What is 1200/830 Simplified? (Reduce 1200/830 to Lowest Terms: 120/83)

Exact Answer

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Problem: Simplify 1200/830 to Lowest Terms
Formula / Expression: 1200/830 = 120/83
Final Answer: 1 37/83 (120/83)
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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 1200: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40
• Factors of 830: 1, 2, 5, 10, 83, 166, 415, 830
Working: GCD(1200, 830) = 10

Step 2: Divide Both by the Greatest Common Divisor (GCD)
The Greatest Common Divisor (GCD) is 10. Divide both the numerator (1200) and denominator (830) by 10.
Working: 1200 ÷ 10/830 ÷ 10 = 120/83

Step 3: Convert Improper Fraction to a Mixed Number
Because 120 is larger than 83, 120/83 can also be written as the mixed number 1 37/83.
Working: 120/83 = 1 37/83

Key Values:
- Simplified Fraction: 120/83
- Mixed Number Form: 1 37/83
- Decimal Value: 1.445783
- Percentage: 144.5783%

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Solved with FractionsCalc:
https://fractionscalc.com/simplify-1200-830/
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1200/830 = 120/83

Simplified Fraction

120/83

Mixed Number

1 37/83

Decimal Value

1.445783

Percentage

144.5783%

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Step-by-Step Solution: 1200/830 = 120/83

Step 1

Find the Factors of the Numerator and Denominator

List the positive factors of both numbers:
• Factors of 1200: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40
• Factors of 830: 1, 2, 5, 10, 83, 166, 415, 830

GCD(1200, 830) = 10

Step 2

Divide Both by the Greatest Common Divisor (GCD)

The Greatest Common Divisor (GCD) is 10. Divide both the numerator (1200) and denominator (830) by 10.

1200 ÷ 10/830 ÷ 10 = 120/83

Step 3

Convert Improper Fraction to a Mixed Number

Because 120 is larger than 83, 120/83 can also be written as the mixed number 1 37/83.

120/83 = 137/83

Visual Representation

The diagram below illustrates Simplify 1200/830 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`120/83`
Mixed Number Form	`1 37/83`
Decimal Form	`1.445783`
Percentage	`144.5783%`

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Frequently Asked Questions

What is 1200/830 in simplest form?

1200/830 simplified to lowest terms is 120/83.

What is the GCD (GCF) of 1200 and 830?

The Greatest Common Divisor (GCD) of 1200 and 830 is 10.

What are equivalent fractions to 1200/830?

Equivalent fractions to 1200/830 include 240/166, 360/249, and 480/332.