What is 2/25 plus 3/8? (Answer: 91/200)

Exact Answer

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Problem: What is 2/25 plus 3/8?
Formula / Expression: 2/25 + 3/8
Final Answer: 91/200
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 8 = 200.
Working: LCD(25, 8) = 200

Step 2: Convert to Equivalent Fractions with Common Denominator 200
Multiply the numerator and denominator of 2/25 by 8, and multiply the numerator and denominator of 3/8 by 25 so both fractions share the common base 200.
Working: 2 × 8/25 × 8 = 16/200 and 3 × 25/8 × 25 = 75/200

Step 3: Add the Numerators
Now add the numerators (16 + 75 = 91) and keep the common denominator 200 unchanged.
Working: 16 + 75/200 = 91/200

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 91 and 200 is 1, confirming that 91/200 cannot be reduced further—it is already in its simplest irreducible form.
Working: 91/200

Step 5: Decimal & Percentage Representation
Dividing the numerator 91 by denominator 200 yields an exact terminating decimal of 0.455 (or 45.5%).
Working: 91 ÷ 200 = 0.455 (45.5%)

Key Values:
- Simplified Fraction: 91/200
- Mixed Number Form: 91/200
- Decimal Value: 0.455
- Percentage: 45.5%

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Solved with FractionsCalc:
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2/25 + 3/8 = 91/200

Simplified Fraction

91/200

Mixed Number

Proper (91/200)

Decimal Value

0.455

Percentage

45.5%

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Step-by-Step Solution: 2/25 + 3/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 8 = 200.

LCD(25, 8) = 200

Step 2

Convert to Equivalent Fractions with Common Denominator 200

Multiply the numerator and denominator of 2/25 by 8, and multiply the numerator and denominator of 3/8 by 25 so both fractions share the common base 200.

2 × 8/25 × 8 = 16/200 and 3 × 25/8 × 25 = 75/200

Step 3

Add the Numerators

Now add the numerators (16 + 75 = 91) and keep the common denominator 200 unchanged.

16 + 75/200 = 91/200

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 91 and 200 is 1, confirming that 91/200 cannot be reduced further—it is already in its simplest irreducible form.

91/200

Step 5

Decimal & Percentage Representation

Dividing the numerator 91 by denominator 200 yields an exact terminating decimal of 0.455 (or 45.5%).

91 ÷ 200 = 0.455 (45.5%)

Visual Representation

The diagram below illustrates 2/25 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`91/200`
Mixed Number Form	`91/200`
Decimal Form	`0.455`
Percentage	`45.5%`

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Frequently Asked Questions

What is 2/25 plus 3/8 as a fraction?

2/25 + 3/8 in simplest fraction form is 91/200.

What is 2/25 plus 3/8 as a decimal?

2/25 + 3/8 converted to a decimal is 0.455.

What is 2/25 plus 3/8 as a percentage?

2/25 + 3/8 expressed as a percentage is 45.5%.

Does 2/25 plus 3/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.455) because the denominator in simplest terms contains only prime factors 2 and/or 5.