Cross Multiply Maze Worksheet
LABYRINTH OF PROPORTIONS
Cross-Multiplication Maze Challenge
Name:
Date:
Class:
Score:
Expedition Objective: Start at Chamber 1 and navigate to Chamber 16. Solve each proportion using cross multiplication (\(a \cdot d = b \cdot c\)). Follow the arrow of your answer into the next chamber. Watch out: incorrect solutions lead to dead ends! Shade your path as you progress.
START • RM 1 Solve for x
\(\frac{x}{8} = \frac{15}{20}\)
\(x = 10\) ↓
\(x = 6\) →
RM 2 Equivalent Ratio
Which ratio equals
\(6 : 9\)?
\(10:15\) ↓
\(8:14\) →
RM 3 Solve for x
\(\frac{4}{7} = \frac{16}{x}\)
\(x = 21\) ↓
\(x = 28\) →
RM 4 DEAD END
BLOCKED DOOR!
Turn back to RM 2
No exit forward
RM 5 Solve for x
\(\frac{9}{x} = \frac{27}{21}\)
↑ \(x = 3\)
\(x = 7\) ↓
RM 6 Word Problem
4 cups sugar make 10 cakes. How many cups for 25 cakes?
← 10 c
12 c →
RM 7 Word Problem
Map scale: 2 in = 15 mi. Two peaks are 6 in apart. Actual miles?
↑ 30 mi
45 mi →
RM 8 Solve for x
\(\frac{16}{24} = \frac{20}{x}\)
← \(x = 25\)
\(x = 30\) ↓
RM 9 Word Problem
A car travels 150 mi on 5 gal of gas. Miles on 8 gal?
200 mi ↓
240 mi →
RM 10 Proportion Test
Is this proportion true?
\(\frac{14}{20} = \frac{21}{30}\)
FALSE ↓
TRUE →
RM 11 Solve for x
\(\frac{12}{18} = \frac{x}{42}\)
↑ \(x = 28\)
\(x = 32\) ↓
RM 12 Word Problem
A machine packs 45 boxes in 3 min. Boxes packed in 8 min?
← 90 bx
120 bx ↓
RM 13 DEAD END
CAVE-IN!
Return to RM 9
Path blocked
RM 14 DEAD END
PITFALL TRAP!
Return to RM 10
Floor collapsed
RM 15 DEAD END
LOCKED GATE!
Return to RM 11
Wrong keyway
FINISH • RM 16 Mastery Vault
Escape Lock
\(\frac{x+2}{15} = \frac{8}{10}\)
Solve on Page 2!
Correct path visits exactly 10 chambers before unlocking Chamber 16.
Page 1 • Maze Board
EXPEDITION CALCULATION LOG
Show Your Cross-Multiplication Proofs
Name:
Period:
Cross-Product Property: If \(\frac{a}{b} = \frac{c}{d}\), then \(a \cdot d = b \cdot c\). Isolate the variable to find your answer.
Show All Steps
Station 1: Chamber 1 \(\frac{x}{8} = \frac{15}{20}\)
Cross Products:
Solve for x:
Path Answer:
Station 2: Chamber 2 Equivalent to \(6 : 9\)
Test Ratios:
Check Products:
Path Answer:
Station 3: Chamber 6 Sugar for Cakes
Proportion:
Cross Multiply:
Path Answer:
Station 4: Chamber 5 \(\frac{9}{x} = \frac{27}{21}\)
Cross Products:
Solve for x:
Path Answer:
Station 5: Chamber 9 Car Fuel & Miles
Proportion:
Cross Multiply:
Path Answer:
Station 6: Chamber 10 \(\frac{14}{20} \stackrel{?}{=} \frac{21}{30}\)
Product 1:
Product 2:
Path Answer:
Station 7: Chamber 11 \(\frac{12}{18} = \frac{x}{42}\)
Cross Products:
Solve for x:
Path Answer:
Station 8: Chamber 7 Map Scale Proportions
Proportion:
Cross Multiply:
Path Answer:
Station 9: Chamber 8 \(\frac{16}{24} = \frac{20}{x}\)
Cross Products:
Solve for x:
Path Answer:
Station 10: Chamber 12 Packaging Machine
Proportion:
Cross Multiply:
Path Answer:
Chamber 16 Final Lock
\(\frac{x+2}{15} = \frac{8}{10}\)
Apply distributive property after cross multiplying.
Equation:
Distribute & Solve:
Escape Key: x = ______
Tip: Double-check your products to guarantee each step before inking your path! Page 2 • Proof Log
