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Answer :
To find the solution to the division problem [tex]\( 20,835 \div 180 \)[/tex], we'll work through it step-by-step to determine which mixed fraction it corresponds to from the given options.
1. Perform the Division: First, calculate the division of 20,835 by 180. The result is 115.75. This means that 180 goes into 20,835 a total of 115 times, with a decimal remainder.
2. Determine the Whole Number and Remainder: The whole number part of our result is 115. Now, we need to determine the remainder to express the decimal as a fraction.
3. Calculate the Remainder: The remainder can be found using the formula:
[tex]\[
\text{Remainder} = 20,835 \mod 180 = 135.
\][/tex]
This means that after multiplying 115 by 180, we have a leftover or remainder of 135.
4. Express as a Mixed Number: We can now express our result as a mixed number:
[tex]\[
115 \frac{135}{180}
\][/tex]
5. Simplify the Fraction: Simplify the fraction [tex]\(\frac{135}{180}\)[/tex] by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 135 and 180 is 45. Dividing both the numerator and denominator by 45 gives us:
[tex]\[
\frac{135 \div 45}{180 \div 45} = \frac{3}{4}
\][/tex]
Thus, the expression of [tex]\( 20,835 \div 180 \)[/tex] as a mixed number is [tex]\( 115 \frac{3}{4} \)[/tex].
Therefore, the correct option from the choices given is:
[tex]\[
115 \frac{3}{4}
\][/tex]
1. Perform the Division: First, calculate the division of 20,835 by 180. The result is 115.75. This means that 180 goes into 20,835 a total of 115 times, with a decimal remainder.
2. Determine the Whole Number and Remainder: The whole number part of our result is 115. Now, we need to determine the remainder to express the decimal as a fraction.
3. Calculate the Remainder: The remainder can be found using the formula:
[tex]\[
\text{Remainder} = 20,835 \mod 180 = 135.
\][/tex]
This means that after multiplying 115 by 180, we have a leftover or remainder of 135.
4. Express as a Mixed Number: We can now express our result as a mixed number:
[tex]\[
115 \frac{135}{180}
\][/tex]
5. Simplify the Fraction: Simplify the fraction [tex]\(\frac{135}{180}\)[/tex] by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 135 and 180 is 45. Dividing both the numerator and denominator by 45 gives us:
[tex]\[
\frac{135 \div 45}{180 \div 45} = \frac{3}{4}
\][/tex]
Thus, the expression of [tex]\( 20,835 \div 180 \)[/tex] as a mixed number is [tex]\( 115 \frac{3}{4} \)[/tex].
Therefore, the correct option from the choices given is:
[tex]\[
115 \frac{3}{4}
\][/tex]
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