Divisibility Detectives Worksheet
Math Crime Stoppers • Case File #402 Grades 3–4
Divisibility Detectives Worksheet
Mission
Simplify Big Fractions
Detective Name:
Date:
Badge #:
Field Guide: 4 Instant Clues to Find Common Factors
Rule: Divide top & bottom by the SAME number!
÷ 10 Super Fast
Both digits end in 0.
\(\frac{3\mathbf{0}}{7\mathbf{0}} \xrightarrow{\div 10} \frac{3}{7}\)
÷ 5 Nickel Clue
Ends in 0 or 5.
\(\frac{1\mathbf{5}}{3\mathbf{5}} \xrightarrow{\div 5} \frac{3}{7}\)
÷ 2 Even Split
Ends in 0, 2, 4, 6, 8.
\(\frac{1\mathbf{4}}{1\mathbf{8}} \xrightarrow{\div 2} \frac{7}{9}\)
÷ 3 Digit Sum
Add the digits: sum is in the 3s family.
\(1+2=3 \implies \div 3\)
1
Case File 1: Quick Clue Spotter
Circle the best shared divisibility rule helper:
A. Fraction: \(\frac{40}{90}\)
Notice the last digits! Which factor jumps out first?
÷ 2 ÷ 5 ÷ 10
B. Fraction: \(\frac{25}{45}\)
Both numbers end in the digit 5. Best divisor?
÷ 2 ÷ 3 ÷ 5
C. Fraction: \(\frac{18}{22}\)
Ends in 8 and 2. Both numbers are even! Best divisor?
÷ 2 ÷ 5 ÷ 10
2
Case File 2: Guided Breakdown Lab
Inspect the clue, write your division factor, and write the simplified fraction!
Suspect #1 Clue: Ends in 0
\(\frac{30}{50}\)
Divide Both By
÷
=
Simplest Form
Check: Can you simplify again? (Yes / No)
Suspect #2 Clue: Ends in 5
\(\frac{15}{20}\)
Divide Both By
÷
=
Simplest Form
Check: Is the numerator smaller than denominator?
Suspect #3 Clue: Both Even (6 & 4)
\(\frac{16}{24}\)
Divide Both By
÷
=
Step 1 Fraction
Bonus: Can you divide by 2 again? Final: _____
Suspect #4 Clue: Sum: 1+2=3, 2+1=3
\(\frac{12}{21}\)
Divide Both By
÷
=
Simplest Form
Hint: Count by 3s: 3, 6, 9, 12, 15, 18, 21!
Detective Golden Rule: A fraction is in simplest form when 1 is the ONLY number that divides both parts!
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Field Work: Independent Investigation
Apply your divisibility clues to solve each case file.
Agent Name:
3
Crack the Fraction: Choose Your Clue & Simplify
Check the clue you spotted first!
#1
\(\frac{40}{60}\)
Clue: Ends in 0 (÷10) Even (÷2)
I Divided By
Simplest Form
#2
\(\frac{25}{35}\)
Clue: Ends in 5 (÷5) Digit Sum (÷3)
I Divided By
Simplest Form
#3
\(\frac{18}{30}\)
Clue: Both Even (÷2) Sum in 3s (÷3)
I Divided By
Simplest Form
#4
\(\frac{14}{20}\)
Clue: Ends in 4 & 0 (÷2) Ends in 0 (÷10)
I Divided By
Simplest Form
#5
\(\frac{30}{70}\)
Clue: Ends in 0 (÷10) Both Even (÷2)
I Divided By
Simplest Form
#6
\(\frac{9}{27}\)
Clue: Sum: 2+7=9 (÷3) Even (÷2)
I Divided By
Simplest Form
4
Top Secret Mission: The Two-Step Shrink!
Challenge Suspect: \(\frac{60}{80}\)
Sometimes one divisibility clue isn't enough to get to the very simplest form! Follow both clues:
\(\frac{60}{80}\)
Clue 1: Ends in 0 Divide by 10 →
→
Clue 2: Both Even! Divide by 2 →
Case Status SOLVED! 🔍
5
Detective Debrief: Explain Your Sleuthing
A rookie detective asks: "How can you instantly tell that \(\frac{50}{70}\) can be simplified without doing long division?"
Grade 3–4 Fractions & Divisibility Clues • Master Key Available
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