Cross Multiplication Worksheets - 15 Worksheets Library - Free Printable

To solve the problems using cross multiplication (also known as cross cancelling), we will simplify the fractions by canceling out common factors in the numerators and denominators before multiplying. Let's go through each problem step by step.

---

Problem 1:

$$
\frac{2}{10} \times \frac{5}{4}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(2\).
- The denominator of the second fraction is \(4\). Both can be divided by \(2\):
$$
\frac{2}{10} \times \frac{5}{4} = \frac{1}{10} \times \frac{5}{2}
$$

2. Simplify further:
- The numerator of the second fraction is \(5\).
- The denominator of the first fraction is \(10\). Both can be divided by \(5\):
$$
\frac{1}{10} \times \frac{5}{2} = \frac{1}{2} \times \frac{1}{2}
$$

3. Multiply the simplified fractions:
$$
\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
$$

Answer:
$$
\boxed{\frac{1}{4}}
$$

---

Problem 2:

$$
\frac{4}{21} \times \frac{9}{24}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(9\).
- The denominator of the first fraction is \(21\). Both can be divided by \(3\):
$$
\frac{4}{21} \times \frac{9}{24} = \frac{4}{7} \times \frac{3}{24}
$$

2. Simplify further:
- The numerator of the second fraction is \(3\).
- The denominator of the second fraction is \(24\). Both can be divided by \(3\):
$$
\frac{4}{7} \times \frac{3}{24} = \frac{4}{7} \times \frac{1}{8}
$$

3. Multiply the simplified fractions:
$$
\frac{4}{7} \times \frac{1}{8} = \frac{4 \times 1}{7 \times 8} = \frac{4}{56}
$$

4. Simplify the result:
- Both \(4\) and \(56\) can be divided by \(4\):
$$
\frac{4}{56} = \frac{1}{14}
$$

Answer:
$$
\boxed{\frac{1}{14}}
$$

---

Problem 3:

$$
\frac{15}{28} \times \frac{4}{3}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(4\).
- The denominator of the first fraction is \(28\). Both can be divided by \(4\):
$$
\frac{15}{28} \times \frac{4}{3} = \frac{15}{7} \times \frac{1}{3}
$$

2. Simplify further:
- The numerator of the first fraction is \(15\).
- The denominator of the second fraction is \(3\). Both can be divided by \(3\):
$$
\frac{15}{7} \times \frac{1}{3} = \frac{5}{7} \times \frac{1}{1}
$$

3. Multiply the simplified fractions:
$$
\frac{5}{7} \times \frac{1}{1} = \frac{5 \times 1}{7 \times 1} = \frac{5}{7}
$$

Answer:
$$
\boxed{\frac{5}{7}}
$$

---

Problem 4:

$$
\frac{15}{63} \times \frac{9}{5}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(15\).
- The denominator of the second fraction is \(5\). Both can be divided by \(5\):
$$
\frac{15}{63} \times \frac{9}{5} = \frac{3}{63} \times \frac{9}{1}
$$

2. Simplify further:
- The numerator of the second fraction is \(9\).
- The denominator of the first fraction is \(63\). Both can be divided by \(9\):
$$
\frac{3}{63} \times \frac{9}{1} = \frac{1}{7} \times \frac{1}{1}
$$

3. Multiply the simplified fractions:
$$
\frac{1}{7} \times \frac{1}{1} = \frac{1 \times 1}{7 \times 1} = \frac{1}{7}
$$

Answer:
$$
\boxed{\frac{1}{7}}
$$

---

Problem 5:

$$
\frac{17}{7} \times \frac{14}{51}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(14\).
- The denominator of the first fraction is \(7\). Both can be divided by \(7\):
$$
\frac{17}{7} \times \frac{14}{51} = \frac{17}{1} \times \frac{2}{51}
$$

2. Simplify further:
- The numerator of the first fraction is \(17\).
- The denominator of the second fraction is \(51\). Both can be divided by \(17\):
$$
\frac{17}{1} \times \frac{2}{51} = \frac{1}{1} \times \frac{2}{3}
$$

3. Multiply the simplified fractions:
$$
\frac{1}{1} \times \frac{2}{3} = \frac{1 \times 2}{1 \times 3} = \frac{2}{3}
$$

Answer:
$$
\boxed{\frac{2}{3}}
$$

---

Problem 6:

$$
\frac{4}{15} \times \frac{9}{48}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(4\).
- The denominator of the second fraction is \(48\). Both can be divided by \(4\):
$$
\frac{4}{15} \times \frac{9}{48} = \frac{1}{15} \times \frac{9}{12}
$$

2. Simplify further:
- The numerator of the second fraction is \(9\).
- The denominator of the second fraction is \(12\). Both can be divided by \(3\):
$$
\frac{1}{15} \times \frac{9}{12} = \frac{1}{15} \times \frac{3}{4}
$$

3. Multiply the simplified fractions:
$$
\frac{1}{15} \times \frac{3}{4} = \frac{1 \times 3}{15 \times 4} = \frac{3}{60}
$$

4. Simplify the result:
- Both \(3\) and \(60\) can be divided by \(3\):
$$
\frac{3}{60} = \frac{1}{20}
$$

Answer:
$$
\boxed{\frac{1}{20}}
$$

---

Problem 7:

$$
\frac{36}{5} \times \frac{5}{12}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(5\).
- The denominator of the first fraction is \(5\). Both can be divided by \(5\):
$$
\frac{36}{5} \times \frac{5}{12} = \frac{36}{1} \times \frac{1}{12}
$$

2. Simplify further:
- The numerator of the first fraction is \(36\).
- The denominator of the second fraction is \(12\). Both can be divided by \(12\):
$$
\frac{36}{1} \times \frac{1}{12} = \frac{3}{1} \times \frac{1}{1}
$$

3. Multiply the simplified fractions:
$$
\frac{3}{1} \times \frac{1}{1} = \frac{3 \times 1}{1 \times 1} = 3
$$

Answer:
$$
\boxed{3}
$$

---

Problem 8:

$$
\frac{25}{35} \times \frac{7}{15}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(25\).
- The denominator of the second fraction is \(15\). Both can be divided by \(5\):
$$
\frac{25}{35} \times \frac{7}{15} = \frac{5}{35} \times \frac{7}{3}
$$

2. Simplify further:
- The numerator of the second fraction is \(7\).
- The denominator of the first fraction is \(35\). Both can be divided by \(7\):
$$
\frac{5}{35} \times \frac{7}{3} = \frac{5}{5} \times \frac{1}{3}
$$

3. Multiply the simplified fractions:
$$
\frac{5}{5} \times \frac{1}{3} = \frac{1}{1} \times \frac{1}{3} = \frac{1}{3}
$$

Answer:
$$
\boxed{\frac{1}{3}}
$$

---

Problem 9:

$$
\frac{15}{26} \times \frac{13}{10}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(13\).
- The denominator of the first fraction is \(26\). Both can be divided by \(13\):
$$
\frac{15}{26} \times \frac{13}{10} = \frac{15}{2} \times \frac{1}{10}
$$

2. Simplify further:
- The numerator of the first fraction is \(15\).
- The denominator of the second fraction is \(10\). Both can be divided by \(5\):
$$
\frac{15}{2} \times \frac{1}{10} = \frac{3}{2} \times \frac{1}{2}
$$

3. Multiply the simplified fractions:
$$
\frac{3}{2} \times \frac{1}{2} = \frac{3 \times 1}{2 \times 2} = \frac{3}{4}
$$

Answer:
$$
\boxed{\frac{3}{4}}
$$

---

Problem 10:

$$
\frac{25}{21} \times \frac{7}{15}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(7\).
- The denominator of the first fraction is \(21\). Both can be divided by \(7\):
$$
\frac{25}{21} \times \frac{7}{15} = \frac{25}{3} \times \frac{1}{15}
$$

2. Simplify further:
- The numerator of the first fraction is \(25\).
- The denominator of the second fraction is \(15\). Both can be divided by \(5\):
$$
\frac{25}{3} \times \frac{1}{15} = \frac{5}{3} \times \frac{1}{3}
$$

3. Multiply the simplified fractions:
$$
\frac{5}{3} \times \frac{1}{3} = \frac{5 \times 1}{3 \times 3} = \frac{5}{9}
$$

Answer:
$$
\boxed{\frac{5}{9}}
$$

---

Problem 11:

$$
\frac{40}{77} \times \frac{11}{8}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(11\).
- The denominator of the first fraction is \(77\). Both can be divided by \(11\):
$$
\frac{40}{77} \times \frac{11}{8} = \frac{40}{7} \times \frac{1}{8}
$$

2. Simplify further:
- The numerator of the first fraction is \(40\).
- The denominator of the second fraction is \(8\). Both can be divided by \(8\):
$$
\frac{40}{7} \times \frac{1}{8} = \frac{5}{7} \times \frac{1}{1}
$$

3. Multiply the simplified fractions:
$$
\frac{5}{7} \times \frac{1}{1} = \frac{5 \times 1}{7 \times 1} = \frac{5}{7}
$$

Answer:
$$
\boxed{\frac{5}{7}}
$$

---

Problem 12:

$$
\frac{8}{25} \times \frac{10}{36}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(10\).
- The denominator of the first fraction is \(25\). Both can be divided by \(5\):
$$
\frac{8}{25} \times \frac{10}{36} = \frac{8}{5} \times \frac{2}{36}
$$

2. Simplify further:
- The numerator of the second fraction is \(2\).
- The denominator of the second fraction is \(36\). Both can be divided by \(2\):
$$
\frac{8}{5} \times \frac{2}{36} = \frac{8}{5} \times \frac{1}{18}
$$

3. Simplify further:
- The numerator of the first fraction is \(8\).
- The denominator of the second fraction is \(18\). Both can be divided by \(2\):
$$
\frac{8}{5} \times \frac{1}{18} = \frac{4}{5} \times \frac{1}{9}
$$

4. Multiply the simplified fractions:
$$
\frac{4}{5} \times \frac{1}{9} = \frac{4 \times 1}{5 \times 9} = \frac{4}{45}
$$

Answer:
$$
\boxed{\frac{4}{45}}
$$

---

Problem 13:

$$
\frac{25}{49} \times \frac{7}{15}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(7\).
- The denominator of the first fraction is \(49\). Both can be divided by \(7\):
$$
\frac{25}{49} \times \frac{7}{15} = \frac{25}{7} \times \frac{1}{15}
$$

2. Simplify further:
- The numerator of the first fraction is \(25\).
- The denominator of the second fraction is \(15\). Both can be divided by \(5\):
$$
\frac{25}{7} \times \frac{1}{15} = \frac{5}{7} \times \frac{1}{3}
$$

3. Multiply the simplified fractions:
$$
\frac{5}{7} \times \frac{1}{3} = \frac{5 \times 1}{7 \times 3} = \frac{5}{21}
$$

Answer:
$$
\boxed{\frac{5}{21}}
$$

---

Problem 14:

$$
\frac{50}{55} \times \frac{11}{45}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(50\).
- The denominator of the second fraction is \(45\). Both can be divided by \(5\):
$$
\frac{50}{55} \times \frac{11}{45} = \frac{10}{55} \times \frac{11}{9}
$$

2. Simplify further:
- The numerator of the second fraction is \(11\).
- The denominator of the first fraction is \(55\). Both can be divided by \(11\):
$$
\frac{10}{55} \times \frac{11}{9} = \frac{10}{5} \times \frac{1}{9}
$$

3. Simplify further:
- The numerator of the first fraction is \(10\).
- The denominator of the first fraction is \(5\). Both can be divided by \(5\):
$$
\frac{10}{5} \times \frac{1}{9} = \frac{2}{1} \times \frac{1}{9}
$$

4. Multiply the simplified fractions:
$$
\frac{2}{1} \times \frac{1}{9} = \frac{2 \times 1}{1 \times 9} = \frac{2}{9}
$$

Answer:
$$
\boxed{\frac{2}{9}}
$$

---

Problem 15:

$$
\frac{10}{21} \times \frac{6}{15}
$$

1. Cancel common factors:
- The numerator of the second fraction is \(6\).
- The denominator of the first fraction is \(21\). Both can be divided by \(3\):
$$
\frac{10}{21} \times \frac{6}{15} = \frac{10}{7} \times \frac{2}{15}
$$

2. Simplify further:
- The numerator of the first fraction is \(10\).
- The denominator of the second fraction is \(15\). Both can be divided by \(5\):
$$
\frac{10}{7} \times \frac{2}{15} = \frac{2}{7} \times \frac{2}{3}
$$

3. Multiply the simplified fractions:
$$
\frac{2}{7} \times \frac{2}{3} = \frac{2 \times 2}{7 \times 3} = \frac{4}{21}
$$

Answer:
$$
\boxed{\frac{4}{21}}
$$

---

Problem 16:

$$
\frac{30}{55} \times \frac{25}{35}
$$

1. Cancel common factors:
- The numerator of the first fraction is \(30\).
- The denominator of the second fraction is \(35\). Both can be divided by \(5\):
$$
\frac{30}{55} \times \frac{25}{35} = \frac{6}{55} \times \frac{5}{7}
$$

2. Simplify further:
- The numerator of the second fraction is \(5\).
- The denominator of the first fraction is \(55\). Both can be divided by \(5\):
$$
\frac{6}{55} \times \frac{5}{7} = \frac{6}{11} \times \frac{1}{7}
$$

3. Multiply the simplified fractions:
$$
\frac{6}{11} \times \frac{1}{7} = \frac{6 \times 1}{11 \times 7} = \frac{6}{77}
$$

Answer:
$$
\boxed{\frac{6}{77}}
$$

---

Final Answers:

$$
\boxed{
\begin{array}{ll}
1) & \frac{1}{4} \\
2) & \frac{1}{14} \\
3) & \frac{5}{7} \\
4) & \frac{1}{7} \\
5) & \frac{2}{3} \\
6) & \frac{1}{20} \\
7) & 3 \\
8) & \frac{1}{3} \\
9) & \frac{3}{4} \\
10) & \frac{5}{9} \\
11) & \frac{5}{7} \\
12) & \frac{4}{45} \\
13) & \frac{5}{21} \\
14) & \frac{2}{9} \\
15) & \frac{4}{21} \\
16) & \frac{6}{77} \\
\end{array}
}
$$