Cross multiplication math worksheet with ten problems to solve for x.

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

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Problem 1:
$\frac{x - 1}{10} = \frac{12}{3}$

Step 1: Simplify the right side: $\frac{12}{3} = 4$
So: $\frac{x - 1}{10} = 4$

Step 2: Multiply both sides by 10:
$x - 1 = 40$

Step 3: Add 1 to both sides:
$x = 41$

✔ Check: $\frac{41 - 1}{10} = \frac{40}{10} = 4$, and $\frac{12}{3} = 4$. Correct.

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Problem 2:
$\frac{12}{x + 1} = \frac{1}{2}$

Cross multiply: $12 \cdot 2 = 1 \cdot (x + 1)$
→ $24 = x + 1$

Subtract 1: $x = 23$

✔ Check: $\frac{12}{23 + 1} = \frac{12}{24} = \frac{1}{2}$. Correct.

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Problem 3:
$\frac{35}{5 + 2x} = \frac{7}{5}$

Cross multiply: $35 \cdot 5 = 7 \cdot (5 + 2x)$
→ $175 = 35 + 14x$

Subtract 35: $140 = 14x$

Divide by 14: $x = 10$

✔ Check: $\frac{35}{5 + 20} = \frac{35}{25} = \frac{7}{5}$. Correct.

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Problem 4:
$\frac{80}{10} = \frac{4x + 8}{3}$

Simplify left: $8 = \frac{4x + 8}{3}$

Multiply both sides by 3: $24 = 4x + 8$

Subtract 8: $16 = 4x$

Divide by 4: $x = 4$

✔ Check: $\frac{4(4) + 8}{3} = \frac{24}{3} = 8$, and $\frac{80}{10} = 8$. Correct.

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Problem 5:
$\frac{12}{42} = \frac{x - 5}{7}$

Simplify left: $\frac{12}{42} = \frac{2}{7}$

So: $\frac{2}{7} = \frac{x - 5}{7}$

Since denominators are same, numerators must be equal:
$2 = x - 5$

Add 5: $x = 7$

✔ Check: $\frac{7 - 5}{7} = \frac{2}{7}$, and $\frac{12}{42} = \frac{2}{7}$. Correct.

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Problem 6:
$\frac{64}{6x - 20} = \frac{8}{2}$

Simplify right: $\frac{8}{2} = 4$

So: $\frac{64}{6x - 20} = 4$

Multiply both sides by $(6x - 20)$:
$64 = 4(6x - 20)$

Divide both sides by 4: $16 = 6x - 20$

Add 20: $36 = 6x$

Divide by 6: $x = 6$

✔ Check: $\frac{64}{6(6) - 20} = \frac{64}{36 - 20} = \frac{64}{16} = 4$, and $\frac{8}{2} = 4$. Correct.

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Problem 7:
$\frac{9}{x - 10} = \frac{81}{18}$

Simplify right: $\frac{81}{18} = \frac{9}{2}$

So: $\frac{9}{x - 10} = \frac{9}{2}$

Numerators are same → denominators must be same:
$x - 10 = 2$

Add 10: $x = 12$

✔ Check: $\frac{9}{12 - 10} = \frac{9}{2}$, and $\frac{81}{18} = \frac{9}{2}$. Correct.

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Problem 8:
$\frac{6}{24} = \frac{x - 8}{48}$

Simplify left: $\frac{6}{24} = \frac{1}{4}$

So: $\frac{1}{4} = \frac{x - 8}{48}$

Cross multiply: $1 \cdot 48 = 4 \cdot (x - 8)$
→ $48 = 4x - 32$

Add 32: $80 = 4x$

Divide by 4: $x = 20$

✔ Check: $\frac{20 - 8}{48} = \frac{12}{48} = \frac{1}{4}$, and $\frac{6}{24} = \frac{1}{4}$. Correct.

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Problem 9:
$\frac{4}{2} = \frac{7x + 45}{26}$

Simplify left: $2 = \frac{7x + 45}{26}$

Multiply both sides by 26: $52 = 7x + 45$

Subtract 45: $7 = 7x$

Divide by 7: $x = 1$

✔ Check: $\frac{7(1) + 45}{26} = \frac{52}{26} = 2$, and $\frac{4}{2} = 2$. Correct.

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Problem 10:
$\frac{3}{2x + 4} = \frac{12}{16}$

Simplify right: $\frac{12}{16} = \frac{3}{4}$

So: $\frac{3}{2x + 4} = \frac{3}{4}$

Numerators same → denominators same:
$2x + 4 = 4$

Subtract 4: $2x = 0$

Divide by 2: $x = 0$

✔ Check: $\frac{3}{2(0) + 4} = \frac{3}{4}$, and $\frac{12}{16} = \frac{3}{4}$. Correct.

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Final Answer:
1) 41
2) 23
3) 10
4) 4
5) 7
6) 6
7) 12
8) 20
9) 1
10) 0