Cross Multiplication worksheet featuring ten equations to solve for x using cross-multiplication method.

Let’s solve each problem step by step using cross multiplication.

Cross multiplication means:
If you have $\frac{a}{b} = \frac{c}{d}$, then $a \cdot d = b \cdot c$.

We’ll apply this to each equation and solve for $x$.

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a) $\frac{x}{5} = \frac{5}{2}$

Cross multiply:
$x \cdot 2 = 5 \cdot 5$
→ $2x = 25$
→ $x = \frac{25}{2} = 12.5$

✔ Check: $\frac{12.5}{5} = 2.5$, and $\frac{5}{2} = 2.5$ → Correct.

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b) $\frac{2x}{6} = \frac{4}{3}$

Cross multiply:
$2x \cdot 3 = 6 \cdot 4$
→ $6x = 24$
→ $x = 4$

✔ Check: $\frac{2(4)}{6} = \frac{8}{6} = \frac{4}{3}$ → Correct.

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c) $\frac{9}{6} = \frac{x}{2}$

Cross multiply:
$9 \cdot 2 = 6 \cdot x$
→ $18 = 6x$
→ $x = 3$

✔ Check: $\frac{9}{6} = 1.5$, $\frac{3}{2} = 1.5$ → Correct.

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d) $\frac{2}{10} = \frac{10}{x}$

Cross multiply:
$2 \cdot x = 10 \cdot 10$
→ $2x = 100$
→ $x = 50$

✔ Check: $\frac{2}{10} = 0.2$, $\frac{10}{50} = 0.2$ → Correct.

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e) $\frac{8}{4} = \frac{2}{x}$

Simplify left side first: $\frac{8}{4} = 2$, so $2 = \frac{2}{x}$
Then: $2x = 2$ → $x = 1$

Or cross multiply directly:
$8 \cdot x = 4 \cdot 2$
→ $8x = 8$
→ $x = 1$

✔ Check: $\frac{8}{4} = 2$, $\frac{2}{1} = 2$ → Correct.

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f) $\frac{x}{8} = \frac{10}{2}$

Right side simplifies to 5: $\frac{10}{2} = 5$, so $\frac{x}{8} = 5$ → $x = 40$

Or cross multiply:
$x \cdot 2 = 8 \cdot 10$
→ $2x = 80$
→ $x = 40$

✔ Check: $\frac{40}{8} = 5$, $\frac{10}{2} = 5$ → Correct.

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g) $\frac{x + 2}{4} = \frac{2}{3}$

Cross multiply:
$(x + 2) \cdot 3 = 4 \cdot 2$
→ $3(x + 2) = 8$
→ $3x + 6 = 8$
→ $3x = 2$
→ $x = \frac{2}{3}$

✔ Check: Left: $\frac{\frac{2}{3} + 2}{4} = \frac{\frac{8}{3}}{4} = \frac{8}{12} = \frac{2}{3}$ → Matches right side.

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h) $\frac{2x + 1}{2} = \frac{5}{2}$

Since denominators are same, numerators must be equal:
$2x + 1 = 5$
→ $2x = 4$
→ $x = 2$

Or cross multiply (same result):
$(2x + 1) \cdot 2 = 2 \cdot 5$
→ $4x + 2 = 10$
→ $4x = 8$
→ $x = 2$

✔ Check: $\frac{2(2)+1}{2} = \frac{5}{2}$ → Correct.

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i) $\frac{x + 2}{x + 3} = \frac{2}{5}$

Cross multiply:
$(x + 2) \cdot 5 = (x + 3) \cdot 2$
→ $5x + 10 = 2x + 6$
Subtract $2x$ from both sides:
→ $3x + 10 = 6$
Subtract 10:
→ $3x = -4$
→ $x = -\frac{4}{3}$

✔ Check:
Left: $\frac{-\frac{4}{3} + 2}{-\frac{4}{3} + 3} = \frac{\frac{2}{3}}{\frac{5}{3}} = \frac{2}{5}$ → Correct.

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j) $\frac{9}{4} = \frac{2x + 1}{x - 1}$

Cross multiply:
$9 \cdot (x - 1) = 4 \cdot (2x + 1)$
→ $9x - 9 = 8x + 4$
Subtract $8x$:
→ $x - 9 = 4$
Add 9:
→ $x = 13$

✔ Check:
Right: $\frac{2(13) + 1}{13 - 1} = \frac{27}{12} = \frac{9}{4}$ → Matches left side.

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Final Answer:

a) 12.5
b) 4
c) 3
d) 50
e) 1
f) 40
g) 2/3
h) 2
i) -4/3
j) 13