What is 2/8 plus 9/25? (Answer: 61/100)

Exact Answer

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Problem: What is 2/8 plus 9/25?
Formula / Expression: 2/8 + 9/25
Final Answer: 61/100
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 200
Multiply the numerator and denominator of 2/8 by 25, and multiply the numerator and denominator of 9/25 by 8 so both fractions share the common base 200.
Working: 2 × 25/8 × 25 = 50/200 and 9 × 8/25 × 8 = 72/200

Step 3: Add the Numerators
Now add the numerators (50 + 72 = 122) and keep the common denominator 200 unchanged.
Working: 50 + 72/200 = 122/200

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 122 and 200, which is 2. Divide both the numerator and denominator by 2.
Working: 122 ÷ 2/200 ÷ 2 = 61/100

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 100 yields an exact terminating decimal of 0.61 (or 61%).
Working: 61 ÷ 100 = 0.61 (61%)

Key Values:
- Simplified Fraction: 61/100
- Mixed Number Form: 61/100
- Decimal Value: 0.61
- Percentage: 61%

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Solved with FractionsCalc:
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2/8 + 9/25 = 61/100

Simplified Fraction

61/100

Mixed Number

Proper (61/100)

Decimal Value

0.61

Percentage

61%

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Step-by-Step Solution: 2/8 + 9/25

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 25) = 200

Step 2

Convert to Equivalent Fractions with Common Denominator 200

Multiply the numerator and denominator of 2/8 by 25, and multiply the numerator and denominator of 9/25 by 8 so both fractions share the common base 200.

2 × 25/8 × 25 = 50/200 and 9 × 8/25 × 8 = 72/200

Step 3

Add the Numerators

Now add the numerators (50 + 72 = 122) and keep the common denominator 200 unchanged.

50 + 72/200 = 122/200

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 122 and 200, which is 2. Divide both the numerator and denominator by 2.

122 ÷ 2/200 ÷ 2 = 61/100

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 100 yields an exact terminating decimal of 0.61 (or 61%).

61 ÷ 100 = 0.61 (61%)

Visual Representation

The diagram below illustrates 2/8 plus 9/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/100`
Mixed Number Form	`61/100`
Decimal Form	`0.61`
Percentage	`61%`

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Frequently Asked Questions

What is 2/8 plus 9/25 as a fraction?

2/8 + 9/25 in simplest fraction form is 61/100.

What is 2/8 plus 9/25 as a decimal?

2/8 + 9/25 converted to a decimal is 0.61.

What is 2/8 plus 9/25 as a percentage?

2/8 + 9/25 expressed as a percentage is 61%.

Does 2/8 plus 9/25 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.61) because the denominator in simplest terms contains only prime factors 2 and/or 5.