What is 2/8 plus 7/25? (Answer: 53/100)

Exact Answer

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Problem: What is 2/8 plus 7/25?
Formula / Expression: 2/8 + 7/25
Final Answer: 53/100
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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 7/25 by 8 so both fractions share the common base 200.
Working: 2 × 25/8 × 25 = 50/200 and 7 × 8/25 × 8 = 56/200

Step 3: Add the Numerators
Now add the numerators (50 + 56 = 106) and keep the common denominator 200 unchanged.
Working: 50 + 56/200 = 106/200

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 106 and 200, which is 2. Divide both the numerator and denominator by 2.
Working: 106 ÷ 2/200 ÷ 2 = 53/100

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 100 yields an exact terminating decimal of 0.53 (or 53%).
Working: 53 ÷ 100 = 0.53 (53%)

Key Values:
- Simplified Fraction: 53/100
- Mixed Number Form: 53/100
- Decimal Value: 0.53
- Percentage: 53%

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Solved with FractionsCalc:
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2/8 + 7/25 = 53/100

Simplified Fraction

53/100

Mixed Number

Proper (53/100)

Decimal Value

0.53

Percentage

53%

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Step-by-Step Solution: 2/8 + 7/25

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 7/25 by 8 so both fractions share the common base 200.

2 × 25/8 × 25 = 50/200 and 7 × 8/25 × 8 = 56/200

Step 3

Add the Numerators

Now add the numerators (50 + 56 = 106) and keep the common denominator 200 unchanged.

50 + 56/200 = 106/200

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 106 and 200, which is 2. Divide both the numerator and denominator by 2.

106 ÷ 2/200 ÷ 2 = 53/100

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 100 yields an exact terminating decimal of 0.53 (or 53%).

53 ÷ 100 = 0.53 (53%)

Visual Representation

The diagram below illustrates 2/8 plus 7/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/100`
Mixed Number Form	`53/100`
Decimal Form	`0.53`
Percentage	`53%`

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Frequently Asked Questions

What is 2/8 plus 7/25 as a fraction?

2/8 + 7/25 in simplest fraction form is 53/100.

What is 2/8 plus 7/25 as a decimal?

2/8 + 7/25 converted to a decimal is 0.53.

What is 2/8 plus 7/25 as a percentage?

2/8 + 7/25 expressed as a percentage is 53%.

Does 2/8 plus 7/25 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.53) because the denominator in simplest terms contains only prime factors 2 and/or 5.