What is 13/55 plus 8/21? (Answer: 713/1155)

Exact Answer

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Problem: What is 13/55 plus 8/21?
Formula / Expression: 13/55 + 8/21
Final Answer: 713/1155
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 55 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 21 = 1155.
Working: LCD(55, 21) = 1155

Step 2: Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 13/55 by 21, and multiply the numerator and denominator of 8/21 by 55 so both fractions share the common base 1155.
Working: 13 × 21/55 × 21 = 273/1155 and 8 × 55/21 × 55 = 440/1155

Step 3: Add the Numerators
Now add the numerators (273 + 440 = 713) and keep the common denominator 1155 unchanged.
Working: 273 + 440/1155 = 713/1155

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 713 and 1155 is 1, confirming that 713/1155 cannot be reduced further—it is already in its simplest irreducible form.
Working: 713/1155

Step 5: Decimal & Percentage Representation
Dividing the numerator 713 by denominator 1155 produces a repeating decimal (approximately 0.617316, or 61.7316%).
Working: 713 ÷ 1155 = 0.617316 (61.7316%)

Key Values:
- Simplified Fraction: 713/1155
- Mixed Number Form: 713/1155
- Decimal Value: 0.617316
- Percentage: 61.7316%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-55-plus-8-21/
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13/55 + 8/21 = 713/1155

Simplified Fraction

713/1155

Mixed Number

Proper (713/1155)

Decimal Value

0.617316

Percentage

61.7316%

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Step-by-Step Solution: 13/55 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 55 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 21 = 1155.

LCD(55, 21) = 1155

Step 2

Convert to Equivalent Fractions with Common Denominator 1155

Multiply the numerator and denominator of 13/55 by 21, and multiply the numerator and denominator of 8/21 by 55 so both fractions share the common base 1155.

13 × 21/55 × 21 = 273/1155 and 8 × 55/21 × 55 = 440/1155

Step 3

Add the Numerators

Now add the numerators (273 + 440 = 713) and keep the common denominator 1155 unchanged.

273 + 440/1155 = 713/1155

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 713 and 1155 is 1, confirming that 713/1155 cannot be reduced further—it is already in its simplest irreducible form.

713/1155

Step 5

Decimal & Percentage Representation

Dividing the numerator 713 by denominator 1155 produces a repeating decimal (approximately 0.617316, or 61.7316%).

713 ÷ 1155 = 0.617316 (61.7316%)

Visual Representation

The diagram below illustrates 13/55 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`713/1155`
Mixed Number Form	`713/1155`
Decimal Form	`0.617316`
Percentage	`61.7316%`

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Frequently Asked Questions

What is 13/55 plus 8/21 as a fraction?

13/55 + 8/21 in simplest fraction form is 713/1155.

What is 13/55 plus 8/21 as a decimal?

13/55 + 8/21 converted to a decimal is 0.617316.

What is 13/55 plus 8/21 as a percentage?

13/55 + 8/21 expressed as a percentage is 61.7316%.

Does 13/55 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.617316...) because the denominator contains prime factors other than 2 and 5.