What is 2/21 plus 3/30? (Answer: 41/210)

Exact Answer

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Problem: What is 2/21 plus 3/30?
Formula / Expression: 2/21 + 3/30
Final Answer: 41/210
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 2/21 by 10, and multiply the numerator and denominator of 3/30 by 7 so both fractions share the common base 210.
Working: 2 × 10/21 × 10 = 20/210 and 3 × 7/30 × 7 = 21/210

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 210 unchanged.
Working: 20 + 21/210 = 41/210

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 210 is 1, confirming that 41/210 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 210 produces a repeating decimal (approximately 0.195238, or 19.5238%).
Working: 41 ÷ 210 = 0.195238 (19.5238%)

Key Values:
- Simplified Fraction: 41/210
- Mixed Number Form: 41/210
- Decimal Value: 0.195238
- Percentage: 19.5238%

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Solved with FractionsCalc:
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2/21 + 3/30 = 41/210

Simplified Fraction

41/210

Mixed Number

Proper (41/210)

Decimal Value

0.195238

Percentage

19.5238%

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Step-by-Step Solution: 2/21 + 3/30

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 2/21 by 10, and multiply the numerator and denominator of 3/30 by 7 so both fractions share the common base 210.

2 × 10/21 × 10 = 20/210 and 3 × 7/30 × 7 = 21/210

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 210 unchanged.

20 + 21/210 = 41/210

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 210 is 1, confirming that 41/210 cannot be reduced further—it is already in its simplest irreducible form.

41/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 210 produces a repeating decimal (approximately 0.195238, or 19.5238%).

41 ÷ 210 = 0.195238 (19.5238%)

Visual Representation

The diagram below illustrates 2/21 plus 3/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/210`
Mixed Number Form	`41/210`
Decimal Form	`0.195238`
Percentage	`19.5238%`

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Frequently Asked Questions

What is 2/21 plus 3/30 as a fraction?

2/21 + 3/30 in simplest fraction form is 41/210.

What is 2/21 plus 3/30 as a decimal?

2/21 + 3/30 converted to a decimal is 0.195238.

What is 2/21 plus 3/30 as a percentage?

2/21 + 3/30 expressed as a percentage is 19.5238%.

Does 2/21 plus 3/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.195238...) because the denominator contains prime factors other than 2 and 5.