What is 3/55 plus 5/21? (Answer: 338/1155)

Exact Answer

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Problem: What is 3/55 plus 5/21?
Formula / Expression: 3/55 + 5/21
Final Answer: 338/1155
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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 3/55 by 21, and multiply the numerator and denominator of 5/21 by 55 so both fractions share the common base 1155.
Working: 3 × 21/55 × 21 = 63/1155 and 5 × 55/21 × 55 = 275/1155

Step 3: Add the Numerators
Now add the numerators (63 + 275 = 338) and keep the common denominator 1155 unchanged.
Working: 63 + 275/1155 = 338/1155

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 338 and 1155 is 1, confirming that 338/1155 cannot be reduced further—it is already in its simplest irreducible form.
Working: 338/1155

Step 5: Decimal & Percentage Representation
Dividing the numerator 338 by denominator 1155 produces a repeating decimal (approximately 0.292641, or 29.2641%).
Working: 338 ÷ 1155 = 0.292641 (29.2641%)

Key Values:
- Simplified Fraction: 338/1155
- Mixed Number Form: 338/1155
- Decimal Value: 0.292641
- Percentage: 29.2641%

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Solved with FractionsCalc:
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3/55 + 5/21 = 338/1155

Simplified Fraction

338/1155

Mixed Number

Proper (338/1155)

Decimal Value

0.292641

Percentage

29.2641%

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Step-by-Step Solution: 3/55 + 5/21

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 3/55 by 21, and multiply the numerator and denominator of 5/21 by 55 so both fractions share the common base 1155.

3 × 21/55 × 21 = 63/1155 and 5 × 55/21 × 55 = 275/1155

Step 3

Add the Numerators

Now add the numerators (63 + 275 = 338) and keep the common denominator 1155 unchanged.

63 + 275/1155 = 338/1155

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 338 and 1155 is 1, confirming that 338/1155 cannot be reduced further—it is already in its simplest irreducible form.

338/1155

Step 5

Decimal & Percentage Representation

Dividing the numerator 338 by denominator 1155 produces a repeating decimal (approximately 0.292641, or 29.2641%).

338 ÷ 1155 = 0.292641 (29.2641%)

Visual Representation

The diagram below illustrates 3/55 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`338/1155`
Mixed Number Form	`338/1155`
Decimal Form	`0.292641`
Percentage	`29.2641%`

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Frequently Asked Questions

What is 3/55 plus 5/21 as a fraction?

3/55 + 5/21 in simplest fraction form is 338/1155.

What is 3/55 plus 5/21 as a decimal?

3/55 + 5/21 converted to a decimal is 0.292641.

What is 3/55 plus 5/21 as a percentage?

3/55 + 5/21 expressed as a percentage is 29.2641%.

Does 3/55 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.292641...) because the denominator contains prime factors other than 2 and 5.