Answer :
To find the sum of the given fractions, let's follow these steps:
1. List the Fractions:
- [tex]\(\frac{31}{40}\)[/tex] (A)
- [tex]\(3 \frac{38}{45} = \frac{173}{45}\)[/tex] (B)
- [tex]\(5\)[/tex] (C)
- [tex]\(6 \frac{1}{6} = \frac{37}{6}\)[/tex] (E)
- [tex]\(\frac{19}{21}\)[/tex] (G)
- [tex]\(\frac{39}{40}\)[/tex] (K)
- [tex]\(4 \frac{7}{8} = \frac{39}{8}\)[/tex] (L)
- [tex]\(\frac{33}{40}\)[/tex] (M)
- [tex]\(3 \frac{17}{30} = \frac{107}{30}\)[/tex] (R)
- [tex]\(\frac{20}{21}\)[/tex] (S)
- [tex]\(8 \frac{5}{12} = \frac{101}{12}\)[/tex] (I)
2. Find a Common Denominator:
To add fractions, we need a common denominator. The least common multiple (LCM) of all the denominators (40, 45, 1, 6, 21, 8, 30, 12) is 2520.
3. Convert Each Fraction to the Common Denominator:
Multiply the numerator and denominator of each fraction by the factor needed to reach the common denominator of 2520. For example:
- [tex]\(\frac{31}{40} \rightarrow \frac{31 \times 63}{40 \times 63}\)[/tex]
- [tex]\(\frac{173}{45} \rightarrow \frac{173 \times 56}{45 \times 56}\)[/tex]
- Convert each fraction in this way.
4. Add the Numerators:
After converting each fraction, add all the numerators together:
[tex]\[
\text{Sum of Numerators} = 91480
\][/tex]
5. Simplify the Resulting Fraction:
The resulting fraction before simplification is [tex]\(\frac{91480}{2520}\)[/tex].
Find the greatest common divisor (GCD) of the numerator and the denominator to simplify:
- [tex]\(\text{GCD}(91480, 2520) = 40\)[/tex]
Simplify by dividing both by the GCD:
[tex]\[
\frac{91480 \div 40}{2520 \div 40} = \frac{2287}{63}
\][/tex]
Therefore, the sum of the fractions simplifies to [tex]\(\frac{2287}{63}\)[/tex].
With this result, you can look up the corresponding letter for each code from the DECODER and solve the riddle:
"What has four wheels and flies?"
The answer is hinted through the coding, where the letters correspond to the number sequence derived from the fractions. By solving the puzzle, it typically reveals a pun or a joke based on the context.
1. List the Fractions:
- [tex]\(\frac{31}{40}\)[/tex] (A)
- [tex]\(3 \frac{38}{45} = \frac{173}{45}\)[/tex] (B)
- [tex]\(5\)[/tex] (C)
- [tex]\(6 \frac{1}{6} = \frac{37}{6}\)[/tex] (E)
- [tex]\(\frac{19}{21}\)[/tex] (G)
- [tex]\(\frac{39}{40}\)[/tex] (K)
- [tex]\(4 \frac{7}{8} = \frac{39}{8}\)[/tex] (L)
- [tex]\(\frac{33}{40}\)[/tex] (M)
- [tex]\(3 \frac{17}{30} = \frac{107}{30}\)[/tex] (R)
- [tex]\(\frac{20}{21}\)[/tex] (S)
- [tex]\(8 \frac{5}{12} = \frac{101}{12}\)[/tex] (I)
2. Find a Common Denominator:
To add fractions, we need a common denominator. The least common multiple (LCM) of all the denominators (40, 45, 1, 6, 21, 8, 30, 12) is 2520.
3. Convert Each Fraction to the Common Denominator:
Multiply the numerator and denominator of each fraction by the factor needed to reach the common denominator of 2520. For example:
- [tex]\(\frac{31}{40} \rightarrow \frac{31 \times 63}{40 \times 63}\)[/tex]
- [tex]\(\frac{173}{45} \rightarrow \frac{173 \times 56}{45 \times 56}\)[/tex]
- Convert each fraction in this way.
4. Add the Numerators:
After converting each fraction, add all the numerators together:
[tex]\[
\text{Sum of Numerators} = 91480
\][/tex]
5. Simplify the Resulting Fraction:
The resulting fraction before simplification is [tex]\(\frac{91480}{2520}\)[/tex].
Find the greatest common divisor (GCD) of the numerator and the denominator to simplify:
- [tex]\(\text{GCD}(91480, 2520) = 40\)[/tex]
Simplify by dividing both by the GCD:
[tex]\[
\frac{91480 \div 40}{2520 \div 40} = \frac{2287}{63}
\][/tex]
Therefore, the sum of the fractions simplifies to [tex]\(\frac{2287}{63}\)[/tex].
With this result, you can look up the corresponding letter for each code from the DECODER and solve the riddle:
"What has four wheels and flies?"
The answer is hinted through the coding, where the letters correspond to the number sequence derived from the fractions. By solving the puzzle, it typically reveals a pun or a joke based on the context.
