What is 11/30 plus 11/21? (Answer: 187/210)

Exact Answer

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Problem: What is 11/30 plus 11/21?
Formula / Expression: 11/30 + 11/21
Final Answer: 187/210
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 11/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.
Working: 11 × 7/30 × 7 = 77/210 and 11 × 10/21 × 10 = 110/210

Step 3: Add the Numerators
Now add the numerators (77 + 110 = 187) and keep the common denominator 210 unchanged.
Working: 77 + 110/210 = 187/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 187 and 210 is 1, confirming that 187/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 187/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 187 by denominator 210 produces a repeating decimal (approximately 0.890476, or 89.0476%).
Working: 187 ÷ 210 = 0.890476 (89.0476%)

Key Values:
- Simplified Fraction: 187/210
- Mixed Number Form: 187/210
- Decimal Value: 0.890476
- Percentage: 89.0476%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-30-plus-11-21/
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11/30 + 11/21 = 187/210

Simplified Fraction

187/210

Mixed Number

Proper (187/210)

Decimal Value

0.890476

Percentage

89.0476%

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Step-by-Step Solution: 11/30 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 11/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.

11 × 7/30 × 7 = 77/210 and 11 × 10/21 × 10 = 110/210

Step 3

Add the Numerators

Now add the numerators (77 + 110 = 187) and keep the common denominator 210 unchanged.

77 + 110/210 = 187/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 187 and 210 is 1, confirming that 187/210 cannot be reduced further—it is already in its simplest irreducible form.

187/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 187 by denominator 210 produces a repeating decimal (approximately 0.890476, or 89.0476%).

187 ÷ 210 = 0.890476 (89.0476%)

Visual Representation

The diagram below illustrates 11/30 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`187/210`
Mixed Number Form	`187/210`
Decimal Form	`0.890476`
Percentage	`89.0476%`

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Frequently Asked Questions

What is 11/30 plus 11/21 as a fraction?

11/30 + 11/21 in simplest fraction form is 187/210.

What is 11/30 plus 11/21 as a decimal?

11/30 + 11/21 converted to a decimal is 0.890476.

What is 11/30 plus 11/21 as a percentage?

11/30 + 11/21 expressed as a percentage is 89.0476%.

Does 11/30 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.890476...) because the denominator contains prime factors other than 2 and 5.