Let’s solve each proportion step by step. Remember: to solve a proportion like $\frac{a}{b} = \frac{c}{d}$, you can cross-multiply: $a \cdot d = b \cdot c$, then solve for the missing variable.
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1. $\frac{4}{9} = \frac{10}{x}$
Cross-multiply: $4 \cdot x = 9 \cdot 10$ → $4x = 90$
Divide both sides by 4: $x = \frac{90}{4} = 22.5$
✔ Answer: 22.5
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2. $\frac{5}{2} = \frac{6}{x}$
Cross-multiply: $5 \cdot x = 2 \cdot 6$ → $5x = 12$
Divide by 5: $x = \frac{12}{5} = 2.4$
✔ Answer: 2.4
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3. $\frac{5}{2} = \frac{2}{x}$
Cross-multiply: $5 \cdot x = 2 \cdot 2$ → $5x = 4$
Divide by 5: $x = \frac{4}{5} = 0.8$
✔ Answer: 0.8
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4. $\frac{21}{27} = \frac{x}{18}$
Cross-multiply: $21 \cdot 18 = 27 \cdot x$ → $378 = 27x$
Divide by 27: $x = \frac{378}{27} = 14$
✔ Answer: 14
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5. $\frac{15}{21} = \frac{20}{y}$
Cross-multiply: $15 \cdot y = 21 \cdot 20$ → $15y = 420$
Divide by 15: $y = \frac{420}{15} = 28$
✔ Answer: 28
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6. $\frac{26}{b} = \frac{39}{9}$
Cross-multiply: $26 \cdot 9 = 39 \cdot b$ → $234 = 39b$
Divide by 39: $b = \frac{234}{39} = 6$
✔ Answer: 6
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7. $\frac{h}{108} = \frac{7}{18}$
Cross-multiply: $h \cdot 18 = 108 \cdot 7$ → $18h = 756$
Divide by 18: $h = \frac{756}{18} = 42$
✔ Answer: 42
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8. $\frac{45}{792} = \frac{70}{w}$
Cross-multiply: $45 \cdot w = 792 \cdot 70$ → $45w = 55440$
Divide by 45: $w = \frac{55440}{45} = 1232$
✔ Answer: 1232
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9. $\frac{16}{120} = \frac{j}{15}$
Cross-multiply: $16 \cdot 15 = 120 \cdot j$ → $240 = 120j$
Divide by 120: $j = \frac{240}{120} = 2$
✔ Answer: 2
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10. $\frac{350}{p} = \frac{1050}{60}$
Cross-multiply: $350 \cdot 60 = 1050 \cdot p$ → $21000 = 1050p$
Divide by 1050: $p = \frac{21000}{1050} = 20$
✔ Answer: 20
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11. $\frac{a}{1134} = \frac{27}{729}$
Cross-multiply: $a \cdot 729 = 1134 \cdot 27$ → $729a = 30618$
Divide by 729: $a = \frac{30618}{729} = 42$
✔ Answer: 42
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12. $\frac{40}{65} = \frac{z}{104}$
Cross-multiply: $40 \cdot 104 = 65 \cdot z$ → $4160 = 65z$
Divide by 65: $z = \frac{4160}{65} = 64$
✔ Answer: 64
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13. $\frac{15}{y} = \frac{40}{12}$
Cross-multiply: $15 \cdot 12 = 40 \cdot y$ → $180 = 40y$
Divide by 40: $y = \frac{180}{40} = 4.5$
✔ Answer: 4.5
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14. $\frac{y}{32} = \frac{16}{10}$
Cross-multiply: $y \cdot 10 = 32 \cdot 16$ → $10y = 512$
Divide by 10: $y = \frac{512}{10} = 51.2$
✔ Answer: 51.2
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15. $\frac{32.5}{25} = \frac{97.5}{q}$
Cross-multiply: $32.5 \cdot q = 25 \cdot 97.5$ → $32.5q = 2437.5$
Divide by 32.5: $q = \frac{2437.5}{32.5} = 75$
✔ Answer: 75
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Final Answer:
1. 22.5
2. 2.4
3. 0.8
4. 14
5. 28
6. 6
7. 42
8. 1232
9. 2
10. 20
11. 42
12. 64
13. 4.5
14. 51.2
15. 75
Parent Tip: Review the logic above to help your child master the concept of proportion worksheets.
