What is 2/53 plus 2/10? (Answer: 63/265)

Exact Answer

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Problem: What is 2/53 plus 2/10?
Formula / Expression: 2/53 + 2/10
Final Answer: 63/265
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 10 = 530.
Working: LCD(53, 10) = 530

Step 2: Convert to Equivalent Fractions with Common Denominator 530
Multiply the numerator and denominator of 2/53 by 10, and multiply the numerator and denominator of 2/10 by 53 so both fractions share the common base 530.
Working: 2 × 10/53 × 10 = 20/530 and 2 × 53/10 × 53 = 106/530

Step 3: Add the Numerators
Now add the numerators (20 + 106 = 126) and keep the common denominator 530 unchanged.
Working: 20 + 106/530 = 126/530

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 530, which is 2. Divide both the numerator and denominator by 2.
Working: 126 ÷ 2/530 ÷ 2 = 63/265

Step 5: Decimal & Percentage Representation
Dividing the numerator 63 by denominator 265 produces a repeating decimal (approximately 0.237736, or 23.7736%).
Working: 63 ÷ 265 = 0.237736 (23.7736%)

Key Values:
- Simplified Fraction: 63/265
- Mixed Number Form: 63/265
- Decimal Value: 0.237736
- Percentage: 23.7736%

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Solved with FractionsCalc:
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2/53 + 2/10 = 63/265

Simplified Fraction

63/265

Mixed Number

Proper (63/265)

Decimal Value

0.237736

Percentage

23.7736%

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Step-by-Step Solution: 2/53 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 10 = 530.

LCD(53, 10) = 530

Step 2

Convert to Equivalent Fractions with Common Denominator 530

Multiply the numerator and denominator of 2/53 by 10, and multiply the numerator and denominator of 2/10 by 53 so both fractions share the common base 530.

2 × 10/53 × 10 = 20/530 and 2 × 53/10 × 53 = 106/530

Step 3

Add the Numerators

Now add the numerators (20 + 106 = 126) and keep the common denominator 530 unchanged.

20 + 106/530 = 126/530

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 530, which is 2. Divide both the numerator and denominator by 2.

126 ÷ 2/530 ÷ 2 = 63/265

Step 5

Decimal & Percentage Representation

Dividing the numerator 63 by denominator 265 produces a repeating decimal (approximately 0.237736, or 23.7736%).

63 ÷ 265 = 0.237736 (23.7736%)

Visual Representation

The diagram below illustrates 2/53 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`63/265`
Mixed Number Form	`63/265`
Decimal Form	`0.237736`
Percentage	`23.7736%`

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Frequently Asked Questions

What is 2/53 plus 2/10 as a fraction?

2/53 + 2/10 in simplest fraction form is 63/265.

What is 2/53 plus 2/10 as a decimal?

2/53 + 2/10 converted to a decimal is 0.237736.

What is 2/53 plus 2/10 as a percentage?

2/53 + 2/10 expressed as a percentage is 23.7736%.

Does 2/53 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.237736...) because the denominator contains prime factors other than 2 and 5.