What is 1/20 plus 11/21? (Answer: 241/420)

Exact Answer

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Problem: What is 1/20 plus 11/21?
Formula / Expression: 1/20 + 11/21
Final Answer: 241/420
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.
Working: LCD(20, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 1/20 by 21, and multiply the numerator and denominator of 11/21 by 20 so both fractions share the common base 420.
Working: 1 × 21/20 × 21 = 21/420 and 11 × 20/21 × 20 = 220/420

Step 3: Add the Numerators
Now add the numerators (21 + 220 = 241) and keep the common denominator 420 unchanged.
Working: 21 + 220/420 = 241/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 241 and 420 is 1, confirming that 241/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 241/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 241 by denominator 420 produces a repeating decimal (approximately 0.57381, or 57.381%).
Working: 241 ÷ 420 = 0.57381 (57.381%)

Key Values:
- Simplified Fraction: 241/420
- Mixed Number Form: 241/420
- Decimal Value: 0.57381
- Percentage: 57.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-20-plus-11-21/
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1/20 + 11/21 = 241/420

Simplified Fraction

241/420

Mixed Number

Proper (241/420)

Decimal Value

0.57381

Percentage

57.381%

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Step-by-Step Solution: 1/20 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.

LCD(20, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 1/20 by 21, and multiply the numerator and denominator of 11/21 by 20 so both fractions share the common base 420.

1 × 21/20 × 21 = 21/420 and 11 × 20/21 × 20 = 220/420

Step 3

Add the Numerators

Now add the numerators (21 + 220 = 241) and keep the common denominator 420 unchanged.

21 + 220/420 = 241/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 241 and 420 is 1, confirming that 241/420 cannot be reduced further—it is already in its simplest irreducible form.

241/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 241 by denominator 420 produces a repeating decimal (approximately 0.57381, or 57.381%).

241 ÷ 420 = 0.57381 (57.381%)

Visual Representation

The diagram below illustrates 1/20 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`241/420`
Mixed Number Form	`241/420`
Decimal Form	`0.57381`
Percentage	`57.381%`

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Frequently Asked Questions

What is 1/20 plus 11/21 as a fraction?

1/20 + 11/21 in simplest fraction form is 241/420.

What is 1/20 plus 11/21 as a decimal?

1/20 + 11/21 converted to a decimal is 0.57381.

What is 1/20 plus 11/21 as a percentage?

1/20 + 11/21 expressed as a percentage is 57.381%.

Does 1/20 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.57381...) because the denominator contains prime factors other than 2 and 5.