Answer :
We start with the fact that the average blue whale weighs
[tex]$$300,\!000 \text{ lbs},$$[/tex]
and that the average man weighs
[tex]$$\frac{1}{1818}$$[/tex]
of a blue whale's weight. Therefore, the man's weight in pounds is given by
[tex]$$\text{Man's weight} = \frac{300,\!000}{1818}.$$[/tex]
To write this result as a mixed number, we first perform the division to obtain the whole number part.
1. Divide 300,000 by 1,818. The integer part (quotient) is 165 since
[tex]$$165 \times 1818 = 299970.$$[/tex]
2. Next, find the remainder by subtracting:
[tex]$$\text{Remainder} = 300,\!000 - 299970 = 30.$$[/tex]
3. This remainder represents the fractional part of the weight as
[tex]$$\frac{30}{1818}.$$[/tex]
4. Now, simplify the fraction [tex]$\frac{30}{1818}$[/tex]. The greatest common divisor (GCD) of 30 and 1818 is 6. Dividing the numerator and denominator by 6 gives
[tex]$$\frac{30 \div 6}{1818 \div 6} = \frac{5}{303}.$$[/tex]
Thus, the average man's weight is
[tex]$$165 \frac{5}{303} \text{ lbs}.$$[/tex]
This is the final answer.
[tex]$$300,\!000 \text{ lbs},$$[/tex]
and that the average man weighs
[tex]$$\frac{1}{1818}$$[/tex]
of a blue whale's weight. Therefore, the man's weight in pounds is given by
[tex]$$\text{Man's weight} = \frac{300,\!000}{1818}.$$[/tex]
To write this result as a mixed number, we first perform the division to obtain the whole number part.
1. Divide 300,000 by 1,818. The integer part (quotient) is 165 since
[tex]$$165 \times 1818 = 299970.$$[/tex]
2. Next, find the remainder by subtracting:
[tex]$$\text{Remainder} = 300,\!000 - 299970 = 30.$$[/tex]
3. This remainder represents the fractional part of the weight as
[tex]$$\frac{30}{1818}.$$[/tex]
4. Now, simplify the fraction [tex]$\frac{30}{1818}$[/tex]. The greatest common divisor (GCD) of 30 and 1818 is 6. Dividing the numerator and denominator by 6 gives
[tex]$$\frac{30 \div 6}{1818 \div 6} = \frac{5}{303}.$$[/tex]
Thus, the average man's weight is
[tex]$$165 \frac{5}{303} \text{ lbs}.$$[/tex]
This is the final answer.
