Adding Fractions Worksheets | Unlike denominators - Free Printable

To solve the given problems, we need to add fractions. The general steps for adding fractions are:

1. Find a common denominator if the denominators are different.
2. Adjust the numerators to reflect the new common denominator.
3. Add the numerators while keeping the denominator the same.
4. Simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Problem i: \( \frac{4}{8} + \frac{9}{33} \)

1. Simplify the fractions:
- \( \frac{4}{8} = \frac{1}{2} \)
- \( \frac{9}{33} = \frac{3}{11} \)

2. Find the least common denominator (LCD):
- Denominators: 2 and 11
- LCD = \( 2 \times 11 = 22 \)

3. Adjust the fractions to have the common denominator:
- \( \frac{1}{2} = \frac{1 \times 11}{2 \times 11} = \frac{11}{22} \)
- \( \frac{3}{11} = \frac{3 \times 2}{11 \times 2} = \frac{6}{22} \)

4. Add the fractions:
\[
\frac{11}{22} + \frac{6}{22} = \frac{11 + 6}{22} = \frac{17}{22}
\]

5. Simplify (if possible):
- \( \frac{17}{22} \) is already in simplest form.

Answer:
\[
\boxed{\frac{17}{22}}
\]

---

Problem ii: \( \frac{10}{15} + \frac{28}{34} \)

1. Simplify the fractions:
- \( \frac{10}{15} = \frac{2}{3} \)
- \( \frac{28}{34} = \frac{14}{17} \)

2. Find the least common denominator (LCD):
- Denominators: 3 and 17
- LCD = \( 3 \times 17 = 51 \)

3. Adjust the fractions to have the common denominator:
- \( \frac{2}{3} = \frac{2 \times 17}{3 \times 17} = \frac{34}{51} \)
- \( \frac{14}{17} = \frac{14 \times 3}{17 \times 3} = \frac{42}{51} \)

4. Add the fractions:
\[
\frac{34}{51} + \frac{42}{51} = \frac{34 + 42}{51} = \frac{76}{51}
\]

5. Simplify (if possible):
- \( \frac{76}{51} \) is already in simplest form.

Answer:
\[
\boxed{\frac{76}{51}}
\]

---

Problem iii: \( \frac{6}{10} + \frac{9}{25} \)

1. Simplify the fractions:
- \( \frac{6}{10} = \frac{3}{5} \)
- \( \frac{9}{25} \) is already in simplest form.

2. Find the least common denominator (LCD):
- Denominators: 5 and 25
- LCD = 25

3. Adjust the fractions to have the common denominator:
- \( \frac{3}{5} = \frac{3 \times 5}{5 \times 5} = \frac{15}{25} \)
- \( \frac{9}{25} \) remains \( \frac{9}{25} \)

4. Add the fractions:
\[
\frac{15}{25} + \frac{9}{25} = \frac{15 + 9}{25} = \frac{24}{25}
\]

5. Simplify (if possible):
- \( \frac{24}{25} \) is already in simplest form.

Answer:
\[
\boxed{\frac{24}{25}}
\]

---

Problem iv: \( \frac{7}{22} + \frac{27}{30} \)

1. Simplify the fractions:
- \( \frac{7}{22} \) is already in simplest form.
- \( \frac{27}{30} = \frac{9}{10} \)

2. Find the least common denominator (LCD):
- Denominators: 22 and 10
- LCD = \( 2 \times 11 \times 5 = 110 \)

3. Adjust the fractions to have the common denominator:
- \( \frac{7}{22} = \frac{7 \times 5}{22 \times 5} = \frac{35}{110} \)
- \( \frac{9}{10} = \frac{9 \times 11}{10 \times 11} = \frac{99}{110} \)

4. Add the fractions:
\[
\frac{35}{110} + \frac{99}{110} = \frac{35 + 99}{110} = \frac{134}{110}
\]

5. Simplify (if possible):
- \( \frac{134}{110} = \frac{67}{55} \)

Answer:
\[
\boxed{\frac{67}{55}}
\]

---

Problem v: \( \frac{3}{37} + \frac{9}{13} \)

1. Find the least common denominator (LCD):
- Denominators: 37 and 13
- LCD = \( 37 \times 13 = 481 \)

2. Adjust the fractions to have the common denominator:
- \( \frac{3}{37} = \frac{3 \times 13}{37 \times 13} = \frac{39}{481} \)
- \( \frac{9}{13} = \frac{9 \times 37}{13 \times 37} = \frac{333}{481} \)

3. Add the fractions:
\[
\frac{39}{481} + \frac{333}{481} = \frac{39 + 333}{481} = \frac{372}{481}
\]

4. Simplify (if possible):
- \( \frac{372}{481} \) is already in simplest form.

Answer:
\[
\boxed{\frac{372}{481}}
\]

---

Problem vi: \( \frac{28}{36} + \frac{9}{31} \)

1. Simplify the fractions:
- \( \frac{28}{36} = \frac{7}{9} \)
- \( \frac{9}{31} \) is already in simplest form.

2. Find the least common denominator (LCD):
- Denominators: 9 and 31
- LCD = \( 9 \times 31 = 279 \)

3. Adjust the fractions to have the common denominator:
- \( \frac{7}{9} = \frac{7 \times 31}{9 \times 31} = \frac{217}{279} \)
- \( \frac{9}{31} = \frac{9 \times 9}{31 \times 9} = \frac{81}{279} \)

4. Add the fractions:
\[
\frac{217}{279} + \frac{81}{279} = \frac{217 + 81}{279} = \frac{298}{279}
\]

5. Simplify (if possible):
- \( \frac{298}{279} \) is already in simplest form.

Answer:
\[
\boxed{\frac{298}{279}}
\]

---

Problem vii: \( \frac{21}{27} + \frac{28}{32} \)

1. Simplify the fractions:
- \( \frac{21}{27} = \frac{7}{9} \)
- \( \frac{28}{32} = \frac{7}{8} \)

2. Find the least common denominator (LCD):
- Denominators: 9 and 8
- LCD = \( 9 \times 8 = 72 \)

3. Adjust the fractions to have the common denominator:
- \( \frac{7}{9} = \frac{7 \times 8}{9 \times 8} = \frac{56}{72} \)
- \( \frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72} \)

4. Add the fractions:
\[
\frac{56}{72} + \frac{63}{72} = \frac{56 + 63}{72} = \frac{119}{72}
\]

5. Simplify (if possible):
- \( \frac{119}{72} \) is already in simplest form.

Answer:
\[
\boxed{\frac{119}{72}}
\]

---

Problem viii: \( \frac{14}{39} + \frac{9}{19} \)

1. Find the least common denominator (LCD):
- Denominators: 39 and 19
- LCD = \( 39 \times 19 = 741 \)

2. Adjust the fractions to have the common denominator:
- \( \frac{14}{39} = \frac{14 \times 19}{39 \times 19} = \frac{266}{741} \)
- \( \frac{9}{19} = \frac{9 \times 39}{19 \times 39} = \frac{351}{741} \)

3. Add the fractions:
\[
\frac{266}{741} + \frac{351}{741} = \frac{266 + 351}{741} = \frac{617}{741}
\]

4. Simplify (if possible):
- \( \frac{617}{741} \) is already in simplest form.

Answer:
\[
\boxed{\frac{617}{741}}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{i. } \frac{17}{22} \\
&\text{ii. } \frac{76}{51} \\
&\text{iii. } \frac{24}{25} \\
&\text{iv. } \frac{67}{55} \\
&\text{v. } \frac{372}{481} \\
&\text{vi. } \frac{298}{279} \\
&\text{vii. } \frac{119}{72} \\
&\text{viii. } \frac{617}{741}
\end{aligned}
}
\]