Simplifying Fractions 100 Worksheets with Answers Maths - Free Printable

To solve the problems involving the addition of mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions (if necessary).
2. Find a common denominator for the fractions.
3. Add the fractions and then add the whole numbers.
4. Simplify the result if possible.

Let's solve each problem step by step.

---

Problem 1: \( 4 \frac{1}{2} + 6 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)
- \( 6 \frac{1}{5} = 6 + \frac{1}{5} = \frac{30}{5} + \frac{1}{5} = \frac{31}{5} \)

#### Step 2: Find a common denominator
The denominators are 2 and 5. The least common denominator (LCD) is 10.

- Convert \( \frac{9}{2} \) to a fraction with denominator 10:
\[
\frac{9}{2} = \frac{9 \times 5}{2 \times 5} = \frac{45}{10}
\]
- Convert \( \frac{31}{5} \) to a fraction with denominator 10:
\[
\frac{31}{5} = \frac{31 \times 2}{5 \times 2} = \frac{62}{10}
\]

#### Step 3: Add the fractions
\[
\frac{45}{10} + \frac{62}{10} = \frac{45 + 62}{10} = \frac{107}{10}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{107}{10} = 10 \frac{7}{10}
\]

Answer:
\[
\boxed{10 \frac{7}{10}}
\]

---

Problem 2: \( 2 \frac{5}{10} + 5 \frac{3}{5} \)

#### Step 1: Simplify and convert mixed numbers
- \( 2 \frac{5}{10} = 2 \frac{1}{2} \) (since \( \frac{5}{10} = \frac{1}{2} \))
- \( 5 \frac{3}{5} \) remains as is.

#### Step 2: Convert to improper fractions
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 5 \frac{3}{5} = 5 + \frac{3}{5} = \frac{25}{5} + \frac{3}{5} = \frac{28}{5} \)

#### Step 3: Find a common denominator
The denominators are 2 and 5. The LCD is 10.

- Convert \( \frac{5}{2} \) to a fraction with denominator 10:
\[
\frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10}
\]
- Convert \( \frac{28}{5} \) to a fraction with denominator 10:
\[
\frac{28}{5} = \frac{28 \times 2}{5 \times 2} = \frac{56}{10}
\]

#### Step 4: Add the fractions
\[
\frac{25}{10} + \frac{56}{10} = \frac{25 + 56}{10} = \frac{81}{10}
\]

#### Step 5: Convert back to a mixed number
\[
\frac{81}{10} = 8 \frac{1}{10}
\]

Answer:
\[
\boxed{8 \frac{1}{10}}
\]

---

Problem 3: \( 3 \frac{4}{5} + 8 \frac{1}{3} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 3 \frac{4}{5} = 3 + \frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5} \)
- \( 8 \frac{1}{3} = 8 + \frac{1}{3} = \frac{24}{3} + \frac{1}{3} = \frac{25}{3} \)

#### Step 2: Find a common denominator
The denominators are 5 and 3. The LCD is 15.

- Convert \( \frac{19}{5} \) to a fraction with denominator 15:
\[
\frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15}
\]
- Convert \( \frac{25}{3} \) to a fraction with denominator 15:
\[
\frac{25}{3} = \frac{25 \times 5}{3 \times 5} = \frac{125}{15}
\]

#### Step 3: Add the fractions
\[
\frac{57}{15} + \frac{125}{15} = \frac{57 + 125}{15} = \frac{182}{15}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{182}{15} = 12 \frac{2}{15}
\]

Answer:
\[
\boxed{12 \frac{2}{15}}
\]

---

Problem 4: \( 2 \frac{4}{5} + 8 \frac{3}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5} \)
- \( 8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \)

#### Step 2: Find a common denominator
The denominators are 5 and 4. The LCD is 20.

- Convert \( \frac{14}{5} \) to a fraction with denominator 20:
\[
\frac{14}{5} = \frac{14 \times 4}{5 \times 4} = \frac{56}{20}
\]
- Convert \( \frac{35}{4} \) to a fraction with denominator 20:
\[
\frac{35}{4} = \frac{35 \times 5}{4 \times 5} = \frac{175}{20}
\]

#### Step 3: Add the fractions
\[
\frac{56}{20} + \frac{175}{20} = \frac{56 + 175}{20} = \frac{231}{20}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{231}{20} = 11 \frac{11}{20}
\]

Answer:
\[
\boxed{11 \frac{11}{20}}
\]

---

Problem 5: \( 3 \frac{2}{3} + 5 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \)
- \( 5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \)

#### Step 2: Find a common denominator
The denominators are 3 and 4. The LCD is 12.

- Convert \( \frac{11}{3} \) to a fraction with denominator 12:
\[
\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}
\]
- Convert \( \frac{21}{4} \) to a fraction with denominator 12:
\[
\frac{21}{4} = \frac{21 \times 3}{4 \times 3} = \frac{63}{12}
\]

#### Step 3: Add the fractions
\[
\frac{44}{12} + \frac{63}{12} = \frac{44 + 63}{12} = \frac{107}{12}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{107}{12} = 8 \frac{11}{12}
\]

Answer:
\[
\boxed{8 \frac{11}{12}}
\]

---

Problem 6: \( 6 \frac{4}{10} + 5 \frac{3}{4} \)

#### Step 1: Simplify and convert mixed numbers
- \( 6 \frac{4}{10} = 6 \frac{2}{5} \) (since \( \frac{4}{10} = \frac{2}{5} \))
- \( 5 \frac{3}{4} \) remains as is.

#### Step 2: Convert to improper fractions
- \( 6 \frac{2}{5} = 6 + \frac{2}{5} = \frac{30}{5} + \frac{2}{5} = \frac{32}{5} \)
- \( 5 \frac{3}{4} = 5 + \frac{3}{4} = \frac{20}{4} + \frac{3}{4} = \frac{23}{4} \)

#### Step 3: Find a common denominator
The denominators are 5 and 4. The LCD is 20.

- Convert \( \frac{32}{5} \) to a fraction with denominator 20:
\[
\frac{32}{5} = \frac{32 \times 4}{5 \times 4} = \frac{128}{20}
\]
- Convert \( \frac{23}{4} \) to a fraction with denominator 20:
\[
\frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20}
\]

#### Step 4: Add the fractions
\[
\frac{128}{20} + \frac{115}{20} = \frac{128 + 115}{20} = \frac{243}{20}
\]

#### Step 5: Convert back to a mixed number
\[
\frac{243}{20} = 12 \frac{3}{20}
\]

Answer:
\[
\boxed{12 \frac{3}{20}}
\]

---

Problem 7: \( 2 \frac{1}{4} + 7 \frac{2}{10} \)

#### Step 1: Simplify and convert mixed numbers
- \( 2 \frac{1}{4} \) remains as is.
- \( 7 \frac{2}{10} = 7 \frac{1}{5} \) (since \( \frac{2}{10} = \frac{1}{5} \))

#### Step 2: Convert to improper fractions
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- \( 7 \frac{1}{5} = 7 + \frac{1}{5} = \frac{35}{5} + \frac{1}{5} = \frac{36}{5} \)

#### Step 3: Find a common denominator
The denominators are 4 and 5. The LCD is 20.

- Convert \( \frac{9}{4} \) to a fraction with denominator 20:
\[
\frac{9}{4} = \frac{9 \times 5}{4 \times 5} = \frac{45}{20}
\]
- Convert \( \frac{36}{5} \) to a fraction with denominator 20:
\[
\frac{36}{5} = \frac{36 \times 4}{5 \times 4} = \frac{144}{20}
\]

#### Step 4: Add the fractions
\[
\frac{45}{20} + \frac{144}{20} = \frac{45 + 144}{20} = \frac{189}{20}
\]

#### Step 5: Convert back to a mixed number
\[
\frac{189}{20} = 9 \frac{9}{20}
\]

Answer:
\[
\boxed{9 \frac{9}{20}}
\]

---

Problem 8: \( 6 \frac{1}{2} + 4 \frac{4}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \)
- \( 4 \frac{4}{5} = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5} \)

#### Step 2: Find a common denominator
The denominators are 2 and 5. The LCD is 10.

- Convert \( \frac{13}{2} \) to a fraction with denominator 10:
\[
\frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10}
\]
- Convert \( \frac{24}{5} \) to a fraction with denominator 10:
\[
\frac{24}{5} = \frac{24 \times 2}{5 \times 2} = \frac{48}{10}
\]

#### Step 3: Add the fractions
\[
\frac{65}{10} + \frac{48}{10} = \frac{65 + 48}{10} = \frac{113}{10}
\]

#### Step 4: Convert back to a mixed number
\[
\frac{113}{10} = 11 \frac{3}{10}
\]

Answer:
\[
\boxed{11 \frac{3}{10}}
\]

---

Problem 9: \( 2 \frac{1}{2} + 9 \frac{6}{10} \)

#### Step 1: Simplify and convert mixed numbers
- \( 2 \frac{1}{2} \) remains as is.
- \( 9 \frac{6}{10} = 9 \frac{3}{5} \) (since \( \frac{6}{10} = \frac{3}{5} \))

#### Step 2: Convert to improper fractions
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{45}{5} + \frac{3}{5} = \frac{48}{5} \)

#### Step 3: Find a common denominator
The denominators are 2 and 5. The LCD is 10.

- Convert \( \frac{5}{2} \) to a fraction with denominator 10:
\[
\frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10}
\]
- Convert \( \frac{48}{5} \) to a fraction with denominator 10:
\[
\frac{48}{5} = \frac{48 \times 2}{5 \times 2} = \frac{96}{10}
\]

#### Step 4: Add the fractions
\[
\frac{25}{10} + \frac{96}{10} = \frac{25 + 96}{10} = \frac{121}{10}
\]

#### Step 5: Convert back to a mixed number
\[
\frac{121}{10} = 12 \frac{1}{10}
\]

Answer:
\[
\boxed{12 \frac{1}{10}}
\]

---

Problem 10: \( 5 \frac{5}{10} + 8 \frac{1}{2} \)

#### Step 1: Simplify and convert mixed numbers
- \( 5 \frac{5}{10} = 5 \frac{1}{2} \) (since \( \frac{5}{10} = \frac{1}{2} \))
- \( 8 \frac{1}{2} \) remains as is.

#### Step 2: Convert to improper fractions
- \( 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \)
- \( 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \)

#### Step 3: Add the fractions
\[
\frac{11}{2} + \frac{17}{2} = \frac{11 + 17}{2} = \frac{28}{2} = 14
\]

Answer:
\[
\boxed{14}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ 10 \frac{7}{10} \\
2) & \ 8 \frac{1}{10} \\
3) & \ 12 \frac{2}{15} \\
4) & \ 11 \frac{11}{20} \\
5) & \ 8 \frac{11}{12} \\
6) & \ 12 \frac{3}{20} \\
7) & \ 9 \frac{9}{20} \\
8) & \ 11 \frac{3}{10} \\
9) & \ 12 \frac{1}{10} \\
10) & \ 14
\end{aligned}
}
\]