A Worksheet on Adding and Multiplying Fractions - Free Printable

Problem Overview:

The task involves solving four sets of calculations involving fractions. The problems are divided into three sections:
1. Red Box: Addition and subtraction of fractions.
2. Green Box: Multiplication and division of fractions.
3. Blue Box: Mixed operations involving addition, subtraction, multiplication, and division, including mixed numbers.

We will solve each problem step by step.

---

Red Box: Addition and Subtraction of Fractions

#### 1) $\frac{4}{6} + \frac{1}{6}$
- Both fractions have the same denominator (6), so we can add the numerators directly:
$$
\frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}
$$

#### 2) $\frac{4}{7} - \frac{3}{7}$
- Both fractions have the same denominator (7), so we subtract the numerators:
$$
\frac{4}{7} - \frac{3}{7} = \frac{4 - 3}{7} = \frac{1}{7}
$$

#### 3) $\frac{8}{10} - \frac{4}{10}$
- Both fractions have the same denominator (10), so we subtract the numerators:
$$
\frac{8}{10} - \frac{4}{10} = \frac{8 - 4}{10} = \frac{4}{10} = \frac{2}{5} \quad (\text{Simplify by dividing by 2})
$$

#### 4) $\frac{1}{6} + \frac{2}{6}$
- Both fractions have the same denominator (6), so we add the numerators:
$$
\frac{1}{6} + \frac{2}{6} = \frac{1 + 2}{6} = \frac{3}{6} = \frac{1}{2} \quad (\text{Simplify by dividing by 3})
$$

#### 5) $\frac{11}{15} - \frac{5}{15}$
- Both fractions have the same denominator (15), so we subtract the numerators:
$$
\frac{11}{15} - \frac{5}{15} = \frac{11 - 5}{15} = \frac{6}{15} = \frac{2}{5} \quad (\text{Simplify by dividing by 3})
$$

#### 6) $\frac{3}{5} + \frac{4}{5}$
- Both fractions have the same denominator (5), so we add the numerators:
$$
\frac{3}{5} + \frac{4}{5} = \frac{3 + 4}{5} = \frac{7}{5} = 1\frac{2}{5} \quad (\text{Convert to a mixed number})
$$

#### 7) $\frac{2}{6} + \frac{1}{3}$
- The denominators are 6 and 3. The least common denominator (LCD) is 6. Convert $\frac{1}{3}$ to a fraction with denominator 6:
$$
\frac{1}{3} = \frac{2}{6}
$$
Now add:
$$
\frac{2}{6} + \frac{2}{6} = \frac{2 + 2}{6} = \frac{4}{6} = \frac{2}{3} \quad (\text{Simplify by dividing by 2})
$$

#### 8) $\frac{9}{10} - \frac{2}{10}$
- Both fractions have the same denominator (10), so we subtract the numerators:
$$
\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}
$$

#### 9) $\frac{3}{5} - \frac{1}{4}$
- The denominators are 5 and 4. The least common denominator (LCD) is 20. Convert both fractions:
$$
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}, \quad \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
$$
Now subtract:
$$
\frac{12}{20} - \frac{5}{20} = \frac{12 - 5}{20} = \frac{7}{20}
$$

#### 10) $\frac{2}{3} + \frac{1}{2}$
- The denominators are 3 and 2. The least common denominator (LCD) is 6. Convert both fractions:
$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}, \quad \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
$$
Now add:
$$
\frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6} = 1\frac{1}{6} \quad (\text{Convert to a mixed number})
$$

---

Green Box: Multiplication and Division of Fractions

#### 1) $\frac{4}{5} \times \frac{1}{5}$
- Multiply the numerators and the denominators:
$$
\frac{4}{5} \times \frac{1}{5} = \frac{4 \times 1}{5 \times 5} = \frac{4}{25}
$$

#### 2) $\frac{2}{7} \times \frac{3}{4}$
- Multiply the numerators and the denominators:
$$
\frac{2}{7} \times \frac{3}{4} = \frac{2 \times 3}{7 \times 4} = \frac{6}{28} = \frac{3}{14} \quad (\text{Simplify by dividing by 2})
$$

#### 3) $\frac{6}{8} \div \frac{1}{3}$
- Dividing by a fraction is equivalent to multiplying by its reciprocal:
$$
\frac{6}{8} \div \frac{1}{3} = \frac{6}{8} \times \frac{3}{1} = \frac{6 \times 3}{8 \times 1} = \frac{18}{8} = \frac{9}{4} = 2\frac{1}{4} \quad (\text{Simplify and convert to a mixed number})
$$

#### 4) $\frac{5}{8} \times \frac{2}{6}$
- Multiply the numerators and the denominators:
$$
\frac{5}{8} \times \frac{2}{6} = \frac{5 \times 2}{8 \times 6} = \frac{10}{48} = \frac{5}{24} \quad (\text{Simplify by dividing by 2})
$$

#### 5) $\frac{8}{10} \div 2$
- Dividing by 2 is equivalent to multiplying by $\frac{1}{2}$:
$$
\frac{8}{10} \div 2 = \frac{8}{10} \times \frac{1}{2} = \frac{8 \times 1}{10 \times 2} = \frac{8}{20} = \frac{2}{5} \quad (\text{Simplify by dividing by 4})
$$

#### 6) $5 \times \frac{4}{6}$
- Multiply the whole number by the fraction:
$$
5 \times \frac{4}{6} = \frac{5 \times 4}{6} = \frac{20}{6} = \frac{10}{3} = 3\frac{1}{3} \quad (\text{Simplify and convert to a mixed number})
$$

#### 7) $5 - \frac{1}{2}$
- Subtract the fraction from the whole number. Convert 5 to a fraction with denominator 2:
$$
5 = \frac{10}{2}, \quad \frac{10}{2} - \frac{1}{2} = \frac{10 - 1}{2} = \frac{9}{2} = 4\frac{1}{2} \quad (\text{Convert to a mixed number})
$$

#### 8) $\frac{10}{12} \times 4$
- Multiply the fraction by the whole number:
$$
\frac{10}{12} \times 4 = \frac{10 \times 4}{12} = \frac{40}{12} = \frac{10}{3} = 3\frac{1}{3} \quad (\text{Simplify and convert to a mixed number})
$$

#### 9) $\frac{4}{5} \times 3$
- Multiply the fraction by the whole number:
$$
\frac{4}{5} \times 3 = \frac{4 \times 3}{5} = \frac{12}{5} = 2\frac{2}{5} \quad (\text{Convert to a mixed number})
$$

#### 10) $\frac{7}{4} \div 4$
- Dividing by 4 is equivalent to multiplying by $\frac{1}{4}$:
$$
\frac{7}{4} \div 4 = \frac{7}{4} \times \frac{1}{4} = \frac{7 \times 1}{4 \times 4} = \frac{7}{16}
$$

#### 11) $6 \times \frac{1}{4}$
- Multiply the whole number by the fraction:
$$
6 \times \frac{1}{4} = \frac{6 \times 1}{4} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2} \quad (\text{Simplify and convert to a mixed number})
$$

---

Blue Box: Mixed Operations Involving Fractions and Mixed Numbers

#### 1) $1\frac{2}{4} + \frac{2}{5}$
- Convert the mixed number to an improper fraction:
$$
1\frac{2}{4} = \frac{4 \times 1 + 2}{4} = \frac{6}{4} = \frac{3}{2}
$$
- Find a common denominator for $\frac{3}{2}$ and $\frac{2}{5}$. The LCD is 10:
$$
\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}, \quad \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
$$
- Add the fractions:
$$
\frac{15}{10} + \frac{4}{10} = \frac{15 + 4}{10} = \frac{19}{10} = 1\frac{9}{10} \quad (\text{Convert to a mixed number})
$$

#### 2) $\frac{2}{8} + 2\frac{1}{6}$
- Simplify $\frac{2}{8}$:
$$
\frac{2}{8} = \frac{1}{4}
$$
- Convert the mixed number to an improper fraction:
$$
2\frac{1}{6} = \frac{6 \times 2 + 1}{6} = \frac{13}{6}
$$
- Find a common denominator for $\frac{1}{4}$ and $\frac{13}{6}$. The LCD is 12:
$$
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}, \quad \frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}
$$
- Add the fractions:
$$
\frac{3}{12} + \frac{26}{12} = \frac{3 + 26}{12} = \frac{29}{12} = 2\frac{5}{12} \quad (\text{Convert to a mixed number})
$$

#### 3) $2\frac{1}{7} + 1\frac{1}{8}$
- Convert both mixed numbers to improper fractions:
$$
2\frac{1}{7} = \frac{7 \times 2 + 1}{7} = \frac{15}{7}, \quad 1\frac{1}{8} = \frac{8 \times 1 + 1}{8} = \frac{9}{8}
$$
- Find a common denominator for $\frac{15}{7}$ and $\frac{9}{8}$. The LCD is 56:
$$
\frac{15}{7} = \frac{15 \times 8}{7 \times 8} = \frac{120}{56}, \quad \frac{9}{8} = \frac{9 \times 7}{8 \times 7} = \frac{63}{56}
$$
- Add the fractions:
$$
\frac{120}{56} + \frac{63}{56} = \frac{120 + 63}{56} = \frac{183}{56} = 3\frac{15}{56} \quad (\text{Convert to a mixed number})
$$

#### 4) $4\frac{2}{5} + 2$
- Convert the mixed number to an improper fraction:
$$
4\frac{2}{5} = \frac{5 \times 4 + 2}{5} = \frac{22}{5}
$$
- Add the whole number:
$$
\frac{22}{5} + 2 = \frac{22}{5} + \frac{10}{5} = \frac{22 + 10}{5} = \frac{32}{5} = 6\frac{2}{5} \quad (\text{Convert to a mixed number})
$$

#### 5) $1\frac{3}{10} + 3$
- Convert the mixed number to an improper fraction:
$$
1\frac{3}{10} = \frac{10 \times 1 + 3}{10} = \frac{13}{10}
$$
- Add the whole number:
$$
\frac{13}{10} + 3 = \frac{13}{10} + \frac{30}{10} = \frac{13 + 30}{10} = \frac{43}{10} = 4\frac{3}{10} \quad (\text{Convert to a mixed number})
$$

#### 6) $5\frac{4}{5} - \frac{2}{6}$
- Simplify $\frac{2}{6}$:
$$
\frac{2}{6} = \frac{1}{3}
$$
- Convert the mixed number to an improper fraction:
$$
5\frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{29}{5}
$$
- Find a common denominator for $\frac{29}{5}$ and $\frac{1}{3}$. The LCD is 15:
$$
\frac{29}{5} = \frac{29 \times 3}{5 \times 3} = \frac{87}{15}, \quad \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$
- Subtract the fractions:
$$
\frac{87}{15} - \frac{5}{15} = \frac{87 - 5}{15} = \frac{82}{15} = 5\frac{7}{15} \quad (\text{Convert to a mixed number})
$$

#### 7) $2\frac{1}{2} - 1\frac{4}{6}$
- Simplify $\frac{4}{6}$:
$$
\frac{4}{6} = \frac{2}{3}
$$
- Convert both mixed numbers to improper fractions:
$$
2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}, \quad 1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
$$
- Find a common denominator for $\frac{5}{2}$ and $\frac{5}{3}$. The LCD is 6:
$$
\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}, \quad \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
$$
- Subtract the fractions:
$$
\frac{15}{6} - \frac{10}{6} = \frac{15 - 10}{6} = \frac{5}{6}
$$

#### 8) $1\frac{1}{7} \times \frac{2}{4}$
- Simplify $\frac{2}{4}$:
$$
\frac{2}{4} = \frac{1}{2}
$$
- Convert the mixed number to an improper fraction:
$$
1\frac{1}{7} = \frac{7 \times 1 + 1}{7} = \frac{8}{7}
$$
- Multiply the fractions:
$$
\frac{8}{7} \times \frac{1}{2} = \frac{8 \times 1}{7 \times 2} = \frac{8}{14} = \frac{4}{7} \quad (\text{Simplify by dividing by 2})
$$

#### 9) $1\frac{4}{5} \times 7$
- Convert the mixed number to an improper fraction:
$$
1\frac{4}{5} = \frac{5 \times 1 + 4}{5} = \frac{9}{5}
$$
- Multiply the fraction by the whole number:
$$
\frac{9}{5} \times 7 = \frac{9 \times 7}{5} = \frac{63}{5} = 12\frac{3}{5} \quad (\text{Convert to a mixed number})
$$

#### 10) $1\frac{1}{2} - \frac{4}{5}$
- Convert the mixed number to an improper fraction:
$$
1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
$$
- Find a common denominator for $\frac{3}{2}$ and $\frac{4}{5}$. The LCD is 10:
$$
\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}, \quad \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
$$
- Subtract the fractions:
$$
\frac{15}{10} - \frac{8}{10} = \frac{15 - 8}{10} = \frac{7}{10}
$$

#### 11) $2\frac{1}{8} + 1\frac{1}{2}$
- Convert both mixed numbers to improper fractions:
$$
2\frac{1}{8} = \frac{8 \times 2 + 1}{8} = \frac{17}{8}, \quad 1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
$$
- Find a common denominator for $\frac{17}{8}$ and $\frac{3}{2}$. The LCD is 8:
$$
\frac{17}{8} = \frac{17}{8}, \quad \frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8}
$$
- Add the fractions:
$$
\frac{17}{8} + \frac{12}{8} = \frac{17 + 12}{8} = \frac{29}{8} = 3\frac{5}{8} \quad (\text{Convert to a mixed number})
$$

---

Final Answers:

#### Red Box:
1. $\frac{5}{6}$
2. $\frac{1}{7}$
3. $\frac{2}{5}$
4. $\frac{1}{2}$
5. $\frac{2}{5}$
6. $1\frac{2}{5}$
7. $\frac{2}{3}$
8. $\frac{7}{10}$
9. $\frac{7}{20}$
10. $1\frac{1}{6}$

#### Green Box:
1. $\frac{4}{25}$
2. $\frac{3}{14}$
3. $2\frac{1}{4}$
4. $\frac{5}{24}$
5. $\frac{2}{5}$
6. $3\frac{1}{3}$
7. $4\frac{1}{2}$
8. $3\frac{1}{3}$
9. $2\frac{2}{5}$
10. $\frac{7}{16}$
11. $1\frac{1}{2}$

#### Blue Box:
1. $1\frac{9}{10}$
2. $2\frac{5}{12}$
3. $3\frac{15}{56}$
4. $6\frac{2}{5}$
5. $4\frac{3}{10}$
6. $5\frac{7}{15}$
7. $\frac{5}{6}$
8. $\frac{4}{7}$
9. $12\frac{3}{5}$
10. $\frac{7}{10}$
11. $3\frac{5}{8}$

Boxed Final Answer:

$$
\boxed{
\begin{aligned}
&\text{Red Box: } \frac{5}{6}, \frac{1}{7}, \frac{2}{5}, \frac{1}{2}, \frac{2}{5}, 1\frac{2}{5}, \frac{2}{3}, \frac{7}{10}, \frac{7}{20}, 1\frac{1}{6} \\
&\text{Green Box: } \frac{4}{25}, \frac{3}{14}, 2\frac{1}{4}, \frac{5}{24}, \frac{2}{5}, 3\frac{1}{3}, 4\frac{1}{2}, 3\frac{1}{3}, 2\frac{2}{5}, \frac{7}{16}, 1\frac{1}{2} \\
&\text{Blue Box: } 1\frac{9}{10}, 2\frac{5}{12}, 3\frac{15}{56}, 6\frac{2}{5}, 4\frac{3}{10}, 5\frac{7}{15}, \frac{5}{6}, \frac{4}{7}, 12\frac{3}{5}, \frac{7}{10}, 3\frac{5}{8}
\end{aligned}
}
$$