What is 102/76 Simplified? (Reduce 102/76 to Lowest Terms: 51/38)

Exact Answer

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Problem: Simplify 102/76 to Lowest Terms
Formula / Expression: 102/76 = 51/38
Final Answer: 1 13/38 (51/38)
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Step-by-Step Solution:

Step 1: Find the Factors of the Numerator and Denominator
List the positive factors of both numbers:
• Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
• Factors of 76: 1, 2, 4, 19, 38, 76
Working: GCD(102, 76) = 2

Step 2: Divide Both by the Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) is 2. Divide both the numerator (102) and denominator (76) by 2.
Working: 102 ÷ 2/76 ÷ 2 = 51/38

Step 3: Convert Improper Fraction to a Mixed Number
Because 51 is larger than 38, 51/38 can also be written as the mixed number 1 13/38.
Working: 51/38 = 1 13/38

Key Values:
- Simplified Fraction: 51/38
- Mixed Number Form: 1 13/38
- Decimal Value: 1.342105
- Percentage: 134.2105%

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Solved with FractionsCalc:
https://fractionscalc.com/simplify-102-76/
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102/76 = 51/38

Simplified Fraction

51/38

Mixed Number

1 13/38

Decimal Value

1.342105

Percentage

134.2105%

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Step-by-Step Solution: 102/76 = 51/38

Step 1

Find the Factors of the Numerator and Denominator

List the positive factors of both numbers:
• Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
• Factors of 76: 1, 2, 4, 19, 38, 76

GCD(102, 76) = 2

Step 2

Divide Both by the Greatest Common Divisor (GCD)

The Greatest Common Divisor (GCD) is 2. Divide both the numerator (102) and denominator (76) by 2.

102 ÷ 2/76 ÷ 2 = 51/38

Step 3

Convert Improper Fraction to a Mixed Number

Because 51 is larger than 38, 51/38 can also be written as the mixed number 1 13/38.

51/38 = 113/38

Visual Representation

The diagram below illustrates Simplify 102/76 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/38`
Mixed Number Form	`1 13/38`
Decimal Form	`1.342105`
Percentage	`134.2105%`

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Frequently Asked Questions

What is 102/76 in simplest form?

102/76 simplified to lowest terms is 51/38.

What is the GCD (GCF) of 102 and 76?

The Greatest Common Divisor (GCD) of 102 and 76 is 2.

What are equivalent fractions to 102/76?

Equivalent fractions to 102/76 include 102/76, 153/114, and 204/152.