What is 3/55 plus 10/21? (Answer: 613/1155)

Exact Answer

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Problem: What is 3/55 plus 10/21?
Formula / Expression: 3/55 + 10/21
Final Answer: 613/1155
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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 10/21 by 55 so both fractions share the common base 1155.
Working: 3 × 21/55 × 21 = 63/1155 and 10 × 55/21 × 55 = 550/1155

Step 3: Add the Numerators
Now add the numerators (63 + 550 = 613) and keep the common denominator 1155 unchanged.
Working: 63 + 550/1155 = 613/1155

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 613 and 1155 is 1, confirming that 613/1155 cannot be reduced further—it is already in its simplest irreducible form.
Working: 613/1155

Step 5: Decimal & Percentage Representation
Dividing the numerator 613 by denominator 1155 produces a repeating decimal (approximately 0.530736, or 53.0736%).
Working: 613 ÷ 1155 = 0.530736 (53.0736%)

Key Values:
- Simplified Fraction: 613/1155
- Mixed Number Form: 613/1155
- Decimal Value: 0.530736
- Percentage: 53.0736%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-55-plus-10-21/
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3/55 + 10/21 = 613/1155

Simplified Fraction

613/1155

Mixed Number

Proper (613/1155)

Decimal Value

0.530736

Percentage

53.0736%

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Step-by-Step Solution: 3/55 + 10/21

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 10/21 by 55 so both fractions share the common base 1155.

3 × 21/55 × 21 = 63/1155 and 10 × 55/21 × 55 = 550/1155

Step 3

Add the Numerators

Now add the numerators (63 + 550 = 613) and keep the common denominator 1155 unchanged.

63 + 550/1155 = 613/1155

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 613 and 1155 is 1, confirming that 613/1155 cannot be reduced further—it is already in its simplest irreducible form.

613/1155

Step 5

Decimal & Percentage Representation

Dividing the numerator 613 by denominator 1155 produces a repeating decimal (approximately 0.530736, or 53.0736%).

613 ÷ 1155 = 0.530736 (53.0736%)

Visual Representation

The diagram below illustrates 3/55 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`613/1155`
Mixed Number Form	`613/1155`
Decimal Form	`0.530736`
Percentage	`53.0736%`

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Frequently Asked Questions

What is 3/55 plus 10/21 as a fraction?

3/55 + 10/21 in simplest fraction form is 613/1155.

What is 3/55 plus 10/21 as a decimal?

3/55 + 10/21 converted to a decimal is 0.530736.

What is 3/55 plus 10/21 as a percentage?

3/55 + 10/21 expressed as a percentage is 53.0736%.

Does 3/55 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.530736...) because the denominator contains prime factors other than 2 and 5.