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Simplifying a fraction means making it simpler by using smaller numbers, but keeping the same value.
Would you rather say "I ate 4 out of 8 slices of pizza" or "I ate half the pizza"?
Both mean the same thing, but "half" is simpler!
4/8 = 1/2
Key Point: When we simplify, the fraction stays equal to the original, but the numbers get smaller and easier to understand.
The shaded area is the same size! That's why 4/8 = 1/2
Simplifying a fraction means reducing it to its simplest form (also called "lowest terms") by dividing both the numerator and denominator by their common factors.
The value of the fraction stays the same!
Example: 6/8 simplified is 3/4
Important: A fraction is in simplest form when the numerator and denominator have no common factors except 1.
Which is easier to picture: 12/16 or 3/4?
Most people find 3/4 much easier to visualize!
Is 6/10 or 9/15 bigger? Hard to tell!
But when simplified: 3/5 or 3/5? Now we see they're equal!
In math, we usually give answers in simplest form. It's like showing your work in its "cleanest" version.
To simplify a fraction, we need to find numbers that divide evenly into both the numerator and denominator. These are called common factors.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
These are the numbers we can use to simplify 12/18!
Let's simplify 12/18 by dividing by a common factor.
Both 12 and 18 can be divided by 2.
12 ÷ 2 = 6
18 ÷ 2 = 9
So 12/18 = 6/9
6 and 9 both divide by 3!
6 ÷ 3 = 2
9 ÷ 3 = 3
So 6/9 = 2/3
Answer: 12/18 simplified is 2/3
Problem 1: Simplify 4/6
Step 1: Find a common factor of 4 and 6
Both divide by 2
Step 2: Divide both by 2
4 ÷ 2 = 2
6 ÷ 2 = 3
Answer: 2/3
Problem 2: Simplify 8/12
Step 1: Find a common factor of 8 and 12
Both divide by 4
Step 2: Divide both by 4
8 ÷ 4 = 2
12 ÷ 4 = 3
Answer: 2/3
Instead of simplifying in multiple steps, we can do it all at once using the Greatest Common Factor (GCF).
The GCF is the largest number that divides evenly into both the numerator and denominator.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
The GCF is 6 (the largest common factor)
Let's simplify 12/18 using the GCF in just ONE step!
The GCF is 6
12 ÷ 6 = 2
18 ÷ 6 = 3
12/18 = 2/3
Done in one step! This is why finding the GCF is so useful!
Step 1: Find the Greatest Common Factor (GCF) of the numerator and denominator.
Step 2: Divide BOTH the numerator and denominator by the GCF.
Step 3: Write the new fraction.
Example:
To simplify 20/30:
• GCF of 20 and 30 is 10
• 20 ÷ 10 = 2 and 30 ÷ 10 = 3
• Answer: 2/3
Find GCF of 24 and 36:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
GCF = 12
Find GCF of 24 and 36:
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common factors: 2 × 2 × 3 = 12
GCF = 12
Problem 3: Find the GCF of 16 and 20, then simplify 16/20
Step 1: Find GCF of 16 and 20
Factors of 16: 1, 2, 4, 8, 16
Factors of 20: 1, 2, 4, 5, 10, 20
GCF = 4
Step 2: Divide both by 4
16 ÷ 4 = 4
20 ÷ 4 = 5
Answer: 4/5
Problem 4: Find the GCF of 18 and 24, then simplify 18/24
Step 1: Find GCF of 18 and 24
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
GCF = 6
Step 2: Divide both by 6
18 ÷ 6 = 3
24 ÷ 6 = 4
Answer: 3/4
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
GCF = 24
48 ÷ 24 = 2
72 ÷ 24 = 3
48/72 = 2/3
Tip: Even with big numbers, the process is the same. Find the GCF and divide!
Problem 5: Simplify 15/25
Step 1: Find GCF of 15 and 25
Factors of 15: 1, 3, 5, 15
Factors of 25: 1, 5, 25
GCF = 5
Step 2: Divide both by 5
15 ÷ 5 = 3
25 ÷ 5 = 5
Answer: 3/5
Problem 6: Simplify 10/15
Step 1: Find GCF of 10 and 15
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 3, 5, 15
GCF = 5
Step 2: Divide both by 5
10 ÷ 5 = 2
15 ÷ 5 = 3
Answer: 2/3
A fraction is in simplest form when the numerator and denominator have no common factors except 1.
Factors of 3: 1, 3
Factors of 7: 1, 7
Common factors: Only 1
Yes! 3/7 is already in simplest form.
Factors of 5: 1, 5
Factors of 8: 1, 2, 4, 8
Common factors: Only 1
Yes! 5/8 is already in simplest form.
Problem 7: Is 7/9 in simplest form? If not, simplify it.
Check for common factors:
Factors of 7: 1, 7
Factors of 9: 1, 3, 9
GCF = 1
Answer: Yes! 7/9 is already in simplest form.
Problem 8: Is 6/9 in simplest form? If not, simplify it.
Check for common factors:
Factors of 6: 1, 2, 3, 6
Factors of 9: 1, 3, 9
GCF = 3
This CAN be simplified!
6 ÷ 3 = 2
9 ÷ 3 = 3
Answer: 2/3
A fraction is in simplest form (or lowest terms) when:
1. The GCF of the numerator and denominator is 1
2. The numerator and denominator share no common factors except 1
Examples of fractions in simplest form:
1/2, 3/4, 5/7, 2/9, 7/10
Examples NOT in simplest form:
2/4 (simplifies to 1/2), 4/6 (simplifies to 2/3)
To simplify 8/12:
"Both numbers have a 4, so I'll subtract 4 from each..."
8 - 4 = 4
12 - 4 = 8
So 8/12 = 4/8 ❌ THIS IS WRONG!
To simplify 8/12:
Find GCF: GCF of 8 and 12 is 4
DIVIDE both by 4:
8 ÷ 4 = 2
12 ÷ 4 = 3
So 8/12 = 2/3 ✅ CORRECT!
Remember: Always DIVIDE by the GCF, never subtract!
To simplify 10/20:
"I'll divide the denominator by 2..."
10/20 = 10/10 ❌ THIS IS WRONG!
You changed the value of the fraction!
To simplify 10/20:
Find GCF: GCF of 10 and 20 is 10
Divide BOTH the numerator and denominator by 10:
10 ÷ 10 = 1
20 ÷ 10 = 2
So 10/20 = 1/2 ✅ CORRECT!
Remember: You MUST divide BOTH parts by the same number!
Problem 9: Simplify 14/21
Step 1: Find GCF of 14 and 21
Factors of 14: 1, 2, 7, 14
Factors of 21: 1, 3, 7, 21
GCF = 7
Step 2: Divide BOTH by 7
14 ÷ 7 = 2
21 ÷ 7 = 3
Answer: 2/3
Problem 10: Simplify 9/12
Step 1: Find GCF of 9 and 12
Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12
GCF = 3
Step 2: Divide BOTH by 3
9 ÷ 3 = 3
12 ÷ 3 = 4
Answer: 3/4
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 3, 4, 6, 12
GCF = 12
36 ÷ 12 = 3
48 ÷ 12 = 4
36/48 = 3/4
Problem 11: Simplify 24/32
Step 1: Find GCF of 24 and 32
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
GCF = 8
Step 2: Divide both by 8
24 ÷ 8 = 3
32 ÷ 8 = 4
Answer: 3/4
Problem 12: Simplify 30/45
Step 1: Find GCF of 30 and 45
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 45: 1, 3, 5, 9, 15, 45
GCF = 15
Step 2: Divide both by 15
30 ÷ 15 = 2
45 ÷ 15 = 3
Answer: 2/3
If you have trouble finding the GCF, you can simplify in smaller steps by dividing by any common factor repeatedly.
24 ÷ 2 = 12
36 ÷ 2 = 18
Now we have 12/18
12 ÷ 2 = 6
18 ÷ 2 = 9
Now we have 6/9
6 ÷ 3 = 2
9 ÷ 3 = 3
Final answer: 2/3
Note: This works, but using the GCF (12) would have been faster!
Problem 13: Simplify 20/28
Step 1: Find GCF of 20 and 28
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 28: 1, 2, 4, 7, 14, 28
GCF = 4
Step 2: Divide both by 4
20 ÷ 4 = 5
28 ÷ 4 = 7
Answer: 5/7
Problem 14: Simplify 12/16
Step 1: Find GCF of 12 and 16
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
GCF = 4
Step 2: Divide both by 4
12 ÷ 4 = 3
16 ÷ 4 = 4
Answer: 3/4
Situation: A recipe calls for 6/8 cup of sugar.
You look in your measuring cup drawer...
You don't have a 1/8 cup measure!
Solution: Simplify 6/8
GCF of 6 and 8 is 2
6 ÷ 2 = 3
8 ÷ 2 = 4
6/8 = 3/4
Now you know to use your 3/4 cup measure! Simplifying helped you cook!
Situation: A basketball player made 18 out of 24 free throws.
What fraction did they make?
Initial answer: 18/24
But coaches prefer simplified statistics:
GCF of 18 and 24 is 6
18 ÷ 6 = 3
24 ÷ 6 = 4
18/24 = 3/4
"The player made 3 out of 4 free throws" is much easier to understand than "18 out of 24"!
Method 1: Step-by-Step
1. Find any common factor
2. Divide both numbers by that factor
3. Repeat until you can't simplify anymore
Method 2: Using GCF (Fastest!)
1. Find the GCF of numerator and denominator
2. Divide BOTH by the GCF
3. Done in one step!
How to Check Your Work:
The numerator and denominator should only have 1 as a common factor when you're done.
Problem 15: Simplify 25/35
Step 1: Find GCF of 25 and 35
Factors of 25: 1, 5, 25
Factors of 35: 1, 5, 7, 35
GCF = 5
Step 2: Divide both by 5
25 ÷ 5 = 5
35 ÷ 5 = 7
Answer: 5/7
Problem 16: Simplify 27/36
Step 1: Find GCF of 27 and 36
Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF = 9
Step 2: Divide both by 9
27 ÷ 9 = 3
36 ÷ 9 = 4
Answer: 3/4
Problem 17: Simplify 42/56
Step 1: Find GCF of 42 and 56
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
GCF = 14
Step 2: Divide both by 14
42 ÷ 14 = 3
56 ÷ 14 = 4
Answer: 3/4
Problem 18: Simplify 45/60
Step 1: Find GCF of 45 and 60
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCF = 15
Step 2: Divide both by 15
45 ÷ 15 = 3
60 ÷ 15 = 4
Answer: 3/4
When the numerator and denominator are the same, the fraction equals 1 whole.
8 ÷ 8 = 1
8 ÷ 8 = 1
8/8 = 1/1 = 1
15 ÷ 15 = 1
15 ÷ 15 = 1
15/15 = 1/1 = 1
Remember: Any fraction where the numerator equals the denominator simplifies to 1!
Problem 19: Simplify 50/75
Step 1: Find GCF of 50 and 75
Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 75: 1, 3, 5, 15, 25, 75
GCF = 25
Step 2: Divide both by 25
50 ÷ 25 = 2
75 ÷ 25 = 3
Answer: 2/3
Problem 20: Simplify 32/40
Step 1: Find GCF of 32 and 40
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
GCF = 8
Step 2: Divide both by 8
32 ÷ 8 = 4
40 ÷ 8 = 5
Answer: 4/5
Mistake #1: Subtracting instead of dividing
❌ WRONG: 8/12 → (8-4)/(12-4) = 4/8
✅ RIGHT: 8/12 → (8÷4)/(12÷4) = 2/3
Mistake #2: Only dividing one part
❌ WRONG: 10/20 → 10/(20÷2) = 10/10
✅ RIGHT: 10/20 → (10÷10)/(20÷10) = 1/2
Mistake #3: Not dividing by the GCF
If you don't use the GCF, you might need multiple steps.
Example: 12/18 ÷ 2 = 6/9, then ÷ 3 = 2/3
Using GCF (6): 12/18 ÷ 6 = 2/3 (one step!)
If both the numerator and denominator are even, they can at least be divided by 2!
Example: 14/22 → Both even → Divide by 2 → 7/11
If both numbers end in 0 or 5, they're divisible by 5!
Example: 15/25 → Both end in 5 → Divide by 5 → 3/5
If digits add up to a multiple of 3, the number is divisible by 3!
Example: 18/27 → (1+8=9, 2+7=9) → Both divisible by 9 → 2/3
Problem 21: Simplify 64/80
Step 1: Find GCF of 64 and 80
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
GCF = 16
Step 2: Divide both by 16
64 ÷ 16 = 4
80 ÷ 16 = 5
Answer: 4/5
Problem 22: Simplify 54/72
Step 1: Find GCF of 54 and 72
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
GCF = 18
Step 2: Divide both by 18
54 ÷ 18 = 3
72 ÷ 18 = 4
Answer: 3/4
1. What is Simplifying?
Making a fraction simpler by using smaller numbers while keeping the same value.
2. Why Simplify?
• Easier to understand
• Easier to compare
• Standard form for answers
3. How to Simplify?
Find the GCF and divide both parts by it!
Divide by any common factor, then check if you can simplify more.
Best when: You're not sure of the GCF
Find the Greatest Common Factor and divide both parts by it.
Best when: You want the fastest solution
✅ Always DIVIDE, never subtract
✅ Divide BOTH the numerator and denominator
✅ A fraction is simplified when GCF = 1
Don't subtract! Always divide.
8/12 ≠ (8-4)/(12-4)
8/12 = (8÷4)/(12÷4) = 2/3 ✅
You must divide BOTH parts by the same number!
10/20 ≠ 10/(20÷10)
10/20 = (10÷10)/(20÷10) = 1/2 ✅
Check that the GCF = 1 when you're done!
24/36 → 12/18 (not done yet!)
24/36 → 12/18 → 6/9 → 2/3 ✅
Quick Challenge: Simplify these in your head!
1. 6/10 = ?
2. 9/12 = ?
3. 15/20 = ?
4. 8/10 = ?
1. 6/10 = 3/5 (divide by 2)
2. 9/12 = 3/4 (divide by 3)
3. 15/20 = 3/4 (divide by 5)
4. 8/10 = 4/5 (divide by 2)
What You Mastered Today:
✓ What simplifying fractions means
✓ Why we simplify fractions
✓ Finding common factors and the GCF
✓ Two methods for simplifying
✓ Common mistakes to avoid
✓ Real-world applications
Coming Soon:
Comparing fractions
Adding & subtracting unlike fractions
Multiplying & dividing fractions
Keep practicing! You're doing amazing! 🌟