Let’s solve each proportion step by step. We’ll use cross-multiplication: if $\frac{A}{B} = \frac{C}{D}$, then $A \cdot D = B \cdot C$. Then we solve for the missing variable.
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a) $\frac{40}{24} = \frac{20}{a}$
Cross-multiply: $40 \cdot a = 24 \cdot 20$
→ $40a = 480$
Divide both sides by 40: $a = 12$
✔ Check: $\frac{40}{24} = \frac{5}{3}$, and $\frac{20}{12} = \frac{5}{3}$ → Correct!
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b) $\frac{33}{a} = \frac{11}{16}$
Cross-multiply: $33 \cdot 16 = 11 \cdot a$
→ $528 = 11a$
Divide by 11: $a = 48$
✔ Check: $\frac{33}{48} = \frac{11}{16}$ → Yes (divide numerator and denominator by 3)
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c) $\frac{20}{b} = \frac{40}{26}$
Cross-multiply: $20 \cdot 26 = 40 \cdot b$
→ $520 = 40b$
Divide by 40: $b = 13$
✔ Check: $\frac{20}{13} = \frac{40}{26}$? → $\frac{40}{26} = \frac{20}{13}$ → Yes!
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d) $\frac{10}{8} = \frac{b}{24}$
Cross-multiply: $10 \cdot 24 = 8 \cdot b$
→ $240 = 8b$
Divide by 8: $b = 30$
✔ Check: $\frac{10}{8} = \frac{5}{4}$, $\frac{30}{24} = \frac{5}{4}$ → Correct!
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e) $\frac{35}{a} = \frac{7}{2}$
Cross-multiply: $35 \cdot 2 = 7 \cdot a$
→ $70 = 7a$
Divide by 7: $a = 10$
✔ Check: $\frac{35}{10} = \frac{7}{2}$ → Yes!
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f) $\frac{44}{c} = \frac{22}{94}$
Cross-multiply: $44 \cdot 94 = 22 \cdot c$
First, calculate $44 \cdot 94$:
$44 \cdot 90 = 3960$, $44 \cdot 4 = 176$, total = $3960 + 176 = 4136$
So: $4136 = 22c$
Divide by 22: $c = 188$
✔ Check: $\frac{44}{188} = \frac{11}{47}$, $\frac{22}{94} = \frac{11}{47}$ → Correct!
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g) $\frac{x}{6} = \frac{22}{44}$
Simplify right side: $\frac{22}{44} = \frac{1}{2}$
So: $\frac{x}{6} = \frac{1}{2}$
Multiply both sides by 6: $x = 3$
✔ Check: $\frac{3}{6} = \frac{1}{2}$ → Yes!
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h) $\frac{y}{10} = \frac{36}{20}$
Simplify right side: $\frac{36}{20} = \frac{9}{5}$
So: $\frac{y}{10} = \frac{9}{5}$
Multiply both sides by 10: $y = 18$
✔ Check: $\frac{18}{10} = \frac{9}{5}$ → Yes!
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i) $\frac{15}{45} = \frac{9}{y}$
Simplify left side: $\frac{15}{45} = \frac{1}{3}$
So: $\frac{1}{3} = \frac{9}{y}$
Cross-multiply: $1 \cdot y = 3 \cdot 9$ → $y = 27$
✔ Check: $\frac{9}{27} = \frac{1}{3}$ → Yes!
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j) $\frac{40}{25} = \frac{b}{20}$
Simplify left side: $\frac{40}{25} = \frac{8}{5}$
So: $\frac{8}{5} = \frac{b}{20}$
Multiply both sides by 20: $b = \frac{8}{5} \cdot 20 = 8 \cdot 4 = 32$
✔ Check: $\frac{32}{20} = \frac{8}{5}$ → Yes!
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k) $\frac{z}{5} = \frac{20}{25}$
Simplify right side: $\frac{20}{25} = \frac{4}{5}$
So: $\frac{z}{5} = \frac{4}{5}$ → $z = 4$
✔ Check: $\frac{4}{5} = \frac{20}{25}$ → Yes!
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l) $\frac{14}{20} = \frac{28}{y}$
Simplify left side: $\frac{14}{20} = \frac{7}{10}$
So: $\frac{7}{10} = \frac{28}{y}$
Cross-multiply: $7y = 280$ → $y = 40$
✔ Check: $\frac{28}{40} = \frac{7}{10}$ → Yes!
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Final Answer:
a = 12
a = 48
b = 13
b = 30
a = 10
c = 188
x = 3
y = 18
y = 27
b = 32
z = 4
y = 40
Parent Tip: Review the logic above to help your child master the concept of proportion worksheet pdf.
