What is 9/25 plus 2/3? (Answer: 77/75)

Exact Answer

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Problem: What is 9/25 plus 2/3?
Formula / Expression: 9/25 + 2/3
Final Answer: 1 2/75 (77/75)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 3 = 75.
Working: LCD(25, 3) = 75

Step 2: Convert to Equivalent Fractions with Common Denominator 75
Multiply the numerator and denominator of 9/25 by 3, and multiply the numerator and denominator of 2/3 by 25 so both fractions share the common base 75.
Working: 9 × 3/25 × 3 = 27/75 and 2 × 25/3 × 25 = 50/75

Step 3: Add the Numerators
Now add the numerators (27 + 50 = 77) and keep the common denominator 75 unchanged.
Working: 27 + 50/75 = 77/75

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 75 is 1, confirming that 77/75 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/75

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (77) is greater than the denominator (75), divide 77 by 75: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/75.
Working: 77/75 = 1 2/75

Step 6: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 75 produces a repeating decimal (approximately 1.026667, or 102.6667%).
Working: 77 ÷ 75 = 1.026667 (102.6667%)

Key Values:
- Simplified Fraction: 77/75
- Mixed Number Form: 1 2/75
- Decimal Value: 1.026667
- Percentage: 102.6667%

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Solved with FractionsCalc:
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9/25 + 2/3 = 77/75

Simplified Fraction

77/75

Mixed Number

1 2/75

Decimal Value

1.026667

Percentage

102.6667%

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Step-by-Step Solution: 9/25 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 3 = 75.

LCD(25, 3) = 75

Step 2

Convert to Equivalent Fractions with Common Denominator 75

Multiply the numerator and denominator of 9/25 by 3, and multiply the numerator and denominator of 2/3 by 25 so both fractions share the common base 75.

9 × 3/25 × 3 = 27/75 and 2 × 25/3 × 25 = 50/75

Step 3

Add the Numerators

Now add the numerators (27 + 50 = 77) and keep the common denominator 75 unchanged.

27 + 50/75 = 77/75

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 75 is 1, confirming that 77/75 cannot be reduced further—it is already in its simplest irreducible form.

77/75

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (77) is greater than the denominator (75), divide 77 by 75: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/75.

77/75 = 12/75

Step 6

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 75 produces a repeating decimal (approximately 1.026667, or 102.6667%).

77 ÷ 75 = 1.026667 (102.6667%)

Visual Representation

The diagram below illustrates 9/25 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/75`
Mixed Number Form	`1 2/75`
Decimal Form	`1.026667`
Percentage	`102.6667%`

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Frequently Asked Questions

What is 9/25 plus 2/3 as a fraction?

9/25 + 2/3 in simplest fraction form is 77/75 (or 1 2/75 as a mixed number).

What is 9/25 plus 2/3 as a decimal?

9/25 + 2/3 converted to a decimal is 1.026667.

What is 9/25 plus 2/3 as a percentage?

9/25 + 2/3 expressed as a percentage is 102.6667%.

How do you write 9/25 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 77/75 can be written as the mixed number 1 2/75.

Does 9/25 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.026667...) because the denominator contains prime factors other than 2 and 5.