What is 2/6 plus 9/25? (Answer: 52/75)

Exact Answer

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Problem: What is 2/6 plus 9/25?
Formula / Expression: 2/6 + 9/25
Final Answer: 52/75
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 25 = 150.
Working: LCD(6, 25) = 150

Step 2: Convert to Equivalent Fractions with Common Denominator 150
Multiply the numerator and denominator of 2/6 by 25, and multiply the numerator and denominator of 9/25 by 6 so both fractions share the common base 150.
Working: 2 × 25/6 × 25 = 50/150 and 9 × 6/25 × 6 = 54/150

Step 3: Add the Numerators
Now add the numerators (50 + 54 = 104) and keep the common denominator 150 unchanged.
Working: 50 + 54/150 = 104/150

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 104 and 150, which is 2. Divide both the numerator and denominator by 2.
Working: 104 ÷ 2/150 ÷ 2 = 52/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 75 produces a repeating decimal (approximately 0.693333, or 69.3333%).
Working: 52 ÷ 75 = 0.693333 (69.3333%)

Key Values:
- Simplified Fraction: 52/75
- Mixed Number Form: 52/75
- Decimal Value: 0.693333
- Percentage: 69.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-9-25/
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2/6 + 9/25 = 52/75

Simplified Fraction

52/75

Mixed Number

Proper (52/75)

Decimal Value

0.693333

Percentage

69.3333%

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Step-by-Step Solution: 2/6 + 9/25

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 25 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 25 = 150.

LCD(6, 25) = 150

Step 2

Convert to Equivalent Fractions with Common Denominator 150

Multiply the numerator and denominator of 2/6 by 25, and multiply the numerator and denominator of 9/25 by 6 so both fractions share the common base 150.

2 × 25/6 × 25 = 50/150 and 9 × 6/25 × 6 = 54/150

Step 3

Add the Numerators

Now add the numerators (50 + 54 = 104) and keep the common denominator 150 unchanged.

50 + 54/150 = 104/150

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 104 and 150, which is 2. Divide both the numerator and denominator by 2.

104 ÷ 2/150 ÷ 2 = 52/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 75 produces a repeating decimal (approximately 0.693333, or 69.3333%).

52 ÷ 75 = 0.693333 (69.3333%)

Visual Representation

The diagram below illustrates 2/6 plus 9/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/75`
Mixed Number Form	`52/75`
Decimal Form	`0.693333`
Percentage	`69.3333%`

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Frequently Asked Questions

What is 2/6 plus 9/25 as a fraction?

2/6 + 9/25 in simplest fraction form is 52/75.

What is 2/6 plus 9/25 as a decimal?

2/6 + 9/25 converted to a decimal is 0.693333.

What is 2/6 plus 9/25 as a percentage?

2/6 + 9/25 expressed as a percentage is 69.3333%.

Does 2/6 plus 9/25 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.693333...) because the denominator contains prime factors other than 2 and 5.