What is 13/53 plus 8/21? (Answer: 697/1113)

Exact Answer

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Problem: What is 13/53 plus 8/21?
Formula / Expression: 13/53 + 8/21
Final Answer: 697/1113
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 21 = 1113.
Working: LCD(53, 21) = 1113

Step 2: Convert to Equivalent Fractions with Common Denominator 1113
Multiply the numerator and denominator of 13/53 by 21, and multiply the numerator and denominator of 8/21 by 53 so both fractions share the common base 1113.
Working: 13 × 21/53 × 21 = 273/1113 and 8 × 53/21 × 53 = 424/1113

Step 3: Add the Numerators
Now add the numerators (273 + 424 = 697) and keep the common denominator 1113 unchanged.
Working: 273 + 424/1113 = 697/1113

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 697 and 1113 is 1, confirming that 697/1113 cannot be reduced further—it is already in its simplest irreducible form.
Working: 697/1113

Step 5: Decimal & Percentage Representation
Dividing the numerator 697 by denominator 1113 produces a repeating decimal (approximately 0.626235, or 62.6235%).
Working: 697 ÷ 1113 = 0.626235 (62.6235%)

Key Values:
- Simplified Fraction: 697/1113
- Mixed Number Form: 697/1113
- Decimal Value: 0.626235
- Percentage: 62.6235%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-53-plus-8-21/
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13/53 + 8/21 = 697/1113

Simplified Fraction

697/1113

Mixed Number

Proper (697/1113)

Decimal Value

0.626235

Percentage

62.6235%

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Step-by-Step Solution: 13/53 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 21 = 1113.

LCD(53, 21) = 1113

Step 2

Convert to Equivalent Fractions with Common Denominator 1113

Multiply the numerator and denominator of 13/53 by 21, and multiply the numerator and denominator of 8/21 by 53 so both fractions share the common base 1113.

13 × 21/53 × 21 = 273/1113 and 8 × 53/21 × 53 = 424/1113

Step 3

Add the Numerators

Now add the numerators (273 + 424 = 697) and keep the common denominator 1113 unchanged.

273 + 424/1113 = 697/1113

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 697 and 1113 is 1, confirming that 697/1113 cannot be reduced further—it is already in its simplest irreducible form.

697/1113

Step 5

Decimal & Percentage Representation

Dividing the numerator 697 by denominator 1113 produces a repeating decimal (approximately 0.626235, or 62.6235%).

697 ÷ 1113 = 0.626235 (62.6235%)

Visual Representation

The diagram below illustrates 13/53 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`697/1113`
Mixed Number Form	`697/1113`
Decimal Form	`0.626235`
Percentage	`62.6235%`

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Frequently Asked Questions

What is 13/53 plus 8/21 as a fraction?

13/53 + 8/21 in simplest fraction form is 697/1113.

What is 13/53 plus 8/21 as a decimal?

13/53 + 8/21 converted to a decimal is 0.626235.

What is 13/53 plus 8/21 as a percentage?

13/53 + 8/21 expressed as a percentage is 62.6235%.

Does 13/53 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.626235...) because the denominator contains prime factors other than 2 and 5.