What is 2/25 plus 2/16? (Answer: 41/200)

Exact Answer

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Problem: What is 2/25 plus 2/16?
Formula / Expression: 2/25 + 2/16
Final Answer: 41/200
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 16 = 400.
Working: LCD(25, 16) = 400

Step 2: Convert to Equivalent Fractions with Common Denominator 400
Multiply the numerator and denominator of 2/25 by 16, and multiply the numerator and denominator of 2/16 by 25 so both fractions share the common base 400.
Working: 2 × 16/25 × 16 = 32/400 and 2 × 25/16 × 25 = 50/400

Step 3: Add the Numerators
Now add the numerators (32 + 50 = 82) and keep the common denominator 400 unchanged.
Working: 32 + 50/400 = 82/400

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 400, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/400 ÷ 2 = 41/200

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 200 yields an exact terminating decimal of 0.205 (or 20.5%).
Working: 41 ÷ 200 = 0.205 (20.5%)

Key Values:
- Simplified Fraction: 41/200
- Mixed Number Form: 41/200
- Decimal Value: 0.205
- Percentage: 20.5%

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Solved with FractionsCalc:
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2/25 + 2/16 = 41/200

Simplified Fraction

41/200

Mixed Number

Proper (41/200)

Decimal Value

0.205

Percentage

20.5%

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Step-by-Step Solution: 2/25 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 16 = 400.

LCD(25, 16) = 400

Step 2

Convert to Equivalent Fractions with Common Denominator 400

Multiply the numerator and denominator of 2/25 by 16, and multiply the numerator and denominator of 2/16 by 25 so both fractions share the common base 400.

2 × 16/25 × 16 = 32/400 and 2 × 25/16 × 25 = 50/400

Step 3

Add the Numerators

Now add the numerators (32 + 50 = 82) and keep the common denominator 400 unchanged.

32 + 50/400 = 82/400

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 400, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/400 ÷ 2 = 41/200

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 200 yields an exact terminating decimal of 0.205 (or 20.5%).

41 ÷ 200 = 0.205 (20.5%)

Visual Representation

The diagram below illustrates 2/25 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/200`
Mixed Number Form	`41/200`
Decimal Form	`0.205`
Percentage	`20.5%`

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Frequently Asked Questions

What is 2/25 plus 2/16 as a fraction?

2/25 + 2/16 in simplest fraction form is 41/200.

What is 2/25 plus 2/16 as a decimal?

2/25 + 2/16 converted to a decimal is 0.205.

What is 2/25 plus 2/16 as a percentage?

2/25 + 2/16 expressed as a percentage is 20.5%.

Does 2/25 plus 2/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.205) because the denominator in simplest terms contains only prime factors 2 and/or 5.