What is 3/25 plus 2/8? (Answer: 37/100)

Exact Answer

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Problem: What is 3/25 plus 2/8?
Formula / Expression: 3/25 + 2/8
Final Answer: 37/100
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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 3/25 by 8, and multiply the numerator and denominator of 2/8 by 25 so both fractions share the common base 200.
Working: 3 × 8/25 × 8 = 24/200 and 2 × 25/8 × 25 = 50/200

Step 3: Add the Numerators
Now add the numerators (24 + 50 = 74) and keep the common denominator 200 unchanged.
Working: 24 + 50/200 = 74/200

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 200, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/200 ÷ 2 = 37/100

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 100 yields an exact terminating decimal of 0.37 (or 37%).
Working: 37 ÷ 100 = 0.37 (37%)

Key Values:
- Simplified Fraction: 37/100
- Mixed Number Form: 37/100
- Decimal Value: 0.37
- Percentage: 37%

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Solved with FractionsCalc:
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3/25 + 2/8 = 37/100

Simplified Fraction

37/100

Mixed Number

Proper (37/100)

Decimal Value

0.37

Percentage

37%

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

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

3 × 8/25 × 8 = 24/200 and 2 × 25/8 × 25 = 50/200

Step 3

Add the Numerators

Now add the numerators (24 + 50 = 74) and keep the common denominator 200 unchanged.

24 + 50/200 = 74/200

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 200, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/200 ÷ 2 = 37/100

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 100 yields an exact terminating decimal of 0.37 (or 37%).

37 ÷ 100 = 0.37 (37%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/100`
Mixed Number Form	`37/100`
Decimal Form	`0.37`
Percentage	`37%`

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Frequently Asked Questions

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

3/25 + 2/8 in simplest fraction form is 37/100.

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

3/25 + 2/8 converted to a decimal is 0.37.

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

3/25 + 2/8 expressed as a percentage is 37%.

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

It results in an exact terminating decimal (0.37) because the denominator in simplest terms contains only prime factors 2 and/or 5.