Worksheets for fraction addition - Free Printable

Problem: Solve the given fraction addition problems.

#### 1a. $\frac{2}{12} + \frac{1}{4} + \frac{3}{4}$

Step 1: Simplify $\frac{2}{12}$.
$$
\frac{2}{12} = \frac{1}{6}
$$

Step 2: Rewrite the problem with the simplified fraction:
$$
\frac{1}{6} + \frac{1}{4} + \frac{3}{4}
$$

Step 3: Find a common denominator for all fractions. The denominators are $6$, $4$, and $4$. The least common denominator (LCD) is $12$.

- Convert $\frac{1}{6}$ to a fraction with denominator $12$:
$$
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
$$

- Convert $\frac{1}{4}$ to a fraction with denominator $12$:
$$
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
$$

- Convert $\frac{3}{4}$ to a fraction with denominator $12$:
$$
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$

Step 4: Add the fractions:
$$
\frac{2}{12} + \frac{3}{12} + \frac{9}{12} = \frac{2 + 3 + 9}{12} = \frac{14}{12}
$$

Step 5: Simplify $\frac{14}{12}$:
$$
\frac{14}{12} = \frac{7}{6}
$$

Final Answer for 1a:
$$
\boxed{\frac{7}{6}}
$$

---

#### 1b. $\frac{3}{9} + \frac{2}{3} + \frac{1}{6}$

Step 1: Simplify $\frac{3}{9}$.
$$
\frac{3}{9} = \frac{1}{3}
$$

Step 2: Rewrite the problem with the simplified fraction:
$$
\frac{1}{3} + \frac{2}{3} + \frac{1}{6}
$$

Step 3: Find a common denominator for all fractions. The denominators are $3$, $3$, and $6$. The least common denominator (LCD) is $6$.

- Convert $\frac{1}{3}$ to a fraction with denominator $6$:
$$
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
$$

- Convert $\frac{2}{3}$ to a fraction with denominator $6$:
$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
$$

- $\frac{1}{6}$ already has the denominator $6$.

Step 4: Add the fractions:
$$
\frac{2}{6} + \frac{4}{6} + \frac{1}{6} = \frac{2 + 4 + 1}{6} = \frac{7}{6}
$$

Final Answer for 1b:
$$
\boxed{\frac{7}{6}}
$$

---

#### 2a. $\frac{3}{6} + \frac{7}{9} + \frac{1}{2}$

Step 1: Simplify $\frac{3}{6}$.
$$
\frac{3}{6} = \frac{1}{2}
$$

Step 2: Rewrite the problem with the simplified fraction:
$$
\frac{1}{2} + \frac{7}{9} + \frac{1}{2}
$$

Step 3: Combine the like terms $\frac{1}{2} + \frac{1}{2}$:
$$
\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1
$$

So the problem simplifies to:
$$
1 + \frac{7}{9}
$$

Step 4: Add $1$ (which is $\frac{9}{9}$) to $\frac{7}{9}$:
$$
1 + \frac{7}{9} = \frac{9}{9} + \frac{7}{9} = \frac{9 + 7}{9} = \frac{16}{9}
$$

Final Answer for 2a:
$$
\boxed{\frac{16}{9}}
$$

---

#### 2b. $\frac{7}{8} + \frac{1}{5} + \frac{5}{6}$

Step 1: Find a common denominator for all fractions. The denominators are $8$, $5$, and $6$. The least common denominator (LCD) is $120$.

- Convert $\frac{7}{8}$ to a fraction with denominator $120$:
$$
\frac{7}{8} = \frac{7 \times 15}{8 \times 15} = \frac{105}{120}
$$

- Convert $\frac{1}{5}$ to a fraction with denominator $120$:
$$
\frac{1}{5} = \frac{1 \times 24}{5 \times 24} = \frac{24}{120}
$$

- Convert $\frac{5}{6}$ to a fraction with denominator $120$:
$$
\frac{5}{6} = \frac{5 \times 20}{6 \times 20} = \frac{100}{120}
$$

Step 2: Add the fractions:
$$
\frac{105}{120} + \frac{24}{120} + \frac{100}{120} = \frac{105 + 24 + 100}{120} = \frac{229}{120}
$$

Final Answer for 2b:
$$
\boxed{\frac{229}{120}}
$$

---

Final Answers:

1a. $\boxed{\frac{7}{6}}$
1b. $\boxed{\frac{7}{6}}$
2a. $\boxed{\frac{16}{9}}$
2b. $\boxed{\frac{229}{120}}$