What is 4/21 plus 11/55? (Answer: 41/105)

Exact Answer

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Problem: What is 4/21 plus 11/55?
Formula / Expression: 4/21 + 11/55
Final Answer: 41/105
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 4/21 by 55, and multiply the numerator and denominator of 11/55 by 21 so both fractions share the common base 1155.
Working: 4 × 55/21 × 55 = 220/1155 and 11 × 21/55 × 21 = 231/1155

Step 3: Add the Numerators
Now add the numerators (220 + 231 = 451) and keep the common denominator 1155 unchanged.
Working: 220 + 231/1155 = 451/1155

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 451 and 1155, which is 11. Divide both the numerator and denominator by 11.
Working: 451 ÷ 11/1155 ÷ 11 = 41/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).
Working: 41 ÷ 105 = 0.390476 (39.0476%)

Key Values:
- Simplified Fraction: 41/105
- Mixed Number Form: 41/105
- Decimal Value: 0.390476
- Percentage: 39.0476%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-11-55/
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4/21 + 11/55 = 41/105

Simplified Fraction

41/105

Mixed Number

Proper (41/105)

Decimal Value

0.390476

Percentage

39.0476%

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Step-by-Step Solution: 4/21 + 11/55

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 55) = 1155

Step 2

Convert to Equivalent Fractions with Common Denominator 1155

Multiply the numerator and denominator of 4/21 by 55, and multiply the numerator and denominator of 11/55 by 21 so both fractions share the common base 1155.

4 × 55/21 × 55 = 220/1155 and 11 × 21/55 × 21 = 231/1155

Step 3

Add the Numerators

Now add the numerators (220 + 231 = 451) and keep the common denominator 1155 unchanged.

220 + 231/1155 = 451/1155

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 451 and 1155, which is 11. Divide both the numerator and denominator by 11.

451 ÷ 11/1155 ÷ 11 = 41/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).

41 ÷ 105 = 0.390476 (39.0476%)

Visual Representation

The diagram below illustrates 4/21 plus 11/55 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/105`
Mixed Number Form	`41/105`
Decimal Form	`0.390476`
Percentage	`39.0476%`

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Frequently Asked Questions

What is 4/21 plus 11/55 as a fraction?

4/21 + 11/55 in simplest fraction form is 41/105.

What is 4/21 plus 11/55 as a decimal?

4/21 + 11/55 converted to a decimal is 0.390476.

What is 4/21 plus 11/55 as a percentage?

4/21 + 11/55 expressed as a percentage is 39.0476%.

Does 4/21 plus 11/55 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.390476...) because the denominator contains prime factors other than 2 and 5.