What is 1600/1300 Simplified? (Reduce 1600/1300 to Lowest Terms: 16/13)

Exact Answer

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Problem: Simplify 1600/1300 to Lowest Terms
Formula / Expression: 1600/1300 = 16/13
Final Answer: 1 3/13 (16/13)
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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 1600: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160
• Factors of 1300: 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325
Working: GCD(1600, 1300) = 100

Step 2: Divide Both by the Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) is 100. Divide both the numerator (1600) and denominator (1300) by 100.
Working: 1600 ÷ 100/1300 ÷ 100 = 16/13

Step 3: Convert Improper Fraction to a Mixed Number
Because 16 is larger than 13, 16/13 can also be written as the mixed number 1 3/13.
Working: 16/13 = 1 3/13

Key Values:
- Simplified Fraction: 16/13
- Mixed Number Form: 1 3/13
- Decimal Value: 1.230769
- Percentage: 123.0769%

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Solved with FractionsCalc:
https://fractionscalc.com/simplify-1600-1300/
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1600/1300 = 16/13

Simplified Fraction

16/13

Mixed Number

1 3/13

Decimal Value

1.230769

Percentage

123.0769%

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Step-by-Step Solution: 1600/1300 = 16/13

Step 1

Find the Factors of the Numerator and Denominator

List the positive factors of both numbers:
• Factors of 1600: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160
• Factors of 1300: 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325

GCD(1600, 1300) = 100

Step 2

Divide Both by the Greatest Common Divisor (GCD)

The Greatest Common Divisor (GCD) is 100. Divide both the numerator (1600) and denominator (1300) by 100.

1600 ÷ 100/1300 ÷ 100 = 16/13

Step 3

Convert Improper Fraction to a Mixed Number

Because 16 is larger than 13, 16/13 can also be written as the mixed number 1 3/13.

16/13 = 13/13

Visual Representation

The diagram below illustrates Simplify 1600/1300 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/13`
Mixed Number Form	`1 3/13`
Decimal Form	`1.230769`
Percentage	`123.0769%`

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Frequently Asked Questions

What is 1600/1300 in simplest form?

1600/1300 simplified to lowest terms is 16/13.

What is the GCD (GCF) of 1600 and 1300?

The Greatest Common Divisor (GCD) of 1600 and 1300 is 100.

What are equivalent fractions to 1600/1300?

Equivalent fractions to 1600/1300 include 32/26, 48/39, and 64/52.