What is 3/53 plus 2/13? (Answer: 145/689)

Exact Answer

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Problem: What is 3/53 plus 2/13?
Formula / Expression: 3/53 + 2/13
Final Answer: 145/689
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 13 = 689.
Working: LCD(53, 13) = 689

Step 2: Convert to Equivalent Fractions with Common Denominator 689
Multiply the numerator and denominator of 3/53 by 13, and multiply the numerator and denominator of 2/13 by 53 so both fractions share the common base 689.
Working: 3 × 13/53 × 13 = 39/689 and 2 × 53/13 × 53 = 106/689

Step 3: Add the Numerators
Now add the numerators (39 + 106 = 145) and keep the common denominator 689 unchanged.
Working: 39 + 106/689 = 145/689

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 145 and 689 is 1, confirming that 145/689 cannot be reduced further—it is already in its simplest irreducible form.
Working: 145/689

Step 5: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 689 produces a repeating decimal (approximately 0.21045, or 21.045%).
Working: 145 ÷ 689 = 0.21045 (21.045%)

Key Values:
- Simplified Fraction: 145/689
- Mixed Number Form: 145/689
- Decimal Value: 0.21045
- Percentage: 21.045%

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Solved with FractionsCalc:
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3/53 + 2/13 = 145/689

Simplified Fraction

145/689

Mixed Number

Proper (145/689)

Decimal Value

0.21045

Percentage

21.045%

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Step-by-Step Solution: 3/53 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 13 = 689.

LCD(53, 13) = 689

Step 2

Convert to Equivalent Fractions with Common Denominator 689

Multiply the numerator and denominator of 3/53 by 13, and multiply the numerator and denominator of 2/13 by 53 so both fractions share the common base 689.

3 × 13/53 × 13 = 39/689 and 2 × 53/13 × 53 = 106/689

Step 3

Add the Numerators

Now add the numerators (39 + 106 = 145) and keep the common denominator 689 unchanged.

39 + 106/689 = 145/689

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 145 and 689 is 1, confirming that 145/689 cannot be reduced further—it is already in its simplest irreducible form.

145/689

Step 5

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 689 produces a repeating decimal (approximately 0.21045, or 21.045%).

145 ÷ 689 = 0.21045 (21.045%)

Visual Representation

The diagram below illustrates 3/53 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/689`
Mixed Number Form	`145/689`
Decimal Form	`0.21045`
Percentage	`21.045%`

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Frequently Asked Questions

What is 3/53 plus 2/13 as a fraction?

3/53 + 2/13 in simplest fraction form is 145/689.

What is 3/53 plus 2/13 as a decimal?

3/53 + 2/13 converted to a decimal is 0.21045.

What is 3/53 plus 2/13 as a percentage?

3/53 + 2/13 expressed as a percentage is 21.045%.

Does 3/53 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.21045...) because the denominator contains prime factors other than 2 and 5.