Fractions Worksheets | Printable Fractions Worksheets for Teachers - Free Printable

To solve for \( x \) in each of these equivalent fraction problems, we will use the principle of cross-multiplication. The general method is as follows:

Given an equation of the form:
\[
\frac{a}{b} = \frac{x}{c}
\]
we can solve for \( x \) by cross-multiplying:
\[
a \cdot c = b \cdot x
\]
Then, solve for \( x \):
\[
x = \frac{a \cdot c}{b}
\]

Let's solve each problem step by step.

---

Problem 1:

\[
\frac{1}{4} = \frac{x}{6}
\]
Cross-multiply:
\[
1 \cdot 6 = 4 \cdot x \implies 6 = 4x
\]
Solve for \( x \):
\[
x = \frac{6}{4} = \frac{3}{2}
\]

Answer: \( x = \frac{3}{2} \)

---

Problem 2:

\[
\frac{7}{13} = \frac{x}{26}
\]
Cross-multiply:
\[
7 \cdot 26 = 13 \cdot x \implies 182 = 13x
\]
Solve for \( x \):
\[
x = \frac{182}{13} = 14
\]

Answer: \( x = 14 \)

---

Problem 3:

\[
\frac{8}{26} = \frac{x}{13}
\]
Cross-multiply:
\[
8 \cdot 13 = 26 \cdot x \implies 104 = 26x
\]
Solve for \( x \):
\[
x = \frac{104}{26} = 4
\]

Answer: \( x = 4 \)

---

Problem 4:

\[
\frac{x}{12} = \frac{6}{8}
\]
Cross-multiply:
\[
x \cdot 8 = 12 \cdot 6 \implies 8x = 72
\]
Solve for \( x \):
\[
x = \frac{72}{8} = 9
\]

Answer: \( x = 9 \)

---

Problem 5:

\[
\frac{1}{6} = \frac{2}{x}
\]
Cross-multiply:
\[
1 \cdot x = 6 \cdot 2 \implies x = 12
\]

Answer: \( x = 12 \)

---

Problem 6:

\[
\frac{x}{9} = \frac{2}{3}
\]
Cross-multiply:
\[
x \cdot 3 = 9 \cdot 2 \implies 3x = 18
\]
Solve for \( x \):
\[
x = \frac{18}{3} = 6
\]

Answer: \( x = 6 \)

---

Problem 7:

\[
\frac{2}{x} = \frac{4}{11}
\]
Cross-multiply:
\[
2 \cdot 11 = 4 \cdot x \implies 22 = 4x
\]
Solve for \( x \):
\[
x = \frac{22}{4} = \frac{11}{2}
\]

Answer: \( x = \frac{11}{2} \)

---

Problem 8:

\[
\frac{x}{7} = \frac{8}{14}
\]
Simplify \( \frac{8}{14} \) to \( \frac{4}{7} \):
\[
\frac{x}{7} = \frac{4}{7}
\]
Cross-multiply:
\[
x \cdot 7 = 7 \cdot 4 \implies 7x = 28
\]
Solve for \( x \):
\[
x = \frac{28}{7} = 4
\]

Answer: \( x = 4 \)

---

Problem 9:

\[
\frac{x}{14} = \frac{6}{7}
\]
Cross-multiply:
\[
x \cdot 7 = 14 \cdot 6 \implies 7x = 84
\]
Solve for \( x \):
\[
x = \frac{84}{7} = 12
\]

Answer: \( x = 12 \)

---

Problem 10:

\[
\frac{x}{12} = \frac{4}{6}
\]
Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \):
\[
\frac{x}{12} = \frac{2}{3}
\]
Cross-multiply:
\[
x \cdot 3 = 12 \cdot 2 \implies 3x = 24
\]
Solve for \( x \):
\[
x = \frac{24}{3} = 8
\]

Answer: \( x = 8 \)

---

Problem 11:

\[
\frac{3}{14} = \frac{x}{7}
\]
Cross-multiply:
\[
3 \cdot 7 = 14 \cdot x \implies 21 = 14x
\]
Solve for \( x \):
\[
x = \frac{21}{14} = \frac{3}{2}
\]

Answer: \( x = \frac{3}{2} \)

---

Problem 12:

\[
\frac{9}{x} = \frac{1}{4}
\]
Cross-multiply:
\[
9 \cdot 4 = 1 \cdot x \implies 36 = x
\]

Answer: \( x = 36 \)

---

Problem 13:

\[
\frac{5}{x} = \frac{9}{14}
\]
Cross-multiply:
\[
5 \cdot 14 = 9 \cdot x \implies 70 = 9x
\]
Solve for \( x \):
\[
x = \frac{70}{9}
\]

Answer: \( x = \frac{70}{9} \)

---

Problem 14:

\[
\frac{4}{5} = \frac{3}{x}
\]
Cross-multiply:
\[
4 \cdot x = 5 \cdot 3 \implies 4x = 15
\]
Solve for \( x \):
\[
x = \frac{15}{4}
\]

Answer: \( x = \frac{15}{4} \)

---

Problem 15:

\[
\frac{6}{7} = \frac{x}{21}
\]
Cross-multiply:
\[
6 \cdot 21 = 7 \cdot x \implies 126 = 7x
\]
Solve for \( x \):
\[
x = \frac{126}{7} = 18
\]

Answer: \( x = 18 \)

---

Problem 16:

\[
\frac{7}{9} = \frac{x}{27}
\]
Cross-multiply:
\[
7 \cdot 27 = 9 \cdot x \implies 189 = 9x
\]
Solve for \( x \):
\[
x = \frac{189}{9} = 21
\]

Answer: \( x = 21 \)

---

Problem 17:

\[
\frac{5}{x} = \frac{2}{9}
\]
Cross-multiply:
\[
5 \cdot 9 = 2 \cdot x \implies 45 = 2x
\]
Solve for \( x \):
\[
x = \frac{45}{2}
\]

Answer: \( x = \frac{45}{2} \)

---

Problem 18:

\[
\frac{1}{6} = \frac{x}{24}
\]
Cross-multiply:
\[
1 \cdot 24 = 6 \cdot x \implies 24 = 6x
\]
Solve for \( x \):
\[
x = \frac{24}{6} = 4
\]

Answer: \( x = 4 \)

---

Problem 19:

\[
\frac{8}{11} = \frac{10}{x}
\]
Cross-multiply:
\[
8 \cdot x = 11 \cdot 10 \implies 8x = 110
\]
Solve for \( x \):
\[
x = \frac{110}{8} = \frac{55}{4}
\]

Answer: \( x = \frac{55}{4} \)

---

Problem 20:

\[
\frac{6}{8} = \frac{x}{16}
\]
Simplify \( \frac{6}{8} \) to \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{x}{16}
\]
Cross-multiply:
\[
3 \cdot 16 = 4 \cdot x \implies 48 = 4x
\]
Solve for \( x \):
\[
x = \frac{48}{4} = 12
\]

Answer: \( x = 12 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{3}{2} \\
2. & 14 \\
3. & 4 \\
4. & 9 \\
5. & 12 \\
6. & 6 \\
7. & \frac{11}{2} \\
8. & 4 \\
9. & 12 \\
10. & 8 \\
11. & \frac{3}{2} \\
12. & 36 \\
13. & \frac{70}{9} \\
14. & \frac{15}{4} \\
15. & 18 \\
16. & 21 \\
17. & \frac{45}{2} \\
18. & 4 \\
19. & \frac{55}{4} \\
20. & 12 \\
\end{array}
}
\]