Our simplify fractions calculator is a mathematical tool designed to reduce fractions to their simplest form. It operates by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by this value.
Let’s simplify the fraction 24/36:
- Find the GCD of 24 and 36 (which is 12)
- Divide both numerator and denominator by 12
Result: 24/36 simplifies to 2/3
Simplify Fractions Calculator
| Original Fraction | Simplified Fraction | Steps |
|---|---|---|
| 18/24 | 3/4 | GCF = 6, 18 ÷ 6 = 3, 24 ÷ 6 = 4 |
| 45/60 | 3/4 | GCF = 15, 45 ÷ 15 = 3, 60 ÷ 15 = 4 |
| 16/20 | 4/5 | GCF = 4, 16 ÷ 4 = 4, 20 ÷ 4 = 5 |
| 30/45 | 2/3 | GCF = 15, 30 ÷ 15 = 2, 45 ÷ 15 = 3 |
| 12/16 | 3/4 | GCF = 4, 12 ÷ 4 = 3, 16 ÷ 4 = 4 |
| 21/28 | 3/4 | GCF = 7, 21 ÷ 7 = 3, 28 ÷ 7 = 4 |
| 36/48 | 3/4 | GCF = 12, 36 ÷ 12 = 3, 48 ÷ 12 = 4 |
| 40/50 | 4/5 | GCF = 10, 40 ÷ 10 = 4, 50 ÷ 10 = 5 |
| 42/56 | 3/4 | GCF = 14, 42 ÷ 14 = 3, 56 ÷ 14 = 4 |
| 63/81 | 7/9 | GCF = 9, 63 ÷ 9 = 7, 81 ÷ 9 = 9 |
| 72/96 | 3/4 | GCF = 24, 72 ÷ 24 = 3, 96 ÷ 24 = 4 |
| 80/100 | 4/5 | GCF = 20, 80 ÷ 20 = 4, 100 ÷ 20 = 5 |
| 84/112 | 3/4 | GCF = 28, 84 ÷ 28 = 3, 112 ÷ 28 = 4 |
| 99/117 | 19/23 | GCF = 9, 99 ÷ 9 = 11, 117 ÷ 9 = 13 |
| 108/144 | 3/4 | GCF = 36, 108 ÷ 36 = 3, 144 ÷ 36 = 4 |
Simplify Fractions Formula
The formula to simplifying fractions is:
Simplified Fraction = (Numerator ÷ GCD) / (Denominator ÷ GCD)Where GCD is the Greatest Common Divisor of the numerator and denominator.
Simplify 18/24: GCD(18, 24) = 6
Simplified fraction = (18 ÷ 6) / (24 ÷ 6) = 3/4
Simplify 35/49: GCD(35, 49) = 7
Simplified fraction = (35 ÷ 7) / (49 ÷ 7) = 5/7
How Do You Simplify a Fraction?
- Find factors: List all factors of both the numerator and denominator.
- Identify common factors: Determine which factors are shared by both.
- Find the GCD: The largest common factor is the GCD.
- Divide: Divide both the numerator and denominator by the GCD.
Let’s simplify 48/64:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64 - Common factors: 1, 2, 4, 8, 16
- GCD = 16
- 48 ÷ 16 = 3, 64 ÷ 16 = 4
Therefore, 48/64 simplifies to 3/4
What is the Proper Fraction for 81 3/14?
To find the proper fraction for 81 3/14, we need to convert this mixed number to an improper fraction:
Multiply the whole number (81) by the denominator (14): 81 × 14 = 1134
Add this result to the numerator: 1134 + 3 = 1137
Place this sum over the original denominator: 1137/14
The proper fraction for 81 3/14 is 1137/14.
To simplify this further:
Find the GCD of 1137 and 14 (which is 7)
Divide both numerator and denominator by 7
Result: 1137/14 simplifies to 162/2, which further simplifies to 81
81 3/14 is equivalent to 81 in its simplest form.
Related Tools:
