What is 2/52 plus 2/10? (Answer: 31/130)

Exact Answer

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Problem: What is 2/52 plus 2/10?
Formula / Expression: 2/52 + 2/10
Final Answer: 31/130
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 260 (which is smaller than their product 52 × 10 = 520, keeping the calculation simpler).
Working: LCD(52, 10) = 260

Step 2: Convert to Equivalent Fractions with Common Denominator 260
Multiply the numerator and denominator of 2/52 by 5, and multiply the numerator and denominator of 2/10 by 26 so both fractions share the common base 260.
Working: 2 × 5/52 × 5 = 10/260 and 2 × 26/10 × 26 = 52/260

Step 3: Add the Numerators
Now add the numerators (10 + 52 = 62) and keep the common denominator 260 unchanged.
Working: 10 + 52/260 = 62/260

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 260, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/260 ÷ 2 = 31/130

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 130 produces a repeating decimal (approximately 0.238462, or 23.8462%).
Working: 31 ÷ 130 = 0.238462 (23.8462%)

Key Values:
- Simplified Fraction: 31/130
- Mixed Number Form: 31/130
- Decimal Value: 0.238462
- Percentage: 23.8462%

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Solved with FractionsCalc:
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2/52 + 2/10 = 31/130

Simplified Fraction

31/130

Mixed Number

Proper (31/130)

Decimal Value

0.238462

Percentage

23.8462%

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Step-by-Step Solution: 2/52 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 260 (which is smaller than their product 52 × 10 = 520, keeping the calculation simpler).

LCD(52, 10) = 260

Step 2

Convert to Equivalent Fractions with Common Denominator 260

Multiply the numerator and denominator of 2/52 by 5, and multiply the numerator and denominator of 2/10 by 26 so both fractions share the common base 260.

2 × 5/52 × 5 = 10/260 and 2 × 26/10 × 26 = 52/260

Step 3

Add the Numerators

Now add the numerators (10 + 52 = 62) and keep the common denominator 260 unchanged.

10 + 52/260 = 62/260

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 260, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/260 ÷ 2 = 31/130

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 130 produces a repeating decimal (approximately 0.238462, or 23.8462%).

31 ÷ 130 = 0.238462 (23.8462%)

Visual Representation

The diagram below illustrates 2/52 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/130`
Mixed Number Form	`31/130`
Decimal Form	`0.238462`
Percentage	`23.8462%`

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Frequently Asked Questions

What is 2/52 plus 2/10 as a fraction?

2/52 + 2/10 in simplest fraction form is 31/130.

What is 2/52 plus 2/10 as a decimal?

2/52 + 2/10 converted to a decimal is 0.238462.

What is 2/52 plus 2/10 as a percentage?

2/52 + 2/10 expressed as a percentage is 23.8462%.

Does 2/52 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.238462...) because the denominator contains prime factors other than 2 and 5.