Problem: Addition and Subtraction of Rational Numbers
We are tasked with solving the given problems involving the addition of rational numbers. Let's solve each problem step by step.
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Problem 1:
$$
\frac{41}{47} + \frac{18}{47} + \frac{3}{47} + \frac{12}{47} + \frac{4}{47}
$$
Solution:
1. All the fractions have the same denominator, which is 47.
2. Add the numerators together:
$$
41 + 18 + 3 + 12 + 4 = 78
$$
3. The sum of the fractions is:
$$
\frac{78}{47}
$$
Final Answer for Problem 1:
$$
\boxed{\frac{78}{47}}
$$
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####
Problem 2:
$$
\frac{1}{13} + \frac{2}{13} + \frac{9}{13} + \frac{12}{13}
$$
Solution:
1. All the fractions have the same denominator, which is 13.
2. Add the numerators together:
$$
1 + 2 + 9 + 12 = 24
$$
3. The sum of the fractions is:
$$
\frac{24}{13}
$$
Final Answer for Problem 2:
$$
\boxed{\frac{24}{13}}
$$
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####
Problem 3:
$$
\frac{39}{82} + \frac{61}{82}
$$
Solution:
1. Both fractions have the same denominator, which is 82.
2. Add the numerators together:
$$
39 + 61 = 100
$$
3. The sum of the fractions is:
$$
\frac{100}{82}
$$
4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{100 \div 2}{82 \div 2} = \frac{50}{41}
$$
Final Answer for Problem 3:
$$
\boxed{\frac{50}{41}}
$$
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Problem 4:
$$
\frac{56}{69} + \frac{13}{69} + \frac{43}{69}
$$
Solution:
1. All the fractions have the same denominator, which is 69.
2. Add the numerators together:
$$
56 + 13 + 43 = 112
$$
3. The sum of the fractions is:
$$
\frac{112}{69}
$$
Final Answer for Problem 4:
$$
\boxed{\frac{112}{69}}
$$
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####
Problem 5:
$$
\frac{52}{70} + \frac{30}{70} + \frac{21}{70}
$$
Solution:
1. All the fractions have the same denominator, which is 70.
2. Add the numerators together:
$$
52 + 30 + 21 = 103
$$
3. The sum of the fractions is:
$$
\frac{103}{70}
$$
Final Answer for Problem 5:
$$
\boxed{\frac{103}{70}}
$$
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Final Answers:
1. $\boxed{\frac{78}{47}}$
2. $\boxed{\frac{24}{13}}$
3. $\boxed{\frac{50}{41}}$
4. $\boxed{\frac{112}{69}}$
5. $\boxed{\frac{103}{70}}$
Parent Tip: Review the logic above to help your child master the concept of subtracting rational numbers worksheet.
