Cross Multiplication Worksheets - 15 Worksheets Library - Free Printable

The task involves solving the addition of proper fractions using cross multiplication. Let's go through each problem step by step.

Cross Multiplication Method

To add two fractions $\frac{a}{b} + \frac{c}{d}$, follow these steps:
1. Multiply the numerator of the first fraction by the denominator of the second fraction: $a \cdot d$.
2. Multiply the numerator of the second fraction by the denominator of the first fraction: $c \cdot b$.
3. Add the results from steps 1 and 2 to get the new numerator: $a \cdot d + c \cdot b$.
4. Multiply the denominators of both fractions to get the new denominator: $b \cdot d$.
5. Simplify the resulting fraction if possible.

Solutions

#### Problem 1: $\frac{3}{5} + \frac{4}{15}$
- Numerators: $3$ and $4$
- Denominators: $5$ and $15$
- Cross multiply:
- $3 \cdot 15 = 45$
- $4 \cdot 5 = 20$
- Add the results: $45 + 20 = 65$
- Multiply the denominators: $5 \cdot 15 = 75$
- Result: $\frac{65}{75}$
- Simplify: $\frac{65}{75} = \frac{13}{15}$ (divide numerator and denominator by 5)

Answer: $\boxed{\frac{13}{15}}$

#### Problem 2: $\frac{1}{3} + \frac{5}{9}$
- Numerators: $1$ and $5$
- Denominators: $3$ and $9$
- Cross multiply:
- $1 \cdot 9 = 9$
- $5 \cdot 3 = 15$
- Add the results: $9 + 15 = 24$
- Multiply the denominators: $3 \cdot 9 = 27$
- Result: $\frac{24}{27}$
- Simplify: $\frac{24}{27} = \frac{8}{9}$ (divide numerator and denominator by 3)

Answer: $\boxed{\frac{8}{9}}$

#### Problem 3: $\frac{1}{4} + \frac{3}{8}$
- Numerators: $1$ and $3$
- Denominators: $4$ and $8$
- Cross multiply:
- $1 \cdot 8 = 8$
- $3 \cdot 4 = 12$
- Add the results: $8 + 12 = 20$
- Multiply the denominators: $4 \cdot 8 = 32$
- Result: $\frac{20}{32}$
- Simplify: $\frac{20}{32} = \frac{5}{8}$ (divide numerator and denominator by 4)

Answer: $\boxed{\frac{5}{8}}$

#### Problem 4: $\frac{1}{4} + \frac{7}{15}$
- Numerators: $1$ and $7$
- Denominators: $4$ and $15$
- Cross multiply:
- $1 \cdot 15 = 15$
- $7 \cdot 4 = 28$
- Add the results: $15 + 28 = 43$
- Multiply the denominators: $4 \cdot 15 = 60$
- Result: $\frac{43}{60}$

Answer: $\boxed{\frac{43}{60}}$

#### Problem 5: $\frac{1}{3} + \frac{4}{10}$
- Numerators: $1$ and $4$
- Denominators: $3$ and $10$
- Cross multiply:
- $1 \cdot 10 = 10$
- $4 \cdot 3 = 12$
- Add the results: $10 + 12 = 22$
- Multiply the denominators: $3 \cdot 10 = 30$
- Result: $\frac{22}{30}$
- Simplify: $\frac{22}{30} = \frac{11}{15}$ (divide numerator and denominator by 2)

Answer: $\boxed{\frac{11}{15}}$

#### Problem 6: $\frac{2}{7} + \frac{1}{14}$
- Numerators: $2$ and $1$
- Denominators: $7$ and $14$
- Cross multiply:
- $2 \cdot 14 = 28$
- $1 \cdot 7 = 7$
- Add the results: $28 + 7 = 35$
- Multiply the denominators: $7 \cdot 14 = 98$
- Result: $\frac{35}{98}$
- Simplify: $\frac{35}{98} = \frac{5}{14}$ (divide numerator and denominator by 7)

Answer: $\boxed{\frac{5}{14}}$

#### Problem 7: $\frac{1}{3} + \frac{7}{15}$
- Numerators: $1$ and $7$
- Denominators: $3$ and $15$
- Cross multiply:
- $1 \cdot 15 = 15$
- $7 \cdot 3 = 21$
- Add the results: $15 + 21 = 36$
- Multiply the denominators: $3 \cdot 15 = 45$
- Result: $\frac{36}{45}$
- Simplify: $\frac{36}{45} = \frac{4}{5}$ (divide numerator and denominator by 9)

Answer: $\boxed{\frac{4}{5}}$

#### Problem 8: $\frac{5}{8} + \frac{1}{3}$
- Numerators: $5$ and $1$
- Denominators: $8$ and $3$
- Cross multiply:
- $5 \cdot 3 = 15$
- $1 \cdot 8 = 8$
- Add the results: $15 + 8 = 23$
- Multiply the denominators: $8 \cdot 3 = 24$
- Result: $\frac{23}{24}$

Answer: $\boxed{\frac{23}{24}}$

#### Problem 9: $\frac{3}{7} + \frac{2}{10}$
- Numerators: $3$ and $2$
- Denominators: $7$ and $10$
- Cross multiply:
- $3 \cdot 10 = 30$
- $2 \cdot 7 = 14$
- Add the results: $30 + 14 = 44$
- Multiply the denominators: $7 \cdot 10 = 70$
- Result: $\frac{44}{70}$
- Simplify: $\frac{44}{70} = \frac{22}{35}$ (divide numerator and denominator by 2)

Answer: $\boxed{\frac{22}{35}}$

#### Problem 10: $\frac{1}{6} + \frac{3}{5}$
- Numerators: $1$ and $3$
- Denominators: $6$ and $5$
- Cross multiply:
- $1 \cdot 5 = 5$
- $3 \cdot 6 = 18$
- Add the results: $5 + 18 = 23$
- Multiply the denominators: $6 \cdot 5 = 30$
- Result: $\frac{23}{30}$

Answer: $\boxed{\frac{23}{30}}$

#### Problem 11: $\frac{1}{4} + \frac{3}{10}$
- Numerators: $1$ and $3$
- Denominators: $4$ and $10$
- Cross multiply:
- $1 \cdot 10 = 10$
- $3 \cdot 4 = 12$
- Add the results: $10 + 12 = 22$
- Multiply the denominators: $4 \cdot 10 = 40$
- Result: $\frac{22}{40}$
- Simplify: $\frac{22}{40} = \frac{11}{20}$ (divide numerator and denominator by 2)

Answer: $\boxed{\frac{11}{20}}$

#### Problem 12: $\frac{7}{15} + \frac{2}{5}$
- Numerators: $7$ and $2$
- Denominators: $15$ and $5$
- Cross multiply:
- $7 \cdot 5 = 35$
- $2 \cdot 15 = 30$
- Add the results: $35 + 30 = 65$
- Multiply the denominators: $15 \cdot 5 = 75$
- Result: $\frac{65}{75}$
- Simplify: $\frac{65}{75} = \frac{13}{15}$ (divide numerator and denominator by 5)

Answer: $\boxed{\frac{13}{15}}$

Final Answers

1. $\boxed{\frac{13}{15}}$
2. $\boxed{\frac{8}{9}}$
3. $\boxed{\frac{5}{8}}$
4. $\boxed{\frac{43}{60}}$
5. $\boxed{\frac{11}{15}}$
6. $\boxed{\frac{5}{14}}$
7. $\boxed{\frac{4}{5}}$
8. $\boxed{\frac{23}{24}}$
9. $\boxed{\frac{22}{35}}$
10. $\boxed{\frac{23}{30}}$
11. $\boxed{\frac{11}{20}}$
12. $\boxed{\frac{13}{15}}$