What is 1/5 plus 11/21? (Answer: 76/105)

Exact Answer

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Problem: What is 1/5 plus 11/21?
Formula / Expression: 1/5 + 11/21
Final Answer: 76/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.
Working: LCD(5, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 1/5 by 21, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 1 × 21/5 × 21 = 21/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (21 + 55 = 76) and keep the common denominator 105 unchanged.
Working: 21 + 55/105 = 76/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 76 and 105 is 1, confirming that 76/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 76/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 105 produces a repeating decimal (approximately 0.72381, or 72.381%).
Working: 76 ÷ 105 = 0.72381 (72.381%)

Key Values:
- Simplified Fraction: 76/105
- Mixed Number Form: 76/105
- Decimal Value: 0.72381
- Percentage: 72.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-plus-11-21/
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1/5 + 11/21 = 76/105

Simplified Fraction

76/105

Mixed Number

Proper (76/105)

Decimal Value

0.72381

Percentage

72.381%

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Step-by-Step Solution: 1/5 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.

LCD(5, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 1/5 by 21, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

1 × 21/5 × 21 = 21/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (21 + 55 = 76) and keep the common denominator 105 unchanged.

21 + 55/105 = 76/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 76 and 105 is 1, confirming that 76/105 cannot be reduced further—it is already in its simplest irreducible form.

76/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 105 produces a repeating decimal (approximately 0.72381, or 72.381%).

76 ÷ 105 = 0.72381 (72.381%)

Visual Representation

The diagram below illustrates 1/5 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/105`
Mixed Number Form	`76/105`
Decimal Form	`0.72381`
Percentage	`72.381%`

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Frequently Asked Questions

What is 1/5 plus 11/21 as a fraction?

1/5 + 11/21 in simplest fraction form is 76/105.

What is 1/5 plus 11/21 as a decimal?

1/5 + 11/21 converted to a decimal is 0.72381.

What is 1/5 plus 11/21 as a percentage?

1/5 + 11/21 expressed as a percentage is 72.381%.

Does 1/5 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.72381...) because the denominator contains prime factors other than 2 and 5.