Let's solve each problem step by step:
---
Problem 1: What is the sum?
$$
\frac{4}{5} + \frac{1}{5}
$$
#### Solution:
- Both fractions have the same denominator, so we can add the numerators directly:
$$
\frac{4}{5} + \frac{1}{5} = \frac{4 + 1}{5} = \frac{5}{5} = 1
$$
#### Answer:
$$
\boxed{A}
$$
---
Problem 2: What is the product?
$$
\frac{4}{5} \times \frac{1}{5}
$$
#### Solution:
- To multiply fractions, multiply the numerators and the denominators:
$$
\frac{4}{5} \times \frac{1}{5} = \frac{4 \times 1}{5 \times 5} = \frac{4}{25}
$$
#### Answer:
$$
\boxed{C}
$$
---
Problem 3: What is the quotient?
$$
\frac{3}{4} \div \frac{3}{8}
$$
#### Solution:
- To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
$$
\frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3}
$$
- Simplify the multiplication:
$$
\frac{3}{4} \times \frac{8}{3} = \frac{3 \times 8}{4 \times 3} = \frac{24}{12} = 2
$$
#### Answer:
$$
\boxed{B}
$$
---
Problem 4: What is the difference?
$$
\frac{9}{14} - \frac{3}{7}
$$
#### Solution:
- First, find a common denominator. The denominators are 14 and 7, and the least common denominator (LCD) is 14.
- Rewrite the second fraction with the denominator 14:
$$
\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}
$$
- Now subtract the fractions:
$$
\frac{9}{14} - \frac{6}{14} = \frac{9 - 6}{14} = \frac{3}{14}
$$
#### Answer:
$$
\boxed{D}
$$
---
Problem 5: Will the answer be positive or negative?
$$
-2 \times (-5) \times (-1) \times (-9)
$$
#### Solution:
- Determine the sign of the product by counting the number of negative factors:
- There are 4 negative factors.
- An even number of negative factors results in a positive product.
- Calculate the absolute value of the product:
$$
2 \times 5 \times 1 \times 9 = 90
$$
- Since the product is positive:
$$
-2 \times (-5) \times (-1) \times (-9) = 90
$$
#### Answer:
$$
\boxed{A}
$$
---
Problem 6: Will the answer be positive or negative?
$$
-2 + (-5) + (-1) + (-9)
$$
#### Solution:
- Add the numbers step by step:
$$
-2 + (-5) = -7
$$
$$
-7 + (-1) = -8
$$
$$
-8 + (-9) = -17
$$
- The result is negative.
#### Answer:
$$
\boxed{B}
$$
---
Final Answers:
1. \( \boxed{A} \)
2. \( \boxed{C} \)
3. \( \boxed{B} \)
4. \( \boxed{D} \)
5. \( \boxed{A} \)
6. \( \boxed{B} \)
Parent Tip: Review the logic above to help your child master the concept of rational numbers worksheet grade 8.
