Add Fractions within 1 – Interactive worksheet with visual fraction models and step-by-step problems.

It looks like you've uploaded a worksheet titled "Add Fractions within 1", which is designed to help students practice adding fractions using visual models (like fraction bars) and converting fractions to have common denominators. The task involves:

1. Converting one fraction in each problem so both fractions have the same denominator.
2. Adding the fractions.
3. Using fraction bars to visually represent the process.
4. Shading the parts of the bars to show the addition.

Let’s solve each problem step-by-step, explaining how to convert, add, and use the visuals.

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🔹 Problem 1:

a. $ \frac{2}{3} + \frac{1}{6} $

#### Step 1: Find a common denominator
- Denominators: 3 and 6 → LCM is 6
- Convert $ \frac{2}{3} $ to sixths:
$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
$$
- So now:
$$
\frac{4}{6} + \frac{1}{6} = \frac{5}{6}
$$

#### Step 2: Fill in the blanks:
$$
\frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6}
$$

#### Step 3: Visuals (Bars)
- First bar (for $ \frac{4}{6} $): Shade 4 out of 6 equal parts.
- Second bar (for $ \frac{1}{6} $): Shade 1 out of 6 parts.
- Combined: Total shaded = 5 out of 6 → $ \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

---

🔹 Problem 2:

b. $ \frac{1}{4} + \frac{5}{8} $

#### Step 1: Common denominator
- Denominators: 4 and 8 → LCM is 8
- Convert $ \frac{1}{4} $ to eighths:
$$
\frac{1}{4} = \frac{2}{8}
$$
- Now:
$$
\frac{2}{8} + \frac{5}{8} = \frac{7}{8}
$$

#### Step 2: Fill in:
$$
\frac{1}{4} + \frac{5}{8} = \frac{2}{8} + \frac{5}{8} = \frac{7}{8}
$$

#### Step 3: Visuals
- First bar: Shade 2 out of 8 parts.
- Second bar: Shade 5 out of 8 parts.
- Total: 7/8

✔ Answer: $ \frac{7}{8} $

---

🔹 Problem 3:

c. $ \frac{3}{5} + \frac{4}{15} $

#### Step 1: Common denominator
- Denominators: 5 and 15 → LCM is 15
- Convert $ \frac{3}{5} $:
$$
\frac{3}{5} = \frac{9}{15}
$$
- Now:
$$
\frac{9}{15} + \frac{4}{15} = \frac{13}{15}
$$

#### Step 2: Fill in:
$$
\frac{3}{5} + \frac{4}{15} = \frac{9}{15} + \frac{4}{15} = \frac{13}{15}
$$

#### Step 3: Visuals
- First bar: 9 out of 15 parts shaded.
- Second bar: 4 out of 15 parts shaded.
- Total: 13/15

✔ Answer: $ \frac{13}{15} $

---

🔹 Problem 4:

d. $ \frac{1}{3} + \frac{3}{10} $

#### Step 1: Common denominator
- Denominators: 3 and 10 → LCM is 30
- Convert:
$$
\frac{1}{3} = \frac{10}{30}, \quad \frac{3}{10} = \frac{9}{30}
$$
- Add:
$$
\frac{10}{30} + \frac{9}{30} = \frac{19}{30}
$$

#### Step 2: Fill in:
$$
\frac{1}{3} + \frac{3}{10} = \frac{10}{30} + \frac{9}{30} = \frac{19}{30}
$$

#### Step 3: Visuals
- Use bars divided into 30 parts (or equivalent).
- First bar: 10/30 shaded.
- Second bar: 9/30 shaded.
- Total: 19/30

✔ Answer: $ \frac{19}{30} $

---

🔹 Problem 5:

e. $ \frac{2}{5} + \frac{1}{15} $

#### Step 1: Common denominator
- 5 and 15 → LCM is 15
- Convert $ \frac{2}{5} $:
$$
\frac{2}{5} = \frac{6}{15}
$$
- Add:
$$
\frac{6}{15} + \frac{1}{15} = \frac{7}{15}
$$

#### Step 2: Fill in:
$$
\frac{2}{5} + \frac{1}{15} = \frac{6}{15} + \frac{1}{15} = \frac{7}{15}
$$

#### Step 3: Visuals
- First bar: 6/15 shaded.
- Second bar: 1/15 shaded.
- Total: 7/15

✔ Answer: $ \frac{7}{15} $

---

🔹 Problem 6:

f. $ \frac{3}{4} + \frac{1}{6} $

#### Step 1: Common denominator
- 4 and 6 → LCM is 12
- Convert:
$$
\frac{3}{4} = \frac{9}{12}, \quad \frac{1}{6} = \frac{2}{12}
$$
- Add:
$$
\frac{9}{12} + \frac{2}{12} = \frac{11}{12}
$$

#### Step 2: Fill in:
$$
\frac{3}{4} + \frac{1}{6} = \frac{9}{12} + \frac{2}{12} = \frac{11}{12}
$$

#### Step 3: Visuals
- First bar: 9/12 shaded.
- Second bar: 2/12 shaded.
- Total: 11/12

✔ Answer: $ \frac{11}{12} $

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✔ Summary of Answers:

| Problem | Expression | Converted | Final Answer |
|--------|------------|-----------|---------------|
| a | $ \frac{2}{3} + \frac{1}{6} $ | $ \frac{4}{6} + \frac{1}{6} $ | $ \frac{5}{6} $ |
| b | $ \frac{1}{4} + \frac{5}{8} $ | $ \frac{2}{8} + \frac{5}{8} $ | $ \frac{7}{8} $ |
| c | $ \frac{3}{5} + \frac{4}{15} $ | $ \frac{9}{15} + \frac{4}{15} $ | $ \frac{13}{15} $ |
| d | $ \frac{1}{3} + \frac{3}{10} $ | $ \frac{10}{30} + \frac{9}{30} $ | $ \frac{19}{30} $ |
| e | $ \frac{2}{5} + \frac{1}{15} $ | $ \frac{6}{15} + \frac{1}{15} $ | $ \frac{7}{15} $ |
| f | $ \frac{3}{4} + \frac{1}{6} $ | $ \frac{9}{12} + \frac{2}{12} $ | $ \frac{11}{12} $ |

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📌 Key Tips:

- Always find the least common denominator (LCD).
- Convert each fraction to an equivalent one with that denominator.
- Add numerators; keep denominator.
- Use visual bars to reinforce understanding — they help see why we need common denominators.

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