,
$\Rightarrow \dfrac{195500}{3}$ pounds
Now to represent our answer in a smaller way we convert it back into tons.
To convert back we divide the value by $2000\;$ .
$\Rightarrow \dfrac{195500}{3\times 2000}$
On evaluation,
$\Rightarrow \dfrac{391}{3\times 4}$
$\Rightarrow \dfrac{391}{12}$ tons
Now write it as a mixed fraction.
$\Rightarrow 32\dfrac{7}{12}$ tones
Hence, when we add $12\dfrac{1}{3}$ tons to $20\;$ tons $500\;$ pounds we get, $32\dfrac{7}{12}$ tons.
Note: Never forget to write the units of the given quantity after the whole evaluation. Units are what give the quantity the recognition and identity. Make sure the units are the same for the quantities while performing any mathematical operation. If they are not of the same units, convert them first and then write the expression.