What is 11/21 plus 3/5? (Answer: 118/105)

Exact Answer

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Problem: What is 11/21 plus 3/5?
Formula / Expression: 11/21 + 3/5
Final Answer: 1 13/105 (118/105)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 11/21 by 5, and multiply the numerator and denominator of 3/5 by 21 so both fractions share the common base 105.
Working: 11 × 5/21 × 5 = 55/105 and 3 × 21/5 × 21 = 63/105

Step 3: Add the Numerators
Now add the numerators (55 + 63 = 118) and keep the common denominator 105 unchanged.
Working: 55 + 63/105 = 118/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 118 and 105 is 1, confirming that 118/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 118/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (118) is greater than the denominator (105), divide 118 by 105: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/105.
Working: 118/105 = 1 13/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 118 by denominator 105 produces a repeating decimal (approximately 1.12381, or 112.381%).
Working: 118 ÷ 105 = 1.12381 (112.381%)

Key Values:
- Simplified Fraction: 118/105
- Mixed Number Form: 1 13/105
- Decimal Value: 1.12381
- Percentage: 112.381%

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11/21 + 3/5 = 118/105

Simplified Fraction

118/105

Mixed Number

1 13/105

Decimal Value

1.12381

Percentage

112.381%

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Step-by-Step Solution: 11/21 + 3/5

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 5) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 11/21 by 5, and multiply the numerator and denominator of 3/5 by 21 so both fractions share the common base 105.

11 × 5/21 × 5 = 55/105 and 3 × 21/5 × 21 = 63/105

Step 3

Add the Numerators

Now add the numerators (55 + 63 = 118) and keep the common denominator 105 unchanged.

55 + 63/105 = 118/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 118 and 105 is 1, confirming that 118/105 cannot be reduced further—it is already in its simplest irreducible form.

118/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (118) is greater than the denominator (105), divide 118 by 105: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/105.

118/105 = 113/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 118 by denominator 105 produces a repeating decimal (approximately 1.12381, or 112.381%).

118 ÷ 105 = 1.12381 (112.381%)

Visual Representation

The diagram below illustrates 11/21 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`118/105`
Mixed Number Form	`1 13/105`
Decimal Form	`1.12381`
Percentage	`112.381%`

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Frequently Asked Questions

What is 11/21 plus 3/5 as a fraction?

11/21 + 3/5 in simplest fraction form is 118/105 (or 1 13/105 as a mixed number).

What is 11/21 plus 3/5 as a decimal?

11/21 + 3/5 converted to a decimal is 1.12381.

What is 11/21 plus 3/5 as a percentage?

11/21 + 3/5 expressed as a percentage is 112.381%.

How do you write 11/21 plus 3/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 118/105 can be written as the mixed number 1 13/105.

Does 11/21 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.12381...) because the denominator contains prime factors other than 2 and 5.