What is 4/25 plus 2/7? (Answer: 78/175)

Exact Answer

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Problem: What is 4/25 plus 2/7?
Formula / Expression: 4/25 + 2/7
Final Answer: 78/175
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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 4/25 by 7, and multiply the numerator and denominator of 2/7 by 25 so both fractions share the common base 175.
Working: 4 × 7/25 × 7 = 28/175 and 2 × 25/7 × 25 = 50/175

Step 3: Add the Numerators
Now add the numerators (28 + 50 = 78) and keep the common denominator 175 unchanged.
Working: 28 + 50/175 = 78/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 78 and 175 is 1, confirming that 78/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 78/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 78 by denominator 175 produces a repeating decimal (approximately 0.445714, or 44.5714%).
Working: 78 ÷ 175 = 0.445714 (44.5714%)

Key Values:
- Simplified Fraction: 78/175
- Mixed Number Form: 78/175
- Decimal Value: 0.445714
- Percentage: 44.5714%

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Solved with FractionsCalc:
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4/25 + 2/7 = 78/175

Simplified Fraction

78/175

Mixed Number

Proper (78/175)

Decimal Value

0.445714

Percentage

44.5714%

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Step-by-Step Solution: 4/25 + 2/7

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 4/25 by 7, and multiply the numerator and denominator of 2/7 by 25 so both fractions share the common base 175.

4 × 7/25 × 7 = 28/175 and 2 × 25/7 × 25 = 50/175

Step 3

Add the Numerators

Now add the numerators (28 + 50 = 78) and keep the common denominator 175 unchanged.

28 + 50/175 = 78/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 78 and 175 is 1, confirming that 78/175 cannot be reduced further—it is already in its simplest irreducible form.

78/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 78 by denominator 175 produces a repeating decimal (approximately 0.445714, or 44.5714%).

78 ÷ 175 = 0.445714 (44.5714%)

Visual Representation

The diagram below illustrates 4/25 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`78/175`
Mixed Number Form	`78/175`
Decimal Form	`0.445714`
Percentage	`44.5714%`

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Frequently Asked Questions

What is 4/25 plus 2/7 as a fraction?

4/25 + 2/7 in simplest fraction form is 78/175.

What is 4/25 plus 2/7 as a decimal?

4/25 + 2/7 converted to a decimal is 0.445714.

What is 4/25 plus 2/7 as a percentage?

4/25 + 2/7 expressed as a percentage is 44.5714%.

Does 4/25 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.445714...) because the denominator contains prime factors other than 2 and 5.