What is 7/25 plus 2/3? (Answer: 71/75)

Exact Answer

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Problem: What is 7/25 plus 2/3?
Formula / Expression: 7/25 + 2/3
Final Answer: 71/75
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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 7/25 by 3, and multiply the numerator and denominator of 2/3 by 25 so both fractions share the common base 75.
Working: 7 × 3/25 × 3 = 21/75 and 2 × 25/3 × 25 = 50/75

Step 3: Add the Numerators
Now add the numerators (21 + 50 = 71) and keep the common denominator 75 unchanged.
Working: 21 + 50/75 = 71/75

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 75 is 1, confirming that 71/75 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 75 produces a repeating decimal (approximately 0.946667, or 94.6667%).
Working: 71 ÷ 75 = 0.946667 (94.6667%)

Key Values:
- Simplified Fraction: 71/75
- Mixed Number Form: 71/75
- Decimal Value: 0.946667
- Percentage: 94.6667%

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Solved with FractionsCalc:
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7/25 + 2/3 = 71/75

Simplified Fraction

71/75

Mixed Number

Proper (71/75)

Decimal Value

0.946667

Percentage

94.6667%

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Step-by-Step Solution: 7/25 + 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 7/25 by 3, and multiply the numerator and denominator of 2/3 by 25 so both fractions share the common base 75.

7 × 3/25 × 3 = 21/75 and 2 × 25/3 × 25 = 50/75

Step 3

Add the Numerators

Now add the numerators (21 + 50 = 71) and keep the common denominator 75 unchanged.

21 + 50/75 = 71/75

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 75 is 1, confirming that 71/75 cannot be reduced further—it is already in its simplest irreducible form.

71/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 75 produces a repeating decimal (approximately 0.946667, or 94.6667%).

71 ÷ 75 = 0.946667 (94.6667%)

Visual Representation

The diagram below illustrates 7/25 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/75`
Mixed Number Form	`71/75`
Decimal Form	`0.946667`
Percentage	`94.6667%`

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Frequently Asked Questions

What is 7/25 plus 2/3 as a fraction?

7/25 + 2/3 in simplest fraction form is 71/75.

What is 7/25 plus 2/3 as a decimal?

7/25 + 2/3 converted to a decimal is 0.946667.

What is 7/25 plus 2/3 as a percentage?

7/25 + 2/3 expressed as a percentage is 94.6667%.

Does 7/25 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.946667...) because the denominator contains prime factors other than 2 and 5.