Task cards for adding tenths and hundredths fractions with questions about simplification.

To solve the problems involving adding fractions with unlike denominators, we need to follow these steps:

1. Find a common denominator: The least common denominator (LCD) is the smallest number that both denominators can divide into evenly.
2. Adjust the fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator of each fraction by the necessary factor.
3. Add the fractions: Add the numerators together while keeping the common denominator.
4. Simplify the result: Reduce the resulting fraction to its simplest form if possible.

Let's solve each problem step by step.

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Problem 1: Add \( \frac{6}{100} + \frac{3}{10} \)

#### Step 1: Find the common denominator
- Denominators: 100 and 10
- The LCD of 100 and 10 is 100.

#### Step 2: Adjust the fractions
- For \( \frac{3}{10} \), multiply both the numerator and the denominator by 10:
\[
\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}
\]
- The first fraction \( \frac{6}{100} \) already has the denominator 100, so it remains unchanged.

#### Step 3: Add the fractions
\[
\frac{6}{100} + \frac{30}{100} = \frac{6 + 30}{100} = \frac{36}{100}
\]

#### Step 4: Simplify the result
- Simplify \( \frac{36}{100} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\]

Final Answer for Problem 1:
\[
\boxed{\frac{9}{25}}
\]

---

Problem 2: Add \( \frac{1}{10} + \frac{15}{100} \)

#### Step 1: Find the common denominator
- Denominators: 10 and 100
- The LCD of 10 and 100 is 100.

#### Step 2: Adjust the fractions
- For \( \frac{1}{10} \), multiply both the numerator and the denominator by 10:
\[
\frac{1}{10} = \frac{1 \times 10}{10 \times 10} = \frac{10}{100}
\]
- The second fraction \( \frac{15}{100} \) already has the denominator 100, so it remains unchanged.

#### Step 3: Add the fractions
\[
\frac{10}{100} + \frac{15}{100} = \frac{10 + 15}{100} = \frac{25}{100}
\]

#### Step 4: Simplify the result
- Simplify \( \frac{25}{100} \) by dividing both the numerator and the denominator by their GCD, which is 25:
\[
\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
\]

Final Answer for Problem 2:
\[
\boxed{\frac{1}{4}}
\]

---

Problem 3: Add \( \frac{8}{10} + \frac{12}{100} \)

#### Step 1: Find the common denominator
- Denominators: 10 and 100
- The LCD of 10 and 100 is 100.

#### Step 2: Adjust the fractions
- For \( \frac{8}{10} \), multiply both the numerator and the denominator by 10:
\[
\frac{8}{10} = \frac{8 \times 10}{10 \times 10} = \frac{80}{100}
\]
- The second fraction \( \frac{12}{100} \) already has the denominator 100, so it remains unchanged.

#### Step 3: Add the fractions
\[
\frac{80}{100} + \frac{12}{100} = \frac{80 + 12}{100} = \frac{92}{100}
\]

#### Step 4: Simplify the result
- Simplify \( \frac{92}{100} \) by dividing both the numerator and the denominator by their GCD, which is 4:
\[
\frac{92 \div 4}{100 \div 4} = \frac{23}{25}
\]

Final Answer for Problem 3:
\[
\boxed{\frac{23}{25}}
\]

---

Problem 4: Add \( \frac{3}{10} + \frac{30}{100} \)

#### Step 1: Find the common denominator
- Denominators: 10 and 100
- The LCD of 10 and 100 is 100.

#### Step 2: Adjust the fractions
- For \( \frac{3}{10} \), multiply both the numerator and the denominator by 10:
\[
\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}
\]
- The second fraction \( \frac{30}{100} \) already has the denominator 100, so it remains unchanged.

#### Step 3: Add the fractions
\[
\frac{30}{100} + \frac{30}{100} = \frac{30 + 30}{100} = \frac{60}{100}
\]

#### Step 4: Simplify the result
- Simplify \( \frac{60}{100} \) by dividing both the numerator and the denominator by their GCD, which is 20:
\[
\frac{60 \div 20}{100 \div 20} = \frac{3}{5}
\]

Final Answer for Problem 4:
\[
\boxed{\frac{3}{5}}
\]

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Summary of Answers:

1. \( \frac{6}{100} + \frac{3}{10} = \boxed{\frac{9}{25}} \)
2. \( \frac{1}{10} + \frac{15}{100} = \boxed{\frac{1}{4}} \)
3. \( \frac{8}{10} + \frac{12}{100} = \boxed{\frac{23}{25}} \)
4. \( \frac{3}{10} + \frac{30}{100} = \boxed{\frac{3}{5}} \)