What is 9/25 plus 3/7? (Answer: 138/175)

Exact Answer

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Problem: What is 9/25 plus 3/7?
Formula / Expression: 9/25 + 3/7
Final Answer: 138/175
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 7 = 175.
Working: LCD(25, 7) = 175

Step 2: Convert to Equivalent Fractions with Common Denominator 175
Multiply the numerator and denominator of 9/25 by 7, and multiply the numerator and denominator of 3/7 by 25 so both fractions share the common base 175.
Working: 9 × 7/25 × 7 = 63/175 and 3 × 25/7 × 25 = 75/175

Step 3: Add the Numerators
Now add the numerators (63 + 75 = 138) and keep the common denominator 175 unchanged.
Working: 63 + 75/175 = 138/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 138 and 175 is 1, confirming that 138/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 138/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 138 by denominator 175 produces a repeating decimal (approximately 0.788571, or 78.8571%).
Working: 138 ÷ 175 = 0.788571 (78.8571%)

Key Values:
- Simplified Fraction: 138/175
- Mixed Number Form: 138/175
- Decimal Value: 0.788571
- Percentage: 78.8571%

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9/25 + 3/7 = 138/175

Simplified Fraction

138/175

Mixed Number

Proper (138/175)

Decimal Value

0.788571

Percentage

78.8571%

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Step-by-Step Solution: 9/25 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 7 = 175.

LCD(25, 7) = 175

Step 2

Convert to Equivalent Fractions with Common Denominator 175

Multiply the numerator and denominator of 9/25 by 7, and multiply the numerator and denominator of 3/7 by 25 so both fractions share the common base 175.

9 × 7/25 × 7 = 63/175 and 3 × 25/7 × 25 = 75/175

Step 3

Add the Numerators

Now add the numerators (63 + 75 = 138) and keep the common denominator 175 unchanged.

63 + 75/175 = 138/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 138 and 175 is 1, confirming that 138/175 cannot be reduced further—it is already in its simplest irreducible form.

138/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 138 by denominator 175 produces a repeating decimal (approximately 0.788571, or 78.8571%).

138 ÷ 175 = 0.788571 (78.8571%)

Visual Representation

The diagram below illustrates 9/25 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`138/175`
Mixed Number Form	`138/175`
Decimal Form	`0.788571`
Percentage	`78.8571%`

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Frequently Asked Questions

What is 9/25 plus 3/7 as a fraction?

9/25 + 3/7 in simplest fraction form is 138/175.

What is 9/25 plus 3/7 as a decimal?

9/25 + 3/7 converted to a decimal is 0.788571.

What is 9/25 plus 3/7 as a percentage?

9/25 + 3/7 expressed as a percentage is 78.8571%.

Does 9/25 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.788571...) because the denominator contains prime factors other than 2 and 5.